A Finite Element Real-Time Analysis Method and System for Multi-Span Continuous Bridges

Abstract

This invention relates to the field of bridge engineering simulation technology, specifically to a real-time finite element analysis method and system for multi-span continuous bridges. The method includes: acquiring real-time health monitoring response data streams and real-time vehicle load spatial distribution data streams for multi-span continuous bridges; performing time-frequency domain feature separation on the monitoring response data streams to obtain a dynamic response feature set; and discretizing the vehicle load data streams by axle load space to obtain a discrete axle load distribution map. The two types of data are input into a pre-trained stiffness inversion surrogate model to solve for the bridge's equivalent stiffness distribution field. This is used to update the material parameter matrix of the baseline finite element model to construct an adaptive finite element model. Through incremental iterative solving, the real-time internal force and deformation distribution state of the bridge is obtained, achieving dynamic updating and real-time simulation analysis of the bridge structure finite element model.

Description

Technical Field

[0001] This invention relates to the field of bridge engineering simulation technology, and in particular to a real-time finite element analysis method and system for multi-span continuous bridges. Background Technology

[0002] In the structural condition analysis of multi-span continuous bridges, traditional finite element analysis often uses fixed working condition parameters for modeling, employing only static monitoring data and idealized vehicle load setpoints in the calculations, without integrating real-time health monitoring response data streams and real-time vehicle load spatial distribution data streams from the bridge site. Monitoring response data is often directly input into the calculation process without time-frequency domain feature separation to extract effective dynamic response information. Furthermore, vehicle load data lacks axle load spatial discretization and regularization processing, failing to form a standardized load distribution representation.

[0003] Conventional analysis methods lack dedicated surrogate models for structural parameter inversion, making it impossible to solve the overall equivalent stiffness distribution of bridges in real time based on monitoring features and load maps. The material parameter matrix of the baseline finite element model remains fixed over time and cannot be dynamically corrected to reflect the actual working state of the structure, resulting in inherent discrepancies between the finite element model and the bridge's actual stress and deformation state. Traditional solution methods often employ fixed iterative patterns to complete calculations in a single step, making it difficult to adapt to the need for refined solutions after dynamic changes in structural parameters.

[0004] For bridge operation and maintenance management, industry standards are proposed for real-time finite element analysis and dynamic sensing of structural internal forces and deformations in multi-span continuous bridges. Engineering applications require the separation of time-frequency domain features from monitoring response data streams and spatial discretization of vehicle load axle loads. This necessitates the use of pre-trained surrogate models to perform inversion calculations of the bridge's equivalent stiffness field. Simultaneously, the finite element model parameters need to be dynamically adjusted based on the stiffness distribution field, and real-time internal force and deformation results should be obtained using an incremental iterative solution method to meet the engineering application requirements for real-time simulation analysis of bridge structures. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing technologies and to propose a real-time finite element analysis method and system for multi-span continuous bridges.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a real-time finite element analysis method for multi-span continuous bridges, comprising: Acquire real-time health monitoring response data stream and real-time vehicle load spatial distribution data stream of the target multi-span continuous bridge; The real-time health monitoring response data stream is subjected to time-frequency domain feature separation processing to obtain a dynamic response feature set, and the real-time vehicle load spatial distribution data stream is subjected to axle load spatial discretization processing to obtain a discrete axle load distribution map. The dynamic response feature set and the discrete axle load distribution map are input into a pre-trained stiffness inversion surrogate model to generate the bridge equivalent stiffness distribution field at the current moment. Based on the bridge's equivalent stiffness distribution field, update the material parameter matrix of the baseline finite element model to generate an adaptive finite element model. The adaptive finite element model is used to perform incremental iterative solutions to obtain the current state of the bridge's internal forces and deformation distribution.

[0007] As a further aspect of the present invention, the steps of performing time-frequency domain feature separation processing on the real-time health monitoring response data stream to obtain a dynamic response feature set, and performing axle load spatial discretization processing on the real-time vehicle load spatial distribution data stream to obtain a discrete axle load distribution map, specifically include: Extract strain time history data and deflection time history data for each monitoring section from the real-time health monitoring response data stream; Empirical mode decomposition is performed on the strain time history data and the deflection time history data respectively to obtain multiple intrinsic mode function components for each monitoring section; Quasi-static components with frequencies lower than a preset vehicle load frequency threshold are selected from multiple intrinsic mode function components of each monitoring section, and the quasi-static components of all monitoring sections are organized into the dynamic response feature set. Extract the number of axles, wheelbase, and axle load data for each vehicle from the real-time vehicle load spatial distribution data stream; Based on the number of axles, wheelbase, and axle load data of each vehicle, the axle load of each vehicle is assigned to the discrete spatial nodes of the bridge span, generating a discrete axle load distribution vector for each bridge span. The discrete axle load distribution vectors of all bridge spans are spliced ​​together in the order of the bridge spans to generate the discrete axle load distribution map.

[0008] As a further aspect of the present invention, the step of inputting the dynamic response feature set and the discrete axle load distribution map into a pre-trained stiffness inversion surrogate model to generate the bridge equivalent stiffness distribution field at the current moment specifically includes: The quasi-static components of each monitoring section in the dynamic response feature set are vectorized and concatenated to form a global response observation vector; The discrete axle load distribution map is matrix-transposed to form a load spatial distribution matrix. The global response observation vector and the load spatial distribution matrix are simultaneously input into the input layer of the pre-trained stiffness inversion surrogate model; In the hidden layer of the pre-trained stiffness inversion surrogate model, a cross-attention transformation is performed on the global response observation vector and the load spatial distribution matrix to generate a response-load joint feature tensor. The response-load joint feature tensor is passed to the output layer of the pre-trained stiffness inversion surrogate model. The stiffness reduction coefficient of each bridge element is obtained through the nonlinear mapping of the output layer. The stiffness reduction coefficients of all bridge elements are arranged according to the element number to generate the equivalent stiffness distribution field of the bridge.

[0009] As a further aspect of the present invention, the step of updating the material parameter matrix of the reference finite element model based on the equivalent stiffness distribution field of the bridge to generate an adaptive finite element model specifically includes: Read the pre-stored reference finite element model, which contains the initial elastic modulus and initial moment of inertia of each bridge element; Extract the stiffness reduction factor corresponding to each bridge element from the equivalent stiffness distribution field of the bridge; The initial elastic modulus of each bridge element is multiplied by its corresponding stiffness reduction factor to generate the updated elastic modulus of each bridge element. The updated moment of inertia of each bridge element is generated by multiplying the initial cross-sectional moment of inertia of each element by its corresponding stiffness reduction factor. The updated elastic modulus and the updated moment of inertia are written into the corresponding element entries in the material parameter matrix of the reference finite element model, respectively, to overwrite the original initial elastic modulus and initial moment of inertia, thereby generating the adaptive finite element model.

