Time-varying fire response prediction method and system for bridge structures based on GNN and GRU

Abstract

The present invention discloses a method and system for predicting time-varying fire response of a bridge structure based on GNN and GRU. The method includes: establishing a FEM model of the bridge structure to be tested and randomly generating a fire curve, combining the two to generate a data set; establishing a graph structure according to the FEM model, embedding static and dynamic features for temperature, stress and displacement prediction in the graph structure nodes; constructing a message transmission layer, GNN is responsible for spatial information transmission, and GRU is responsible for time information transmission; using the message transmission formula combined with the two to simulate the heat conduction formula; receiving a node input vector including temperature, stress and displacement prediction features from the graph structure; determining a loss function and separately training the GNN+GRU network for temperature, stress and displacement prediction; when the bridge structure to be tested encounters a fire, obtaining the fire response of the bridge structure to be tested through the trained model. The problem that the traditional GNN model can only predict non-time-varying boundary fire response is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of civil engineering structure health monitoring, and in particular to a method and system for predicting time-varying fire response of a bridge structure based on GNN and GRU. Background Art

[0002] Bridge health monitoring technology can quickly evaluate bridge fire safety through monitoring data, thus providing strong support for disaster relief, personnel evacuation, and post-disaster rapid assessment. Many important bridges and tunnels are also equipped with temperature sensors to monitor fire temperature changes, but these temperature sensors are not only sparse, but can only measure temperature changes in the air, and it is difficult to directly obtain the heat conduction and mechanical response inside the structure. Therefore, in bridge health monitoring projects, it is still necessary to use sensor data as thermal boundaries and use numerical analysis software to calculate the thermal and mechanical responses of the structure during the duration of the fire. However, due to the non-stationary time-varying boundary temperature and the long fire duration, the traditional numerical calculation method requires a large number of steps and iterations, which leads to problems such as difficult convergence and low calculation efficiency.

[0003] Therefore, it is necessary to develop a method for rapid prediction of the structural response (temperature, displacement, stress) of bridges in non-stationary time-varying fires, so that the time-series thermal and mechanical response data of bridge structures can provide support for structural safety performance assessment and emergency response in extreme high temperature scenarios. The proxy prediction model based on neural networks can simulate the temperature spatiotemporal distribution and mechanical response of real structures under fire to a certain extent, thereby quickly predicting the fire response of bridge structures with the support of fire air temperature data obtained by field sensors or simulations.

[0004] Since the heat conduction equation and heat displacement formula involve solving partial differential equations, the traditional fire response calculation is based on the finite element method (FEM). The traditional calculation method first uses computational fluid dynamics (CFD) software, the heating curve in the technical specifications or the temperature sensor data to obtain the time-varying air heat convection and heat radiation temperature, and then uses it as the input of the FEM heat conduction calculation to calculate the time series temperature of each node; in order to calculate the structural stress and displacement at a specified number of time steps, it is necessary to input the structural temperature field at these time steps into the static analysis model for calculation. This method of FEM thermal calculation is called the sequential thermal coupling method. Although the results of the numerical calculation fit the real data well, it involves the independent calculation of multiple models, the operation is cumbersome, the step-by-step iteration of heat conduction and the nonlinearity of static calculation lead to slow calculation speed, and it takes up a lot of storage space and computing resources, making it difficult to achieve the monitoring goal of real-time calculation and rapid prediction in the case of sudden fire.

[0005] In recent years, with the development of artificial intelligence, the use of machine learning to develop surrogate models of traditional numerical calculation methods has become a novel method to solve the above difficulties. Based on simple artificial neural networks (ANN), convolutional neural networks (CNN) and some other simple machine learning algorithms, it is possible to predict single-step thermal stress and thermal deformation under a given temperature boundary at a certain moment. When the fire boundary temperature changes with time, for the mechanical response of a few key nodes in the structure (such as the vertical displacement of the mid-span of the frame structure beam), the fire curve can be used as the input of algorithms such as support vector machines (SVM), random forests (RF) and long short-term memory networks (LSTM) to predict the time series response at each node separately. However, these methods are difficult to work for complex large structures with many nodes, require a large number of samples for training, and lack the interpretability of physical processes.

