A bridge-crossing displacement monitoring data reconstruction method, device and equipment

Abstract

The application discloses a kind of cross bridge displacement monitoring data reconstruction method, device and equipment, belong to bridge structure health monitoring and data processing technical field.The method comprises: obtaining the monitoring data of first bridge;Determine the time-varying delay that monitoring data is mapped to the time axis of second bridge based on the space-time transmission characteristics of homologous excitation;First bridge modal characteristics are obtained by projecting monitoring data to modal characteristic space;The graph neural network model based on structural dynamics constraint, macro energy constraint and historical deformation mode constraint is updated to learn the transverse coupling relationship between second bridge space measuring points;Predicted modal characteristics are output based on modal characteristics and time-varying delay using the model and reconstructing second bridge monitoring data.The application realizes the fusion of physical mechanism and data driving, effectively solves the problem of single-bridge data missing, and improves the physical consistency and confidence of reconstructed data.

Description

Technical Field

[0001] This invention relates to the field of bridge structural health monitoring and data processing technology, specifically to a method, apparatus, and equipment for reconstructing cross-bridge displacement monitoring data. Background Technology

[0002] In the field of bridge structural health monitoring, lightweight monitoring systems for small- and medium-span bridge clusters are becoming increasingly popular. In lightweight monitoring systems, displacement response, as a core state parameter that macroscopically characterizes the stiffness degradation, deformation evolution, and overall stress state of bridge structures, determines the confidence and scientific validity of subsequent structural dynamic parameter analysis, damage evolution law extraction, and full life cycle state assessment.

[0003] However, due to the complex operating environment of bridges and the instability of hardware, such as the long-term exposure of monitoring equipment to the outdoors, environmental loads such as strong winds, extreme temperature variations, and complex electromagnetic interference, coupled with hardware failures such as communication link fading and intermittent power outages, displacement monitoring data often suffers from random gaps or large-scale continuous data interruptions. Long-term data gaps not only render many bridge health assessment reports invalid due to insufficient data support, but also mask early, subtle structural damage signals, seriously affecting the safe operation of the road network.

[0004] Existing data reconstruction methods are mainly limited to the single-bridge system. On the one hand, traditional numerical interpolation methods are difficult to handle the strong nonlinear dynamic response caused by vehicle loads, which easily leads to the loss of high-frequency features. On the other hand, although emerging data-driven deep learning models have nonlinear mapping capabilities, they are prone to overfitting under underdetermined conditions due to the lack of constraints from physical mechanisms such as structural dynamics. This results in false responses that violate physical boundary conditions, leading to insufficient confidence in the reconstructed data and failing to meet the needs of high-precision structural state assessment. Summary of the Invention

[0005] Purpose of the invention: To address the problems of long-term missing single-bridge monitoring data and the lack of physical constraints in existing reconstruction methods leading to distorted results, this application provides a method and apparatus for reconstructing bridge displacement monitoring data, achieving high-precision data reconstruction based on spatiotemporal transmission of co-source excitation and multidimensional physical constraints.

[0006] Technical Solution: A method for reconstructing monitoring data of a cross-bridge, comprising: acquiring monitoring data of a first bridge; determining the time-varying delay of the monitoring data of the first bridge mapped to the time axis of a second bridge based on the spatiotemporal transmission characteristics of the same excitation; projecting the monitoring data of the first bridge onto a modal feature space to obtain the modal features of the first bridge; acquiring a graph neural network model, wherein the graph neural network model is obtained by constructing a loss function to update parameters based on structural dynamic constraints, macroscopic energy constraints, and historical deformation mode constraints, and is configured to learn the lateral coupling relationship between spatial measurement points of the second bridge; using the graph neural network model, based on the modal features of the first bridge and the time-varying delay, outputting the predicted modal features of the second bridge, and reconstructing the monitoring data of the second bridge based on the predicted modal features.

[0007] Furthermore, based on the spatiotemporal transmission characteristics of the same source excitation, the time-varying delay of the monitoring data of the first bridge mapped to the time axis of the second bridge is determined, including: extracting the effective excitation time window of the load from the monitoring data of the first bridge; tracking the traffic flow wave velocity based on the effective excitation time window of the load; and calculating the time-varying delay of the vehicle arriving at the second bridge based on the traffic flow wave velocity and the bridge spacing.

[0008] Further, the effective excitation time window of the load is extracted from the monitoring data of the first bridge, including: using the Teager-Kaiser energy operator to perform nonlinear envelope extraction on the monitoring data of the first bridge to obtain an energy sequence; introducing the absolute median difference to calculate an adaptive dynamic threshold, and extracting the time interval of continuously crossing the adaptive dynamic threshold as the effective excitation time window of the load; tracking the traffic flow wave velocity based on the effective excitation time window of the load, including: calculating the time interval between adjacent loads arriving at the first bridge to convert it into instantaneous vehicle speed; constructing a one-dimensional Kalman filter, and through time update and measurement update, outputting the optimal posterior estimate of the road segment vehicle flow wave velocity as the traffic flow wave velocity.