[0010] As a further aspect of the present invention, the step of using the adaptive finite element model to perform incremental iterative solution to obtain the current bridge internal force and deformation distribution state specifically includes: The real-time vehicle load spatial distribution data stream at the current moment is applied as an external load boundary condition to all nodes of the adaptive finite element model to generate load increment steps. The global stiffness matrix is ​​assembled in the adaptive finite element model, and the nodal displacement increment vector is calculated based on the load increment step. The total nodal displacement vector of the adaptive finite element model is updated based on the nodal displacement increment vector, and the element internal force increment of each element is calculated. Determine whether the norm of the node displacement increment vector in the current iteration step is less than the preset convergence tolerance; When the norm of the node displacement increment vector is less than the preset convergence tolerance, the iteration stops and the current total node displacement vector and the element internal force increment of each element are organized into the distribution state of the bridge internal force and deformation. When the norm of the nodal displacement increment vector is greater than or equal to the preset convergence tolerance, repeat the operations of assembling the global stiffness matrix, calculating the nodal displacement increment vector, and updating the total nodal displacement vector.

[0011] As a further aspect of the present invention, before performing time-frequency domain feature separation processing on the real-time health monitoring response data stream, the method further includes: The real-time health monitoring response data stream is subjected to outlier removal and missing value imputation to generate a cleaned health monitoring response data stream; Perform vehicle trajectory smoothing and lane attribution determination on the real-time vehicle load spatial distribution data stream to generate a cleaned vehicle load spatial distribution data stream; The post-cleaning health monitoring response data stream and the post-cleaning vehicle load spatial distribution data stream are timestamped to generate a time-synchronized response-load data pair sequence. The time-synchronized response-load data pair sequence is used as input data for subsequent steps.

[0012] As a further aspect of the present invention, after generating the current state of the bridge's internal forces and deformation distribution, the method further includes: The bending moment and deflection values ​​of each key section of the main beam are extracted from the internal force and deformation distribution state of the bridge. The bending moment and deflection values ​​of each key section of the main beam are compared with the preset section bearing capacity threshold and deflection limit to generate an over-limit mark for each key section of the main beam. When the over-limit marker of any key section of the main beam indicates that the bending moment value exceeds the section bearing capacity threshold or the deflection value exceeds the deflection limit, an early warning signal is triggered. Based on the location number of the key section of the main beam that triggered the early warning signal, the stiffness reduction coefficient corresponding to the location number is extracted from the equivalent stiffness distribution field of the bridge, and a stiffness degradation location report is generated.

[0013] As a further aspect of the present invention, after the warning signal is triggered, the method further includes: Bridge units whose stiffness reduction coefficients recorded in the stiffness degradation location report exceed the severe degradation threshold are marked as damaged units; Extract the span number of the bridge span where the damaged unit is located, and extract the discrete axle load distribution vector of the corresponding bridge span from the discrete axle load distribution map based on the span number; The total axle load of the bridge span is obtained by summing the discrete distribution vectors of the axle loads of the corresponding bridge spans. The total axle load is compared with the historical axle load for the same period to generate a load anomaly identification result, and the load anomaly identification result is attached to the stiffness degradation location report.

[0014] As a further aspect of the present invention, the pre-trained stiffness inversion surrogate model is constructed in the following manner: Acquire historical health monitoring response data and historical vehicle load data of the target multi-span continuous bridge; Empirical mode decomposition is performed on the historical health monitoring response data to extract the quasi-static strain components and quasi-static deflection components of each monitoring section. The quasi-static strain components and quasi-static deflection components of each monitoring section are then concatenated to generate historical dynamic response feature samples. The historical vehicle load data is subjected to axle load spatial discretization processing, and the axle load of each vehicle is allocated to the discrete spatial nodes of the corresponding bridge span. The discrete distribution vectors of axle loads of each bridge span are spliced ​​in the order of the bridge spans to generate historical load distribution samples. Using the historical load distribution samples as input and the corresponding historical dynamic response feature samples as output, a training dataset is constructed by generating sample pairs covering different stiffness damage conditions through three-dimensional finite element forward modeling. Construct a neural network model with an input layer, a hidden layer, and an output layer, wherein the hidden layer includes a cross-attention module; The historical load distribution samples and historical dynamic response feature samples in the training dataset are simultaneously input into the neural network model. The model parameters are optimized using the gradient descent algorithm until the loss function between the stiffness reduction coefficient predicted by the model and the preset stiffness reduction coefficient in the three-dimensional finite element forward modeling converges, thus obtaining the pre-trained stiffness inversion surrogate model.

[0015] As a further aspect of the present invention, the present invention also includes a real-time finite element analysis system for multi-span continuous bridges. The invention includes a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, it implements the steps of the real-time finite element analysis of multi-span continuous bridges as described above.

[0016] Compared with the prior art, the advantages and positive effects of the present invention are as follows: Multi-dimensional feature extraction is performed on historical meteorological observation data to separate key meteorological factors affecting photovoltaic power output, forming a standardized feature data set. Through time-series alignment processing, meteorological features are correlated with photovoltaic power output data to construct a suitable input structure for the prediction model, reducing redundant information interference and enabling the model to accurately capture the intrinsic relationship between meteorology and photovoltaic power output, thereby improving the adaptability of the prediction model.

[0017] By combining actual operating parameters of photovoltaic power plants, a dedicated prediction model is built. Relying on multi-dimensional meteorological data, photovoltaic power output prediction is conducted, eliminating the need for manual experience-based judgment and achieving automation and standardization of the prediction process. The model can adapt to power output variation patterns under different meteorological conditions, mitigating the impact of external environmental factors on the prediction results and improving the stability and consistency of the prediction outcomes.

[0018] To address the operational needs of energy storage systems, a dynamic charging and discharging strategy is developed based on predicted photovoltaic (PV) output data. The charging and discharging sequence of the energy storage system is dynamically adjusted according to fluctuations in PV output, ensuring that the operating status of the energy storage system remains synchronized with changes in PV output. This avoids waste of energy storage resources and ensures coordinated operation between the energy storage system and PV output, meeting the long-term stable operation requirements of PV power plants.