[0006] As an emerging network architecture in recent years, graph neural network (GNN) has been widely used in the field of developing structural health monitoring agent models because it can fully utilize adjacent nodes to obtain global information. It has greatly improved the computational efficiency and accuracy in predicting earthquake response, concrete cracking and fluid movement. However, in the field of predicting structural fire response, GNN can only predict the thermal conduction, thermal stress and thermal deformation of the structure under the premise of non-time-varying, and it is difficult to make accurate multi-step response predictions under non-stationary time-varying fire curves. Summary of the invention

[0007] In order to solve the problem that it is difficult to analyze the thermal and mechanical responses of structures under time-varying thermal boundaries in fire in the prior art, as a first aspect of the present invention, the present invention provides a method for predicting the time-varying fire response of bridge structures based on GNN and GRU, comprising the following steps:

[0008] S1. Establish a FEM model of the bridge structure to be tested and randomly generate a fire curve; use the fire curve as the input of the FEM thermal-mechanical coupling model of the bridge structure to generate a data set;

[0009] S2. Establish the graph structure according to the FEM model. The steps are as follows:

[0010] Select the severely affected areas in the FEM model;

[0011] Mapping the FEM model nodes in the selected severely damaged sub-area to nodes of the graph structure;

[0012] Mapping the edges in the sub-regions of the FEM model to the edges of the graph structure;

[0013] Embed static features and dynamic features for temperature prediction, stress prediction and displacement prediction in graph structure nodes;

[0014] S3. Construction and training of combined model of GNN and GRU:

[0015] Construct a message passing layer, GNN is responsible for spatial information transmission, and GRU is responsible for temporal information transmission;

[0016] Use the message passing formula of GNN+GRU to simulate the heat conduction formula;

[0017] receiving node input vectors including temperature, stress, and displacement prediction features from a graph structure;

[0018] According to the temperature, stress, and displacement prediction targets, set the time series data corresponding to the output layer;

[0019] The mean square error is used as the loss function for back propagation to train the GNN+GRU networks for temperature, stress, and displacement prediction separately;

[0020] S4. When the bridge structure to be tested encounters a fire, the time-varying fire temperature data is input into the features of the fire node, and the features of the bridge geometry and constraint information are input into the trained model together to obtain the fire response of the bridge structure to be tested.

[0021] Furthermore, the fire curve in S1 is generated according to existing technical specifications. The fire curve has an ascending section and a stable section, and some curves have a descending section. At the same time, it is ensured that the stable sections of all curves have a certain volatility; the fire curve includes the time-varying radiation temperature calculated as FEM heat conduction and convection temperature ,in .

[0022] Furthermore, the specific method for generating the data set described in S1 is: randomly selecting the fire area in the FEM model, applying the radiation temperature and convection temperature As thermal loads, data sets are generated in batches according to a sequential thermal-mechanical coupling method, and the data sets include: node temperature, node displacement, and equivalent node stress.

[0023] Furthermore, the static features in S2 include: the three-dimensional distance between the node and the fire center, the two-dimensional distance between the node and the nearest cable anchor point, the one-dimensional distance between the node and the nearest simply supported edge in the long direction, the initial stress and displacement under the action of deadweight, and multi-label coding to distinguish special mechanical nodes from ordinary nodes; the special mechanical nodes include: the cable anchor point, the nodes where the upper and lower flanges of the bridge main beam are connected to the web, and the nodes located on the simply supported edge of the main beam.

[0024] Furthermore, the method for constructing GRU in S3 is:

[0025] Reset gate information is calculated by formula:

[0026] (3)

[0027] In the formula, is to reset the matrix, is the weight matrix of the reset gate, is the weight matrix input to the reset gate, represents the previous moment, i.e. The hidden state of the step, represents an activation function (usually a sigmoid function), Indicates the current moment, i.e. The input vector of the step;

[0028] Update gate information by calculating the formula:

[0029] (4)

[0030] In the formula, is the update matrix, is the weight matrix of the update gate, is the weight matrix input to the update gate, represents the previous moment, i.e. The hidden state of the step, represents an activation function (usually a sigmoid function), Indicates the current moment, i.e. The input vector of the step;

[0031] The candidate hidden state is calculated by the formula:

[0032] (5)

[0033] In the formula, is the candidate hidden state matrix, represents the element-by-element product of matrices, i.e., the Hadamard product, is the weight matrix of the candidate hidden states, is the weight matrix input to the candidate hidden state;

[0034] Hidden state update: Hidden state at the moment It can be calculated by the following formula:

[0035] (6)

[0036] In the formula, is the update weight factor calculated by the update gate, is the hidden state at the previous moment, Perform a weighted sum of candidate hidden states, is the hidden state at the current moment.