[0019] The entire processing flow requires no manual intervention, forming a complete link from meteorological feature extraction and model prediction to energy storage scheduling. It adapts to the normalized operation needs of photovoltaic power plants, realizes efficient connection between photovoltaic output prediction and energy storage scheduling, improves overall operating efficiency, and meets the industry requirements for refined operation of photovoltaic power plants. Attached Figure Description

[0020] Figure 1 This is a state diagram of a real-time finite element analysis method for multi-span continuous bridges as described in this invention. Figure 2 A flowchart for generating dynamic response characteristics and discrete axle load distribution maps; Figure 3 A flowchart for generating the equivalent stiffness distribution field of a bridge for a stiffness inversion proxy model. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0022] In the description of this invention, it should be understood that the terms "length," "width," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, in the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0023] See Figure 1 This invention provides a real-time finite element analysis method for multi-span continuous bridges, the specific method comprising: The system acquires real-time health monitoring response data streams and real-time vehicle load spatial distribution data streams for a target multi-span continuous bridge. It performs time-frequency domain feature separation processing on the real-time health monitoring response data streams to obtain a dynamic response feature set, and performs axle load spatial discretization processing on the real-time vehicle load spatial distribution data streams to obtain a discrete axle load distribution map. The system inputs the dynamic response feature set and the discrete axle load distribution map into a pre-trained stiffness inversion surrogate model to generate the bridge's equivalent stiffness distribution field at the current moment. Based on the bridge's equivalent stiffness distribution field, it updates the material parameter matrix of the baseline finite element model to generate an adaptive finite element model. Finally, it uses the adaptive finite element model to perform incremental iterative solving to obtain the bridge's internal force and deformation distribution state at the current moment. Before performing time-frequency domain feature separation processing, outlier removal and missing value imputation are performed on the real-time health monitoring response data stream to generate a cleaned health monitoring response data stream. Outlier removal uses the Laida criterion, and missing value imputation uses linear interpolation. Vehicle trajectory smoothing and lane assignment determination are performed on the real-time vehicle load spatial distribution data stream to generate a cleaned vehicle load spatial distribution data stream. Vehicle trajectory smoothing uses the Kalman filter algorithm, and lane assignment determination is based on comparing the vehicle's lateral position with the lane marking coordinates. The cleaned health monitoring response data stream and the cleaned vehicle load spatial distribution data stream are timestamped to generate a time-synchronized response-load data pair sequence. The time-synchronized response-load data pair sequence is used as input data for subsequent steps.

[0024] In one embodiment of the present invention, see [reference] Figure 2The strain time history data and deflection time history data of each monitoring section are extracted from the real-time health monitoring response data stream. Empirical mode decomposition is performed on the strain time history data and the deflection time history data to obtain multiple intrinsic mode function components of each monitoring section. Quasi-static components with frequencies lower than a preset vehicle load frequency threshold are selected from the multiple intrinsic mode function components of each monitoring section, and the quasi-static components of all monitoring sections are organized into the dynamic response feature set. The number of axles, wheelbase, and axle load data of each vehicle are extracted from the real-time vehicle load spatial distribution data stream. Based on the number of axles, wheelbase, and axle load data of each vehicle, the axle load of each vehicle is allocated to the discrete spatial nodes of the bridge span to generate the discrete axle load distribution vector of each bridge span. The discrete axle load distribution vectors of all bridge spans are spliced ​​together in the order of the bridge spans to generate the discrete axle load distribution map. Outlier removal and missing value imputation are performed on the real-time health monitoring response data stream to generate a cleaned health monitoring response data stream; vehicle trajectory smoothing and lane attribution determination are performed on the real-time vehicle load spatial distribution data stream to generate a cleaned vehicle load spatial distribution data stream; the cleaned health monitoring response data stream and the cleaned vehicle load spatial distribution data stream are timestamped to generate a time-synchronized response-load data pair sequence; the time-synchronized response-load data pair sequence is used as input data for subsequent steps.

[0025] In specific implementation, taking a three-span prestressed concrete continuous box girder bridge as the object, nine monitoring sections are arranged at the mid-span and support sections of each span. Each monitoring section is equipped with a vibrating wire strain gauge and a magnetostrictive displacement sensor. The collected strain time history data and deflection time history data are combined to form a real-time health monitoring response data stream. Simultaneously, a dynamic weighing system and cameras deployed on the bridge deck acquire information on the number of axles, wheelbase, axle load, and lane position of each passing vehicle, forming a real-time vehicle load spatial distribution data stream. The strain time history data and deflection time history data of each monitoring section are extracted from the real-time health monitoring response data stream. Empirical mode decomposition (EMD) is performed on the strain time history data and the deflection time history data respectively. The iterative process of EMD is expressed as follows: in: This represents a time series of original strain time history data or original deflection time history data. Indicates the first Each intrinsic mode function component This represents the total number of intrinsic mode function components obtained from the decomposition. The residual function is represented by the process of filtering out extreme points, constructing upper and lower envelopes and calculating the envelope mean, and repeatedly stripping away the detailed signals until the two definition conditions of the intrinsic mode function are met, thus obtaining multiple intrinsic mode function components for each monitoring section.

[0026] In some embodiments, quasi-static components with frequencies lower than a preset vehicle load frequency threshold are selected from multiple intrinsic mode function components of each monitoring section. The preset vehicle load frequency threshold is 0.5 Hz. The intrinsic mode function components with frequencies lower than 0.5 Hz are used as quasi-static components, and the quasi-static components of all monitoring sections are organized into a dynamic response feature set according to the monitoring section number and component order. Optionally, the number of axles, wheelbase, and axle load data of each vehicle are extracted from the real-time vehicle load spatial distribution data stream. Based on the number of axles, wheelbase, and axle load data of each vehicle, the axle load of each vehicle is allocated to discrete spatial nodes of the bridge span. The discrete spatial nodes are arranged longitudinally at the bottom of the beam of each bridge span at a spacing of 2 meters. During allocation, the axle load on the same axle is proportionally allocated to two adjacent discrete spatial nodes using a lever method, generating a discrete axle load distribution vector for each bridge span. The discrete axle load distribution vectors of all bridge spans are spliced ​​together in the order from the first bridge span to the third bridge span to generate a discrete axle load distribution map.

[0027] In specific implementations, outlier removal and missing value imputation are performed on the real-time health monitoring response data stream to generate a cleaned health monitoring response data stream. Outlier removal uses the Laida criterion, calculating the mean and standard deviation of all data within the current sliding window. Data points deviating from the mean by more than three times the standard deviation are identified as outliers and removed. Missing value imputation uses linear interpolation, calculating an estimate of the missing time using the values ​​of two adjacent valid data points before and after the missing time. In some embodiments, vehicle trajectory smoothing and lane assignment determination are performed on the real-time vehicle load spatial distribution data stream to generate a cleaned vehicle load spatial distribution data stream. Vehicle trajectory smoothing uses the Kalman filter algorithm, with the vehicle's position coordinates and speed as state variables. Position jump points are removed through a two-step recursive calculation of prediction and update. Lane assignment determination is based on comparing the vehicle's lateral position with the lane marking coordinates. When the vehicle's lateral position is between the left and right lane markings, the current vehicle is identified as belonging to the corresponding lane.

[0028] It is understood that the timestamps of the post-cleaning health monitoring response data stream and the post-cleaning vehicle load spatial distribution data stream are aligned to generate a time-synchronized response-load data pair sequence. Specifically, the nearest neighbor matching method is used to pair the timestamp of each data in the post-cleaning health monitoring response data stream with the data in the post-cleaning vehicle load spatial distribution data stream with the smallest absolute time difference value that is less than 0.1 seconds. Each paired data contains both response data and load data at the same time. All pairing results are arranged in ascending order of time to form a time-synchronized response-load data pair sequence.

[0029] In one embodiment of the present invention, see [reference] Figure 3 The quasi-static components of each monitoring section in the dynamic response feature set are vectorized and concatenated to form a global response observation vector; the discrete axle load distribution map is matrix-transposed to form a load spatial distribution matrix; the global response observation vector and the load spatial distribution matrix are simultaneously input into the input layer of the pre-trained stiffness inversion proxy model; in the hidden layer of the pre-trained stiffness inversion proxy model, a cross-attention transformation is performed on the global response observation vector and the load spatial distribution matrix to generate a response-load joint feature tensor; the response-load joint feature tensor is passed to the output layer of the pre-trained stiffness inversion proxy model, and the stiffness reduction coefficient of each bridge element is obtained through the nonlinear mapping of the output layer, and the stiffness reduction coefficients of all bridge elements are arranged according to the element number to generate the equivalent stiffness distribution field of the bridge. The pre-trained stiffness inversion surrogate model is constructed as follows: Historical health monitoring response data and historical vehicle load data of the target multi-span continuous bridge are acquired; empirical mode decomposition is performed on the historical health monitoring response data to extract the quasi-static strain and quasi-static deflection components of each monitoring section, and the quasi-static strain and quasi-static deflection components of each monitoring section are concatenated to generate historical dynamic response feature samples; axle load spatial discretization is performed on the historical vehicle load data, distributing the axle load of each vehicle to the discrete spatial nodes of the corresponding bridge span, and the discrete distribution vectors of the axle loads of each bridge span are concatenated in the order of the bridge spans to generate historical load distribution samples; the historical load distribution samples are then used to generate historical load distribution samples. Using the historical load distribution samples and the corresponding historical dynamic response feature samples as outputs, a training dataset is constructed by generating sample pairs covering different stiffness damage conditions through three-dimensional finite element forward modeling. A neural network model with an input layer, a hidden layer, and an output layer is built, wherein the hidden layer includes a cross-attention module. The historical load distribution samples and the historical dynamic response feature samples in the training dataset are simultaneously input into the neural network model, and the model parameters are optimized using the gradient descent algorithm until the loss function between the stiffness reduction coefficient predicted by the model and the preset stiffness reduction coefficient in the three-dimensional finite element forward modeling converges, thus obtaining the pre-trained stiffness inversion surrogate model.

[0030] In practical implementation, taking a three-span prestressed concrete continuous box girder bridge as the object, the quasi-static components collected from nine monitoring sections are vectorized and spliced ​​together end-to-end according to the ascending order of the monitoring section numbers to form a global response observation vector. The dimension of the global response observation vector is equal to the number of monitoring sections multiplied by the number of quasi-static components retained at each section. The discrete axle load distribution vectors of each span in the discrete axle load distribution map are arranged in rows to form a matrix, and then transposed so that each column of the matrix corresponds to a discrete spatial node and each row corresponds to a span, forming a load spatial distribution matrix. The global response observation vector and the load spatial distribution matrix are simultaneously input into the input layer of a pre-trained stiffness inversion surrogate model. The input layer contains two independent input channels, each receiving a dimension of... The global response observation vector and dimension are The load spatial distribution matrix, where This represents the length of the global response observation vector. The number of rows in the load spatial distribution matrix represents the total number of bridge spans. The number of columns in the load spatial distribution matrix represents the total number of discrete spatial nodes in each bridge span.

[0031] In some embodiments, in the hidden layer of the pre-trained stiffness inversion surrogate model, a cross-attention transformation is performed on the global response observation vector and the load spatial distribution matrix to generate a response-load joint feature tensor. The cross-attention transformation first transforms the global response observation vector through a linear transformation matrix. Mapped to query matrix The load spatial distribution matrix is ​​transformed by a linear transformation matrix. Mapped to a key matrix And through linear transformation matrix Mapped to a value matrix Then calculate the attention weight matrix. ,in The dimension of the key matrix is ​​represented by the value matrix. Finally, the attention weight matrix is ​​multiplied by the value matrix to obtain the response-load joint feature tensor. The hidden layer contains four cross attention heads that are computed in parallel and the computation results are concatenated along the feature dimension.

[0032] Optionally, the response-load joint feature tensor is passed to the output layer of the pre-trained stiffness inversion surrogate model. The stiffness reduction coefficient of each bridge element is obtained through the nonlinear mapping of the output layer. The output layer contains two fully connected sublayers and a modified linear unit activation function. The first fully connected sublayer maps the response-load joint feature tensor to an intermediate feature vector, and the modified linear unit activation function performs an operation on the intermediate feature vector. In the second fully connected sublayer, the activated intermediate feature vector is mapped to an output vector with a dimension equal to the total number of bridge elements. Each element of the output vector corresponds to the stiffness reduction coefficient of a bridge element. The stiffness reduction coefficients of all bridge elements are arranged in ascending order of element number to generate the equivalent stiffness distribution field of the bridge.