[0037] Furthermore, the message passing formula derivation method of GNN+GRU in S3 is:

[0038] Bundle As a packaged function, the hidden state of the previous time step and the input of the current time step ,but and It can be calculated by the following two formulas:

[0039] (7)

[0040] (8)

[0041] The message passing formula of GNN+GRU is written comprehensively as:

[0042] (9)

[0043] In the formula, Indicates The hidden state of the time step, Indicates The hidden state of the time step, is the nonlinear activation function ReLu, For the GNN message passing weight matrix on time step, express The adjacent nodes The hidden state of represents a nonlinear operation, Indicates the target node Its own hidden layer representation , Indicates Input in time steps;

[0044] In the formula, the node Hidden State First, the spatial information is transmitted through GNN, then the temporal information is transmitted through GRU, and finally updated to the next time step. .

[0045] Furthermore, the mean square error calculation method in S3 is:

[0046] The mean square error is used as a loss function to measure the difference between the network prediction result and the true value:

[0047] (1)

[0048] In the formula, represents the mean square error loss function, is the result of FEM calculation. It is the temperature, stress or displacement predicted by the GNN+GRU network. is the total number of nodes in the graph structure.

[0049] Furthermore, the fire response of the bridge structure to be tested obtained in S4 includes: accurate time series data of temperature, stress and deformation.

[0050] As a second aspect of the present invention, it also relates to a bridge structure time-varying fire response prediction system based on GNN and GRU, comprising:

[0051] A data generation unit is used to establish a FEM model of the bridge structure to be tested and randomly generate a fire curve; the fire curve is coupled with the FEM model of the bridge structure to generate a data set;

[0052] A graph structure and feature embedding unit is used to establish a graph structure according to the FEM model: select a severely damaged area in the FEM model; map the FEM model nodes in the selected severely damaged sub-area to nodes of the graph structure; map the edges in the FEM model sub-area to edges of the graph structure; embed features for temperature prediction, stress prediction and displacement prediction in the graph structure nodes;

[0053] GNN and GRU construction and training unit, used for GNN and GRU combined model construction and training: build message passing layer, GNN is responsible for spatial information transmission, GRU is responsible for temporal information transmission; receive node input vectors including temperature, stress, and displacement prediction features from graph structure; set the time series data corresponding to the output layer according to the temperature, stress, and displacement prediction targets; use mean square error as loss function for back propagation to train GNN+GRU networks for temperature, stress, and displacement prediction separately;

[0054] The fire response prediction and efficiency evaluation unit is used to input the time-varying fire temperature data into the characteristics of the fire node when the bridge structure to be tested encounters a fire, and input the characteristics of the bridge geometry and constraint information into the trained model together to obtain the fire response of the bridge structure to be tested.

[0055] As a third aspect of the present invention, it also relates to a computer-readable storage medium on which a computer program is stored, characterized in that the computer program is executed by a processor to perform the above-mentioned method for predicting time-varying fire response of bridge structures based on GNN and GRU.

[0056] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0057] 1. The rapid prediction method for time-varying fire response of bridge structure of the present invention effectively solves the problem of inaccurate prediction of traditional GNN proxy model under long sequence non-stationary time-varying fire curve by introducing GRU, and can more accurately predict the temperature, stress and deformation time series data of bridge structure in fire, so that the prediction results are more in line with the actual situation, providing a reliable basis for bridge fire safety assessment.

[0058] 2. The rapid prediction method for time-varying fire response of bridge structures of the present invention simulates the heat conduction formula through the space-time dual message passing formula of GNN + GRU, so that the operation logic of the network is closely connected with the physical process. Compared with the traditional black-box machine learning model, the model of the present invention has greatly improved the interpretability of the physical process, which is convenient for professionals to understand and optimize the model, and also helps to make better decisions based on the model results in engineering applications.

[0059] 3. The rapid prediction method for time-varying fire response of bridge structure of the present invention directly uses time-varying fire temperature data instead of the node temperature calculated by the temperature prediction model as input in the stress prediction and displacement prediction links, thereby successfully bypassing the one-step cumulative error that may be caused by the intermediate calculation links, further improving the accuracy of stress and displacement prediction, and ensuring the accuracy and reliability of the entire prediction system. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 A flow chart of the implementation method in a preferred embodiment of the present invention;

[0061] Figure 2 It is a flowchart of a method for rapid prediction of time-varying fire response of a bridge structure based on a graph neural network and a gated recurrent unit in a preferred embodiment of the present invention;

[0062] Figure 3 This is the GNN+GRU network architecture in the preferred embodiment of the present invention;

[0063] Figure 4 This is the GRU network architecture in the preferred embodiment of the present invention;

[0064] Figure 5 The finite element model of the cable-stayed bridge in the preferred embodiment of the present invention;

[0065] Figure 6 is the mean absolute error (MAE) of the bridge temperature, displacement and stress prediction over 40 time steps in the preferred embodiment of the present invention;

[0066] Figure 7 is the mean absolute percentage error (MAPE) of the bridge temperature, displacement and stress prediction over 40 time steps in the preferred embodiment of the present invention;

[0067] Figure 8This is a cloud diagram of bridge deck temperature error distribution in a preferred embodiment of the present invention;

[0068] Fig. 9 A curve diagram comparing the predicted temperature value and the actual temperature value of some nodes under the action of fire in a preferred embodiment of the present invention;

[0069] Fig.10 The error distribution cloud diagram of the comparison between the predicted value and the true value of the stress of the main beam under the action of fire in the preferred embodiment of the present invention;

[0070] Fig.11 A comparison curve diagram of stress prediction values ​​and actual values ​​of some nodes under fire in a preferred embodiment of the present invention;

[0071] Fig.12 The error distribution cloud diagram of the comparison between the predicted value and the true value of the displacement of the main beam under the action of fire in the preferred embodiment of the present invention;

[0072] Fig.13 This is a comparison curve of the displacement prediction value and the actual value of some nodes under the action of fire in a preferred embodiment of the present invention, and the downward displacement is positive. DETAILED DESCRIPTION

[0073] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0074] Example 1

[0075] Please refer to Figure 1 as well as Figure 2 This embodiment 1 provides a method for predicting time-varying fire response of a bridge structure based on GNN and GRU, including:

[0076] S1. Model construction and fire scene simulation

[0077] (1) Establishment of bridge finite element model

[0078] Please refer to Figure 5 , a finite element model of a cable-stayed bridge of a specific specification was constructed, with a bridge length of 198m, a bridge deck width of 15m, and 32 cable stays. In the modeling process, the concrete deck, piers, and bridge towers were deliberately ignored, and the simple support effect of the ground and piers on the main beam was focused on. At the same time, the self-weight of the bridge and the prestress of the cables were taken into account in the model. This model will serve as the basic structural model for subsequent fire response analysis.

[0079] (2) Fire curve generation and parameter setting

[0080] According to the existing technical specifications, several fire curves are created by random generation. These fire curves have typical fire temperature variation characteristics, that is, they all contain rising segments and stable segments, and some curves also have additional falling segments. In addition, in order to highly simulate the temperature fluctuations in real fire scenes, it is ensured that the stable segments of all curves have a certain degree of volatility. These generated fire curves will be used as the time-varying radiation temperature in the subsequent finite element heat conduction calculation. and convection temperature For the radiation temperature and the convection temperature, a specific physical relationship setting is satisfied (such as the relationship clearly given in the relevant implementation manner).

[0081] The time period of the entire fire simulation is determined to be 40 minutes, and the temperature data is set to be output once every minute, so as to accurately capture the details of temperature changes during the fire process and provide sufficient data support for subsequent thermal stress and thermal displacement calculations.

[0082] (3) Sequential thermal-mechanical coupling simulation and data generation

[0083] With the help of professional ABAQUS finite element software, sequential thermal-mechanical coupling simulation operations were carried out. The 40 previously generated temperature data were sequentially input into the finite element force model, and the thermal stress and thermal displacement data at each time step were calculated through the model. In the data generation process, the training samples and test samples were carefully divided, and the number of samples used for training was set to 192 fire scenes, while the number of samples used for testing was set to 16 fire scenes, in order to provide a data basis for subsequent model training and performance verification.

[0084] S2. Graph structure and feature embedding

[0085] (1) Graph structure generation

[0086] Based on the finite element model of the cable-stayed bridge structure to be tested, we set out to create the corresponding graph structure. First, we screened out the areas in the finite element model that were severely affected, and then accurately mapped the nodes and edges in the sub-area to the nodes and edges in the graph structure. Through this mapping method, the spatial structure information in the finite element model is converted into graph structure information, so that the graph neural network can be used for subsequent information processing.

[0087] (2) Feature Embedding

[0088] 2.1 Temperature prediction feature embedding: For the temperature prediction task, specific node static features are embedded into the node input vector of the graph structure. These static features include the precise three-dimensional distance information of the node from the center of the fire, as well as multi-label encoding information for distinguishing special thermal nodes (such as the anchor points of the inclined cables, the nodes where the upper and lower flanges of the bridge main beam are connected to the web, and the nodes at the edge of the bridge deck) from ordinary nodes. Through the embedding of these features, rich structural and location-related information is provided for temperature prediction.