[0033] In specific implementation, the pre-trained stiffness inversion proxy model is constructed in the following way: Historical health monitoring response data and historical vehicle load data of the target three-span prestressed concrete continuous box girder bridge are acquired. The historical health monitoring response data covers monitoring records for different temperature ranges in four quarters of the year, and the historical vehicle load data includes load spectra of five typical vehicle types with axle loads ranging from 10 kN to 300 kN. Empirical mode decomposition (EMD) processing is performed on the historical health monitoring response data to extract the quasi-static strain and quasi-static deflection components of each monitoring section. These components are then concatenated according to the monitoring section number to generate historical dynamic response feature samples. Axle load spatial discretization processing is performed on the historical vehicle load data to allocate the axle load of each vehicle to the discrete spatial nodes of the corresponding bridge span. The discrete axle load distribution vectors of each bridge span are then concatenated in bridge span order to generate historical load distribution samples.

[0034] It is understood that, using the historical load distribution samples as input and the corresponding historical dynamic response feature samples as output, sample pairs covering different stiffness damage conditions are generated through three-dimensional finite element forward modeling to construct a training dataset. The different stiffness damage conditions include stiffness reduction of 10%, 20%, and 30% for a single element, stiffness reduction of 15% for two adjacent elements, and stiffness reduction of 5% to 25% for three random elements. Each damage condition corresponds to the application of five sets of historical load distribution samples at different locations, generating a total of 2000 sample pairs.

[0035] In some embodiments, a neural network model with an input layer, a hidden layer, and an output layer is constructed. The hidden layer includes a cross-attention module, the input dimension of which is set to 512, the number of attention heads is set to 8, the hidden layer dimension of the feedforward network is set to 2048, and the total number of parameters of the entire neural network model is 8.5 million. The historical load distribution samples and the historical dynamic response feature samples in the training dataset are simultaneously input into the neural network model, and the model parameters are optimized using the gradient descent algorithm. The gradient descent algorithm adopts an adaptive moment estimation optimizer, the initial learning rate is set to 0.001, the batch size is set to 32, and the number of training epochs is set to 200.

[0036] Optionally, the pre-trained stiffness inversion surrogate model is obtained when the loss function between the stiffness reduction coefficient predicted by the model and the preset stiffness reduction coefficient in the three-dimensional finite element forward modeling converges. The loss function adopts the root mean square error function. in: This represents the value of the loss function. This represents the total number of sample pairs in the training dataset. Indicates the total number of bridge units. Indicates the first In the nth sample Predicted stiffness reduction factor for each bridge element. This indicates the preset first step in the three-dimensional finite element forward modeling calculation. In the nth sample The true value of the stiffness reduction factor of each bridge element is considered convergent when the decrease in the loss function value is less than 0.001 for five consecutive training rounds.

[0037] In one embodiment of the present invention, the pre-stored reference finite element model is read, the reference finite element model including the initial elastic modulus and initial section moment of inertia of each bridge element; the stiffness reduction factor corresponding to each bridge element is extracted from the equivalent stiffness distribution field of the bridge; the initial elastic modulus of each bridge element is multiplied by its corresponding stiffness reduction factor to generate the updated elastic modulus of each bridge element; the initial section moment of inertia of each bridge element is multiplied by its corresponding stiffness reduction factor to generate the updated section moment of inertia of each bridge element; the updated elastic modulus and the updated section moment of inertia are written into the corresponding element entry positions in the material parameter matrix of the reference finite element model, respectively, overwriting the original initial elastic modulus and initial section moment of inertia, to generate the adaptive finite element model.

[0038] In practical implementation, a three-span prestressed concrete continuous box girder bridge is taken as the object. Each span is divided into 10 beam elements, for a total of 30 beam elements for the entire bridge. Each beam element is assigned a unique element number from 1 to 30. A pre-stored reference finite element model is read. The reference finite element model contains the initial elastic modulus and initial moment of inertia of each bridge element. The initial elastic modulus adopts the design value of the elastic modulus of C50 concrete. The initial cross-sectional moment of inertia is calculated to be 2.85 meters to the fourth power based on the box girder cross-sectional dimensions. The reference finite element model is stored in text format on a local server, where the entries for each bridge element are arranged in order of element number, and each entry contains the element number, the initial elastic modulus value, and the initial cross-sectional moment of inertia value.

[0039] In some embodiments, the stiffness reduction factor corresponding to each bridge element is extracted from the equivalent stiffness distribution field of the bridge. The equivalent stiffness distribution field of the bridge is a sequence of stiffness reduction factors indexed by the element number. The value range of the stiffness reduction factor is 0.65 to 1.00. During extraction, the stiffness reduction factor corresponding to each bridge element is read sequentially according to the element number from 1 to 30. The 30 stiffness reduction factors read are recorded in a temporary array. Referring to Table 1, the values ​​of the initial elastic modulus, initial section moment of inertia, stiffness reduction factor, and updated elastic modulus and updated section moment of inertia of some bridge elements are given.

[0040] Table 1: Comparison Table of Updated Parameters for Some Bridge Units It can be understood that the updated elastic modulus of each bridge element is generated by multiplying its initial elastic modulus by its corresponding stiffness reduction factor. This multiplication operation is expressed as: in: Indicates the unit number is The updated elastic modulus of the bridge unit. The element number extracted from the equivalent stiffness distribution field of the bridge is indicated by... The stiffness reduction factor of the bridge element, The element number read from the reference finite element model is... The initial elastic modulus of the bridge element.

[0041] In practice, the initial moment of inertia of each bridge element is multiplied by its corresponding stiffness reduction factor to generate the updated moment of inertia of each bridge element. The multiplication operation uses the same stiffness reduction factor as the updated elastic modulus. ,Right now ,in Indicates the unit number is The updated moment of inertia of the bridge element section, The element number read from the reference finite element model is... The initial cross-sectional moment of inertia of the bridge element.

[0042] Optionally, the updated elastic modulus and the updated moment of inertia are written into the corresponding element entries in the material parameter matrix of the reference finite element model, respectively, overwriting the original initial elastic modulus and initial moment of inertia, to generate the adaptive finite element model. The writing operation is performed one by one according to the element number. For the bridge element with element number 1, the updated elastic modulus is written into the first row and second column of the material parameter matrix. The updated cross-sectional moment of inertia of 2.7075 m to the power of 4 is written in the 1st row and 3rd column. This process is repeated for bridge elements numbered 2 to 30. After all element entries are covered, a finite element model with the updated material parameter matrix is ​​obtained, which serves as the adaptive finite element model.

[0043] In one embodiment of the present invention, the real-time vehicle load spatial distribution data stream at the current moment is applied as an external load boundary condition to all nodes of the adaptive finite element model to generate a load increment step; a global stiffness matrix is ​​assembled in the adaptive finite element model, and the node displacement increment vector is calculated based on the load increment step; the total node displacement vector of the adaptive finite element model is updated according to the node displacement increment vector, and the element internal force increment of each element is calculated; it is determined whether the norm of the node displacement increment vector of the current iteration step is less than a preset convergence tolerance; when the norm of the node displacement increment vector is less than the preset convergence tolerance, the iteration is stopped and the current total node displacement vector and the element internal force increment of each element are organized into the bridge internal force and deformation distribution state; when the norm of the node displacement increment vector is greater than or equal to the preset convergence tolerance, the operations of assembling the global stiffness matrix, calculating the node displacement increment vector, and updating the total node displacement vector are repeated.

[0044] In the specific implementation, an adaptive finite element model of a three-span prestressed concrete continuous box girder bridge is used as the object. The adaptive finite element model contains 30 beam elements and 31 nodes. Each node has two degrees of freedom: vertical displacement and rotation. The real-time vehicle load spatial distribution data stream records that there are three trucks on the bridge deck at the current moment. The first truck is located 12 meters from the left support of the first span, with axle loads of 60 kN and 60 kN. The second truck is located 8 meters from the left support of the second span, with axle loads of 80 kN, 80 kN, and 80 kN. The third truck is located 15 meters from the left support of the third span, with axle loads of 50 kN and 50 kN. The real-time vehicle load spatial distribution data stream at the current moment is used as the external load boundary condition and applied to all nodes of the adaptive finite element model to generate load increment steps. The nodal equivalent load method is used when applying the load, and the weight of each axle is distributed to the two adjacent nodes according to the lever principle. The concentrated forces on all nodes constitute the load increment step vector. Its dimension is 62 (31 nodes multiplied by 2 degrees of freedom per node).

[0045] In some embodiments, a global stiffness matrix is ​​assembled in the adaptive finite element model. The dimensions are 62×62. During assembly, 30 beam elements are traversed. For element numbered... The beam element, based on the element length Updated elastic modulus and the updated moment of inertia of the cross section Calculate the element stiffness matrix Then The elements in the matrix are superimposed onto the global stiffness matrix according to the element node degrees of freedom numbering. At the corresponding position, the nodal displacement increment vector is calculated based on the load increment step. The calculation formula is: ,in The matrix representing the inverse of the global stiffness matrix. The dimension is 62.

[0046] It can be understood that, based on the aforementioned node displacement increment vector Update the total nodal displacement vector of the adaptive finite element model. The update formula is: in: Indicates the first The total displacement vector of the nodes after the next iteration step. Indicates the first The total displacement vector of the nodes after the next iteration step. Indicates the first The nodal displacement increment vector calculated in the next iteration step, at the initial iteration step It is a zero vector, and the element internal force increment of each element is calculated simultaneously. For element numbered as Beam element, element internal force increment From the element stiffness matrix It is obtained by multiplying the degree of freedom components of the two nodes corresponding to the nodal displacement increment vector.

[0047] In specific implementation, it is determined whether the norm of the node displacement increment vector in the current iteration step is less than a preset convergence tolerance, wherein the preset convergence tolerance is set to a value. The norm of the nodal displacement increment vector is calculated using the Euclidean norm, and the calculation formula is as follows: ,in The first term in the nodal displacement increment vector represents the... Each component.

[0048] Optionally, when the norm of the nodal displacement increment vector is less than the preset convergence tolerance... When the iteration stops, the current total displacement vector of the nodes and the increment of the internal force of each element are organized into the distribution state of the internal force and deformation of the bridge. Referring to Table 2, the displacement values ​​of three typical nodes and the internal force values ​​of three typical elements at the convergence time are given.

[0049] Table 2: Bridge node displacements and element internal forces at convergence time In one embodiment of the present invention, the bending moment and deflection values ​​of each key section of the main beam are extracted from the internal force and deformation distribution state of the bridge; the bending moment and deflection values ​​of each key section of the main beam are compared with preset section bearing capacity thresholds and deflection limits to generate an over-limit marker for each key section of the main beam; when the over-limit marker of any key section of the main beam indicates that the bending moment value exceeds the section bearing capacity threshold or the deflection value exceeds the deflection limit, an early warning signal is triggered; according to the location number of the key section of the main beam that triggered the early warning signal, the stiffness reduction coefficient corresponding to the location number is extracted from the equivalent stiffness distribution field of the bridge to generate a stiffness degradation location report. After the warning signal is triggered, bridge units whose stiffness reduction coefficients recorded in the stiffness degradation location report exceed the severe degradation threshold are marked as damaged units; the span number of the bridge span where the damaged unit is located is extracted, and the discrete axle load distribution vector of the corresponding bridge span is extracted from the discrete axle load distribution map according to the span number; the discrete axle load distribution vectors of the corresponding bridge span are summed to obtain the total axle load of the bridge span; the total axle load is compared with the historical axle load of the same period to generate a load anomaly discrimination result, and the load anomaly discrimination result is attached to the stiffness degradation location report.

[0050] In the specific implementation, taking a three-span prestressed concrete continuous box girder bridge as the object, the bending moment and deflection values ​​of each key section of the main girder were extracted from the internal force and deformation distribution state of the bridge. The key sections of the main girder include the mid-span sections of the first, second, and third spans. The bending moment value of the mid-span section of the first span and the deflection value of the mid-span section of the bridge were recorded as -2150 kN·m and -8.7 mm, respectively, and the bending moment value of the mid-span section of the second span was 2780 kN·m. The deflection value is -12.4 mm. The bending moment value at the mid-span section of the third bridge span is -1890 kN·m and the deflection value is -7.2 mm. The bending moment and deflection values ​​of each key section of the main beam are compared with the preset section bearing capacity threshold and deflection limit to generate an over-limit mark for each key section of the main beam. The preset section bearing capacity threshold is 2500 kN·m and the preset deflection limit is L / 800, where L is the bridge span length of 40 meters. The calculated deflection limit is 50 mm.