[0089] 2.2 Embedding of stress (displacement) prediction features: For stress and displacement prediction tasks, the relevant node static features are also embedded into the graph structure node input vector. These features include the three-dimensional distance of the node from the fire center, the two-dimensional distance of the node from the nearest cable anchor point, the one-dimensional distance of the node from the nearest simply supported edge in the long direction, the initial stress (displacement) information under the action of deadweight, and multi-label encoding information for distinguishing special mechanical nodes (such as cable anchor points, nodes where the upper and lower flanges of the bridge main beam are connected to the web, and nodes located on the simply supported edge of the main beam) and ordinary nodes. These features comprehensively consider multiple factors such as the mechanical properties and geometric position of the structure, laying the foundation for accurate stress and displacement prediction.

[0090] S3.GNN and GRU construction and training

[0091] (1) GNN spatial information transmission construction

[0092] The mean aggregation method is used to construct the GNN spatial information transfer formula:

[0093] (2)

[0094] This formula uses the mean aggregation method, where the target node is , whose adjacent nodes are , For the GNN message passing weight matrix on time step, is the nonlinear activation function ReLu, represents a nonlinear operation. Formula (2) aggregates the target nodes All adjacent nodes of The hidden layer representation of and its own hidden layer representation , update it to the state .

[0095] In this formula, the target node As the core processing object, its adjacent nodes Hidden layer representation in the set First average, then compare with the target node’s own hidden layer representation Perform nonlinear operations Processing (such as addition, concatenation, etc., depending on the design of the model), passing the weight matrix with the corresponding GNN message After multiplying and summing to obtain the linearly transformed node features, they are then passed through a nonlinear activation function. Processing (using ReLu function here) to get the updated state This spatial information transmission method can effectively integrate the information of adjacent nodes, thereby transmitting and fusing spatial information in the graph structure and extracting key spatial feature information for subsequent prediction tasks.

[0096] (2) GRU time information transmission construction

[0097] Please refer to Figure 4 :

[0098] 2.1 Reset gate calculation: Calculate the reset gate information through the formula:

[0099] (3)

[0100] in is to reset the matrix, is the weight matrix of the reset gate, is the weight matrix input to the reset gate, Indicates the previous moment ( step), represents an activation function (usually a sigmoid function), Indicates the current moment ( step) of the input vector.

[0101] In this formula, first the hidden state of the previous moment is Through the weight matrix Perform a linear transformation and convert the current input vector Through the weight matrix Then add the two transformed results and pass the activation function (usually a sigmoid function) to process, and finally get the reset gate at the Step output This output will be used to control the influence of the previous hidden state information on the calculation of the current candidate hidden state. Through comprehensive calculation with the input vector, a weight factor is determined for the generation of subsequent candidate hidden states.

[0102] 2.2 Update gate calculation: Use the formula to calculate the update gate information:

[0103] (4)

[0104] In the formula, is the update matrix, is the weight matrix of the update gate, is the weight matrix input to the update gate, represents the previous moment, i.e. The hidden state of the step, represents an activation function (usually a sigmoid function), Indicates the current moment, i.e. The input vector of the step.

[0105] In this formula, first the hidden state of the previous moment is Through the weight matrix Perform a linear transformation and convert the current input vector Through the weight matrix Then add the two transformed results and pass the activation function (usually sigmoid function) to process, and finally get the update gate at the Step output This output will be used to determine the relative weights of the previous hidden state and the current candidate hidden state when updating the current hidden state. By collaborative calculation with the input vector, an update weight factor is obtained.

[0106] 2.3 Candidate hidden state calculation: The candidate hidden state is calculated using the formula:

[0107] (5)

[0108] In the formula, is the candidate hidden state matrix, represents the element-by-element product of matrices, namely the Hadamard product. is the weight matrix of the candidate hidden states, is the weight matrix input to the candidate hidden state.

[0109] During the calculation process, first calculate the result according to the reset gate The hidden state of the previous moment Adjust and then compare with the input vector And the corresponding weight matrix The candidate hidden state is calculated together, and the candidate hidden state is a potential update value of the hidden state at the current moment.

[0110] 2.4 Hidden state update: Hidden state at the moment It can be calculated by the following formula:

[0111] (6)

[0112] The update weight factor calculated according to the update gate , the previous hidden state and candidate hidden states Perform weighted summation to get the hidden state at the current moment , thereby completing the transmission of time information and the update of hidden states, enabling the network to handle the time dependencies in time series data.