[0051] In some embodiments, when the over-limit marker of any key section of the main girder indicates that the bending moment value exceeds the section bearing capacity threshold or the deflection value exceeds the deflection limit, an early warning signal is triggered. For the mid-span section of the second bridge span, the bending moment value of 2780 kN·m exceeds the section bearing capacity threshold of 2500 kN·m, triggering an early warning signal. For the mid-span sections of the first and third bridge spans, neither the bending moment nor the deflection value exceeds the corresponding threshold and limit, so no early warning signal is triggered. Based on the location number of the key section of the main girder that triggered the early warning signal, data is extracted from the equivalent stiffness distribution field of the bridge. The stiffness reduction coefficient corresponding to the location number is taken to generate a stiffness degradation location report. The key section of the main beam that triggers the early warning signal is the mid-span section of the second bridge span. Its location number corresponds to bridge unit numbers 15 to 17. The stiffness reduction coefficient of unit 15 is 0.73, the stiffness reduction coefficient of unit 16 is 0.68, and the stiffness reduction coefficient of unit 17 is 0.71 extracted from the bridge equivalent stiffness distribution field. This information is integrated into a stiffness degradation location report, which includes the location number, the corresponding unit number, and the stiffness reduction coefficient of each unit.

[0052] In specific implementation, after the early warning signal is triggered, bridge units whose stiffness reduction coefficient recorded in the stiffness degradation location report exceeds the severe degradation threshold are marked as damaged units. The severe degradation threshold is 0.75. Bridge units with a stiffness reduction coefficient less than 0.75 are marked as damaged units. The stiffness reduction coefficient of unit 15 is 0.73, which is less than 0.75; the stiffness reduction coefficient of unit 16 is 0.68, which is less than 0.75; and the stiffness reduction coefficient of unit 17 is 0.71, which is less than 0.75. Therefore, units 15, 16, and 17 are all marked as damaged units. The span number of the bridge span where the damaged unit is located is extracted. The damaged units are all located in the second span, and the extracted span number is 2.

[0053] It is understood that, based on the bridge span number, the discrete axle load distribution vector of the corresponding bridge span is extracted from the discrete axle load distribution map. The discrete axle load distribution map is stored in the order of the first bridge span, the second bridge span, and the third bridge span. The discrete axle load distribution vector of each bridge span contains axle load values ​​at 20 discrete spatial nodes. The discrete axle load distribution vector corresponding to bridge span number 2 is extracted. Its elements are represented as The unit is kilonewtons; the total axle load of the bridge span is obtained by summing the discrete distribution vectors of the axle loads of the corresponding bridge spans. The calculation formula is: in: This indicates the total axle load of the second bridge span. Indicates the second span of the bridge The axle load values ​​at each discrete spatial node are summed to obtain the result. Thousand Oxen.

[0054] Optionally, the total axle load is compared with the historical axle load for the same period to generate a load anomaly judgment result, and the load anomaly judgment result is attached to the stiffness degradation positioning report. The historical axle load for the same period is taken from the statistical value of the daily average axle load of the second bridge span in the same month of the past three years. The historical axle load for the same period is 350 kN. The ratio of the total axle load of 420 kN to the historical axle load of 350 kN is 1.2. The load anomaly judgment result is set to determine that the overload anomaly occurs when the ratio is greater than 1.15. Therefore, the generated load anomaly judgment result is "overload anomaly, the current total axle load has increased by 20% compared with the historical same period".

[0055] In some embodiments, the stiffness degradation location report includes a report generation timestamp, the section location number that triggered the warning signal, a list of damaged unit numbers, the stiffness reduction factor corresponding to the damaged unit, the total axial load of the bridge span, and the load anomaly discrimination result. The load anomaly discrimination result is appended to the stiffness degradation location report to form a complete report, and the complete report is saved in the form of a text file on a local storage device.

[0056] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments that can be applied to other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for real-time analysis of a multi-span continuous bridge finite element, characterized in that, The method includes: Acquire real-time health monitoring response data stream and real-time vehicle load spatial distribution data stream of the target multi-span continuous bridge; The real-time health monitoring response data stream is subjected to time-frequency domain feature separation processing to obtain a dynamic response feature set, and the real-time vehicle load spatial distribution data stream is subjected to axle load spatial discretization processing to obtain a discrete axle load distribution map. The dynamic response feature set and the discrete axle load distribution map are input into a pre-trained stiffness inversion surrogate model to generate the bridge equivalent stiffness distribution field at the current moment. Based on the bridge's equivalent stiffness distribution field, update the material parameter matrix of the baseline finite element model to generate an adaptive finite element model. The adaptive finite element model is used to perform incremental iterative solutions to obtain the current state of the bridge's internal forces and deformation distribution.

2. The finite element real-time analysis method for multi-span continuous bridges according to claim 1, characterized in that, The steps of performing time-frequency domain feature separation processing on the real-time health monitoring response data stream to obtain a dynamic response feature set, and performing axle load spatial discretization processing on the real-time vehicle load spatial distribution data stream to obtain a discrete axle load distribution map, specifically include: Extract strain time history data and deflection time history data for each monitoring section from the real-time health monitoring response data stream; Empirical mode decomposition is performed on the strain time history data and the deflection time history data respectively to obtain multiple intrinsic mode function components for each monitoring section; Quasi-static components with frequencies lower than a preset vehicle load frequency threshold are selected from multiple intrinsic mode function components of each monitoring section, and the quasi-static components of all monitoring sections are organized into the dynamic response feature set. Extract the number of axles, wheelbase, and axle load data for each vehicle from the real-time vehicle load spatial distribution data stream; Based on the number of axles, wheelbase, and axle load data of each vehicle, the axle load of each vehicle is assigned to the discrete spatial nodes of the bridge span, generating a discrete axle load distribution vector for each bridge span. The discrete axle load distribution vectors of all bridge spans are spliced ​​together in the order of the bridge spans to generate the discrete axle load distribution map.

3. The finite element real-time analysis method for multi-span continuous bridges according to claim 1, characterized in that, The steps of inputting the dynamic response feature set and the discrete axle load distribution map into a pre-trained stiffness inversion surrogate model to generate the bridge's equivalent stiffness distribution field at the current moment specifically include: The quasi-static components of each monitoring section in the dynamic response feature set are vectorized and concatenated to form a global response observation vector; The discrete axle load distribution map is matrix-transposed to form a load spatial distribution matrix. The global response observation vector and the load spatial distribution matrix are simultaneously input into the input layer of the pre-trained stiffness inversion surrogate model; In the hidden layer of the pre-trained stiffness inversion surrogate model, a cross-attention transformation is performed on the global response observation vector and the load spatial distribution matrix to generate a response-load joint feature tensor. The response-load joint feature tensor is passed to the output layer of the pre-trained stiffness inversion surrogate model. The stiffness reduction coefficient of each bridge element is obtained through the nonlinear mapping of the output layer. The stiffness reduction coefficients of all bridge elements are arranged according to the element number to generate the equivalent stiffness distribution field of the bridge.