[0113] (3) GNN+GRU message passing formula synthesis and heat conduction formula simulation

[0114] Please refer to Figure 3 , if As a packaged function, the two variables it needs are the hidden state of the previous time step and the input of the current time step ,but and It can be calculated by the following two formulas:

[0115] (7)

[0116] (8)

[0117] Then the message passing formula of GNN+GRU can be written comprehensively as:

[0118] (9)

[0119] This formula shows that the node Hidden State After the spatial information transmission of GNN and the temporal information transmission of GRU, it is finally updated to the next time step. The complete process.

[0120] By comparing the two-dimensional transient form of the heat conduction formula in depth:

[0121] (10)

[0122] in is the material density, is the specific heat capacity of the material, is the convective heat transfer coefficient, is the surface emissivity of the material, is the Stefan-Boltzmann constant, approximately .

[0123] And its difference format under uniform grid:

[0124] (11)

[0125] Can be further organized into:

[0126] (12)

[0127] If and In conjunction with this, and following the principle that the superscript time and the subscript node number correspond to each other, the left side of formula (9) and formula (12) both contain the first Information at the moment and On the right side of the two formulas, GNN aggregates the part represented by the hidden vector of adjacent nodes Aggregation with temperature Correspondingly, the spliced ​​node features and In Correspondingly, Input features at time and Convection temperature included in With radiation temperature In summary, the hidden state in the message passing formula of the GNN+GRU can correspond to the temperature variable in the heat conduction formula one-to-one, and the message passing formula of the GNN+GRU can simulate the heat conduction formula in the form of a network, making the neural network interpretable.

[0128] (4) GNN+GRU network training

[0129] The GNN+GRU networks used for temperature prediction, stress prediction, and displacement prediction are trained independently. During the training process, the mean square error (MSE) is used as the loss function to measure the difference between the network prediction results and the true value:

[0130] (1)

[0131] In the formula, represents the mean square error loss function, is the result of FEM calculation. It is the temperature, stress or displacement predicted by the GNN+GRU network. is the total number of nodes in the graph structure.

[0132] The network parameters are optimized and adjusted through the back propagation algorithm. Through iterative training with a large amount of training data, the network can learn an accurate prediction model and improve the prediction ability of the time-varying fire response of the bridge structure.

[0133] S4. Fire response prediction and efficiency assessment

[0134] (1) Fire response prediction

[0135] When the cable-stayed bridge structure to be tested encounters an actual fire, the time-varying fire temperature data is quickly input into the features of the fire node, and other static features reflecting the bridge geometry and constraint information (such as various distances, encodings, and other static features previously embedded in the graph structure node input vector) are input into the GNN+GRU network that has been trained for heat conduction, thermal stress, and thermal displacement. In this embodiment, please refer to the specific model data performance Figures 6 to 13 Through the rapid calculation of the network, the response of the cable-stayed bridge structure to be tested in a fire can be obtained in a timely manner, including accurate time series data of temperature, stress and deformation. These predicted data can provide important basis for fire safety assessment of bridges, emergency rescue and disaster relief decision-making, etc.

[0136] (2) Efficiency evaluation

[0137] In order to comprehensively evaluate the advantages of the GNN+GRU network in terms of prediction efficiency, a detailed comparison is made between it and the finite element analysis (FEM) speed of the traditional ABAQUS software. For the three key prediction contents of temperature, stress, and deformation, the analysis time of the FEM and GNN+GRU networks is recorded respectively. For example, in terms of temperature prediction, the FEM analysis time is as long as 629.49 seconds, while the GNN+GRU network only takes 5.76 seconds; in terms of stress and deformation prediction, the FEM takes 3481.38 seconds, while the GNN+GRU network only takes 15.85 seconds (8.74 seconds + 7.11 seconds = 15.85 seconds). In terms of total time, the FEM takes a total of 4110.87 seconds, while the GNN+GRU network only takes 21.61 seconds. Through these comparative data, it can be clearly seen that the GNN+GRU network has a significant improvement in prediction efficiency, which can meet the monitoring goals of real-time calculation and rapid prediction of bridge structure fire response in the event of a sudden fire, and provides efficient technical support for the safety of bridge structures in fire scenarios.

[0138] Table 1 Comparison of prediction time between FEM and GNN+GRU proxy model (unit: seconds)

[0139]

[0140] Example 2

[0141] This embodiment 2 provides a bridge structure time-varying fire response prediction system based on GNN and GRU, including:

[0142] The model building and fire scene simulation unit is used to establish the FEM model of the bridge structure to be tested and randomly generate fire curves; the fire curves are coupled with the FEM model of the bridge structure to generate a data set; the data set includes: node temperature, node displacement and equivalent node stress;

[0143] A graph structure and feature embedding unit is used to establish a graph structure according to the FEM model: select a severely damaged area in the FEM model; map the FEM model nodes in the selected severely damaged sub-area to nodes of the graph structure; map the edges in the FEM model sub-area to edges of the graph structure; embed features for temperature prediction, stress prediction and displacement prediction in the graph structure nodes;

[0144] GNN and GRU construction and training unit, used for GNN and GRU combined model construction and training: build message passing layer, GNN is responsible for spatial information transmission, GRU is responsible for temporal information transmission; receive node input vectors including temperature, stress, and displacement prediction features from graph structure; set the time series data corresponding to the output layer according to the temperature, stress, and displacement prediction targets; use mean square error as loss function for back propagation to train GNN+GRU networks for temperature, stress, and displacement prediction separately;

[0145] The fire response prediction and efficiency evaluation unit is used to input the time-varying fire temperature data into the characteristics of the fire node when the bridge structure to be tested encounters a fire, and input the characteristics of the bridge geometry and constraint information into the trained model together to obtain the fire response of the bridge structure to be tested.

[0146] Example 3

[0147] This embodiment 3 also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of any of the above-mentioned methods for predicting time-varying fire response of bridge structures based on GNN and GRU can be implemented.

[0148] The computer-readable storage medium may include: a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, and other media that can store program codes.

[0149] For an introduction to the computer-readable storage medium provided in this application, please refer to the above method embodiment, and this application will not go into details here.

[0150] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for predicting time-varying fire response of bridge structure based on GNN and GRU, characterized in that: The following steps are involved: S1. Establish a FEM model of the bridge structure to be tested and randomly generate a fire curve; use the fire curve as the input of the FEM thermal-mechanical coupling model of the bridge structure to generate a data set; S2. Establish the graph structure according to the FEM model. The steps are as follows: Select the severely affected areas in the FEM model; Mapping the FEM model nodes in the selected severely damaged sub-area to nodes of the graph structure; Mapping the edges in the sub-regions of the FEM model to the edges of the graph structure; Embed static features and dynamic features for temperature prediction, stress prediction and displacement prediction in graph structure nodes; S3. Construction and training of combined model of GNN and GRU: Construct a message passing layer, GNN is responsible for spatial information transmission, and GRU is responsible for temporal information transmission; Use the message passing formula of GNN+GRU to simulate the heat conduction formula; receiving node input vectors including temperature, stress, and displacement prediction features from a graph structure; According to the temperature, stress, and displacement prediction targets, set the time series data corresponding to the output layer; The mean square error is used as the loss function for back propagation to train the GNN+GRU networks for temperature, stress, and displacement prediction separately; The derivation method of the message passing formula of GNN+GRU is: Bundle As a packaged function, the hidden state of the previous time step and the input of the current time step ,but and It can be calculated by the following two formulas: , , The message passing formula of GNN+GRU is written comprehensively as: , In the formula, Indicates The hidden state of the time step, Indicates The hidden state of the time step, is the nonlinear activation function ReLu, For the GNN message passing weight matrix on time step, express Adjacent nodes The hidden state of represents a nonlinear operation, Indicates the target node Its own hidden layer representation , Indicates Input in time steps; In the formula, the node Hidden State First, the spatial information is transmitted through GNN, then the temporal information is transmitted through GRU, and finally updated to the next time step. ; S4. When the bridge structure to be tested encounters a fire, the time-varying fire temperature data is input into the features of the fire node, and the features of the bridge geometry and constraint information are input into the trained model together to obtain the fire response of the bridge structure to be tested.

2. According to claim 1, a method for predicting time-varying fire response of bridge structure based on GNN and GRU is characterized in that: The fire curve in S1 is generated according to the existing technical specifications. The fire curve has an ascending section and a stable section, and some curves have a descending section. At the same time, it is ensured that the stable sections of all curves have a certain volatility; the fire curve contains the time-varying radiation temperature calculated as the FEM heat conduction and convection temperature ,in .

3. According to claim 2, a method for predicting time-varying fire response of bridge structure based on GNN and GRU is characterized in that: The specific method for generating the data set described in S1 is: randomly select the fire area in the FEM model, apply the radiation temperature and convection temperature As thermal loads, data sets are generated in batches according to a sequential thermal-mechanical coupling method, and the data sets include: node temperature, node displacement, and equivalent node stress.