4. The finite element real-time analysis method for multi-span continuous bridges according to claim 1, characterized in that, The steps for generating an adaptive finite element model by updating the material parameter matrix of the baseline finite element model based on the equivalent stiffness distribution field of the bridge specifically include: Read the pre-stored reference finite element model, which contains the initial elastic modulus and initial moment of inertia of each bridge element; Extract the stiffness reduction factor corresponding to each bridge element from the equivalent stiffness distribution field of the bridge; The initial elastic modulus of each bridge element is multiplied by its corresponding stiffness reduction factor to generate the updated elastic modulus of each bridge element. The updated moment of inertia of each bridge element is generated by multiplying the initial cross-sectional moment of inertia of each element by its corresponding stiffness reduction factor. The updated elastic modulus and the updated moment of inertia are written into the corresponding element entries in the material parameter matrix of the reference finite element model, respectively, to overwrite the original initial elastic modulus and initial moment of inertia, thereby generating the adaptive finite element model.

5. The finite element real-time analysis method for multi-span continuous bridges according to claim 1, characterized in that, The steps for performing incremental iterative solutions using the adaptive finite element model to obtain the current bridge internal force and deformation distribution state specifically include: The real-time vehicle load spatial distribution data stream at the current moment is applied as an external load boundary condition to all nodes of the adaptive finite element model to generate load increment steps. The global stiffness matrix is ​​assembled in the adaptive finite element model, and the nodal displacement increment vector is calculated based on the load increment step. The total nodal displacement vector of the adaptive finite element model is updated based on the nodal displacement increment vector, and the element internal force increment of each element is calculated. Determine whether the norm of the node displacement increment vector in the current iteration step is less than the preset convergence tolerance; When the norm of the node displacement increment vector is less than the preset convergence tolerance, the iteration stops and the current total node displacement vector and the element internal force increment of each element are organized into the distribution state of the bridge internal force and deformation. When the norm of the nodal displacement increment vector is greater than or equal to the preset convergence tolerance, repeat the operations of assembling the global stiffness matrix, calculating the nodal displacement increment vector, and updating the total nodal displacement vector.

6. The finite element real-time analysis method for multi-span continuous bridges according to claim 1, characterized in that, Before performing time-frequency domain feature separation processing on the real-time health monitoring response data stream, the process further includes: The real-time health monitoring response data stream is subjected to outlier removal and missing value imputation to generate a cleaned health monitoring response data stream; Perform vehicle trajectory smoothing and lane attribution determination on the real-time vehicle load spatial distribution data stream to generate a cleaned vehicle load spatial distribution data stream; The post-cleaning health monitoring response data stream and the post-cleaning vehicle load spatial distribution data stream are timestamped to generate a time-synchronized response-load data pair sequence. The time-synchronized response-load data pair sequence is used as input data for subsequent steps.

7. The finite element real-time analysis method for multi-span continuous bridges according to claim 1, characterized in that, After generating the current bridge internal force and deformation distribution, the following steps are also included: The bending moment and deflection values ​​of each key section of the main beam are extracted from the internal force and deformation distribution state of the bridge. The bending moment and deflection values ​​of each key section of the main beam are compared with the preset section bearing capacity threshold and deflection limit to generate an over-limit mark for each key section of the main beam. When the over-limit marker of any key section of the main beam indicates that the bending moment value exceeds the section bearing capacity threshold or the deflection value exceeds the deflection limit, an early warning signal is triggered. Based on the location number of the key section of the main beam that triggered the early warning signal, the stiffness reduction coefficient corresponding to the location number is extracted from the equivalent stiffness distribution field of the bridge, and a stiffness degradation location report is generated.

8. The finite element real-time analysis method for multi-span continuous bridges according to claim 7, characterized in that, After the warning signal is triggered, the method further includes: Bridge units whose stiffness reduction coefficients recorded in the stiffness degradation location report exceed the severe degradation threshold are marked as damaged units; Extract the span number of the bridge span where the damaged unit is located, and extract the discrete axle load distribution vector of the corresponding bridge span from the discrete axle load distribution map based on the span number; The total axle load of the bridge span is obtained by summing the discrete distribution vectors of the axle loads of the corresponding bridge spans. The total axle load is compared with the historical axle load for the same period to generate a load anomaly identification result, and the load anomaly identification result is attached to the stiffness degradation location report.

9. The finite element real-time analysis method for multi-span continuous bridges according to claim 1, characterized in that, The pre-trained stiffness inversion surrogate model is constructed in the following way: Acquire historical health monitoring response data and historical vehicle load data of the target multi-span continuous bridge; Empirical mode decomposition is performed on the historical health monitoring response data to extract the quasi-static strain components and quasi-static deflection components of each monitoring section. The quasi-static strain components and quasi-static deflection components of each monitoring section are then concatenated to generate historical dynamic response feature samples. The historical vehicle load data is subjected to axle load spatial discretization processing, and the axle load of each vehicle is allocated to the discrete spatial nodes of the corresponding bridge span. The discrete distribution vectors of axle loads of each bridge span are spliced ​​in the order of the bridge spans to generate historical load distribution samples. Using the historical load distribution samples as input and the corresponding historical dynamic response feature samples as output, a training dataset is constructed by generating sample pairs covering different stiffness damage conditions through three-dimensional finite element forward modeling. Construct a neural network model with an input layer, a hidden layer, and an output layer, wherein the hidden layer includes a cross-attention module; The historical load distribution samples and historical dynamic response feature samples in the training dataset are simultaneously input into the neural network model. The model parameters are optimized using the gradient descent algorithm until the loss function between the stiffness reduction coefficient predicted by the model and the preset stiffness reduction coefficient in the three-dimensional finite element forward modeling converges, thus obtaining the pre-trained stiffness inversion surrogate model.

10. A real-time finite element analysis system for a multi-span continuous bridge, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the steps of real-time finite element analysis of a multi-span continuous bridge as described in any one of claims 1 to 9.

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