4. The method for predicting time-varying fire response of bridge structure based on GNN and GRU according to claim 1 is characterized in that: The static features in S2 include: the three-dimensional distance between the node and the fire center, the two-dimensional distance between the node and the nearest cable anchor point, the one-dimensional distance between the node and the nearest simply supported edge in the long direction, the initial stress and displacement under the action of deadweight, and multi-label coding to distinguish special mechanical nodes from ordinary nodes; the special mechanical nodes include: the cable anchor point, the nodes where the upper and lower flanges of the bridge main beam are connected to the web, and the nodes located on the simply supported edge of the main beam.

5. The method for predicting time-varying fire response of bridge structure based on GNN and GRU according to claim 4 is characterized in that: The method for constructing GRU in S3 is: Reset gate information is calculated by formula: , In the formula, is to reset the matrix, is the weight matrix of the reset gate, is the weight matrix input to the reset gate, represents the previous moment, i.e. The hidden state of the step, represents an activation function, Indicates the current moment, i.e. The input vector of the step; Update gate information by calculating the formula: , In the formula, is the update matrix, is the weight matrix of the update gate, is the weight matrix input to the update gate, represents the previous moment, i.e. The hidden state of the step, represents an activation function, Indicates the current moment, i.e. The input vector of the step; The candidate hidden state is calculated by the formula: , In the formula, is the candidate hidden state matrix, represents the element-by-element product of matrices, i.e., the Hadamard product, is the weight matrix of the candidate hidden states, is the weight matrix input to the candidate hidden state; Hidden state update: Hidden state at the moment It can be calculated by the following formula: , In the formula, is the update weight factor calculated by the update gate, is the hidden state at the previous moment, Perform a weighted sum of candidate hidden states, is the hidden state at the current moment.

6. The method for predicting time-varying fire response of bridge structure based on GNN and GRU according to claim 1, characterized in that: The mean square error calculation method in S3 is: The mean square error is used as a loss function to measure the difference between the network prediction result and the true value: , In the formula, represents the mean square error loss function, is the result of FEM calculation. It is the temperature, stress or displacement predicted by the GNN+GRU network. is the total number of nodes in the graph structure.

7. A method for predicting time-varying fire response of bridge structure based on GNN and GRU according to any one of claims 1 to 6, characterized in that: The fire response of the bridge structure to be tested obtained in S4 includes: accurate time series data of temperature, stress and deformation.

8. A bridge structure time-varying fire response prediction system based on GNN and GRU, characterized in that: include: A data generation unit is used to establish a FEM model of the bridge structure to be tested and randomly generate a fire curve; the fire curve is coupled with the FEM model of the bridge structure to generate a data set; A graph structure and feature embedding unit is used to establish a graph structure according to the FEM model: select a severely damaged area in the FEM model; map the FEM model nodes in the selected severely damaged sub-area to nodes of the graph structure; map the edges in the FEM model sub-area to edges of the graph structure; embed features for temperature prediction, stress prediction and displacement prediction in the graph structure nodes; GNN and GRU construction and training unit, used for GNN and GRU combined model construction and training: build message passing layer, GNN is responsible for spatial information transmission, GRU is responsible for temporal information transmission; receive node input vectors including temperature, stress, and displacement prediction features from graph structure; set the time series data corresponding to the output layer according to the temperature, stress, and displacement prediction targets; use mean square error as loss function for back propagation to train GNN+GRU networks for temperature, stress, and displacement prediction separately; The derivation method of the message passing formula of GNN+GRU is: Bundle As a packaged function, the hidden state of the previous time step and the input of the current time step ,but And As a packaged function, the hidden state of the previous time step and the input of the current time step ,but and It can be calculated by the following two formulas: , , The message passing formula of GNN+GRU is written comprehensively as: , In the formula, Indicates The hidden state of the time step, Indicates The hidden state of the time step, is the nonlinear activation function ReLu, For the GNN message passing weight matrix on time step, express Adjacent nodes The hidden state of represents a nonlinear operation, Indicates the target node Its own hidden layer representation , Indicates Input in time steps; In the formula, the node Hidden State First, the spatial information is transmitted through GNN, then the temporal information is transmitted through GRU, and finally updated to the next time step. ; The fire response prediction and efficiency evaluation unit is used to input the time-varying fire temperature data into the characteristics of the fire node when the bridge structure to be tested encounters a fire, and input the characteristics of the bridge geometry and constraint information into the trained model together to obtain the fire response of the bridge structure to be tested.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: The computer program is executed by a processor to implement the method for predicting time-varying fire response of a bridge structure based on GNN and GRU as described in any one of claims 1 to 7.

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