[0009] Furthermore, the graph neural network model is constructed based on structural dynamic constraints, macroscopic energy constraints, and historical deformation mode constraints to update parameters using a loss function, and is configured to learn the lateral coupling relationship between spatial measurement points of the second bridge. This includes: instantiating each spatial measurement point within the cross-section of the second bridge as a graph node; adaptively generating connection weights between the graph nodes by the graph neural network model to implicitly learn the lateral coupling relationship between the spatial measurement points of the second bridge; and using the graph neural network model to output the predicted modal features of the second bridge based on the modal features of the first bridge and the time-varying delay, including: using the modal features of the first bridge as input to the graph neural network model, transmitting and aggregating information between the graph nodes through graph convolutional layers, and outputting the predicted modal features of the second bridge.

[0010] Furthermore, the graph neural network model is obtained by constructing a loss function to update the parameters based on structural dynamics constraints, macroscopic energy constraints, and historical deformation mode constraints. This includes: the structural dynamics constraints are determined based on the residuals of the free decay vibration differential equation; the macroscopic energy constraints are determined based on the ratio of the square discrete integral of the measured displacement and the reconstructed displacement within the effective excitation time window of the load; the historical deformation mode constraints are determined based on the projection of the historical dominant deformation mode; and the loss function is constructed based on the structural dynamics constraints, the macroscopic energy constraints, the historical deformation mode constraints, and the data fitting loss to update the parameters of the graph neural network model.

[0011] Furthermore, the structural dynamic constraints are determined based on the residuals of the free decay vibration differential equation, including: extracting the segments of the predicted modal features within the vehicle departure time window; obtaining the modal velocities and modal accelerations of each order using automatic differentiation technology; substituting the modal velocities and modal accelerations of each order into the free decay vibration differential equation composed of pre-identified modal parameters, and using the physical residuals as the structural dynamic constraints.

[0012] Furthermore, the macroscopic energy constraint is determined based on the ratio of the squared discrete integral of the measured displacement and the reconstructed displacement within the effective excitation time window of the load, including: performing squared discrete integrals on the measured displacement of the first bridge and the reconstructed displacement of the second bridge respectively within the effective excitation time window of the load; introducing an energy mapping ratio coefficient calibrated by historical complete data to constrain the integral ratio relationship between the measured displacement and the reconstructed displacement as the macroscopic energy constraint; the historical deformation mode constraint is determined based on the projection of the historical dominant deformation mode, including: using the historical intact data of the second bridge, performing principal component analysis on the mid-span section displacement to extract the statistical basis vector characterizing the dominant lateral deformation mode; projecting the reconstructed displacement onto the statistical basis vector to constrain the statistical characteristics of the reconstructed displacement to be consistent with those of the historical intact data as the historical deformation mode constraint.

[0013] Further, the monitoring data of the first bridge is projected onto the modal feature space to obtain the modal features of the first bridge, including: projecting the monitoring data of the first bridge onto the modal feature space based on the mode shape matrix; the mode shape matrix is ​​obtained by: constructing an iterative denoising model that integrates Bayesian inference and modal confidence criteria based on the historical intact data of the first bridge and the second bridge; removing false modes based on the iterative denoising model, and extracting the modal frequencies, damping ratios and mode shape matrices of the first bridge and the second bridge.

[0014] Furthermore, the present invention also provides a cross-bridge displacement monitoring data reconstruction device, comprising: a data acquisition module for acquiring monitoring data of a first bridge; a time delay determination module for determining the time-varying delay of the monitoring data of the first bridge mapped to the time axis of a second bridge based on the spatiotemporal transmission characteristics of the same source excitation; a feature projection module for projecting the monitoring data of the first bridge onto a modal feature space to obtain the modal features of the first bridge; a model acquisition module for acquiring a graph neural network model, wherein the graph neural network model is obtained by constructing a loss function to update parameters based on structural dynamic constraints, macroscopic energy constraints, and historical deformation mode constraints, and is configured to learn the lateral coupling relationship between spatial measurement points of the second bridge; and a data reconstruction module for using the graph neural network model, based on the modal features of the first bridge and the time-varying delay, to output the predicted modal features of the second bridge, and to reconstruct the monitoring data of the second bridge based on the predicted modal features.

[0015] In addition, the present invention also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the bridge displacement monitoring data reconstruction method as described above.

[0016] Beneficial Effects: This invention introduces a spatially adjacent first bridge as the data source and utilizes the spatiotemporal consistency of vehicle load transfer among bridge groups. Combined with nonlinear envelope extraction and Kalman filtering dynamic time delay tracking techniques, a high-precision spatiotemporal mapping mechanism for bridge crossings is established. This allows for the acquisition of high-fidelity external excitation information as a basis for reconstruction even when target bridge monitoring data is missing for extended periods, fundamentally solving the problem of data source scarcity under underdetermined conditions. Furthermore, this invention projects the high-dimensional displacement field into a modal feature space and uses an adaptive weighted graph neural network to learn spatial coupling relationships, enabling the model to perform efficient inference within a compact physical semantic space. Simultaneously, a multi-dimensional physical constraint loss function is introduced during model training, incorporating free decay dynamic residuals, macroscopic integral energy conservation, and historical dominant deformation modes. This multi-dimensional constraint mechanism forces the neural network's learning process to follow the fundamental principles of structural mechanics and historical statistical laws, effectively curbing the overfitting tendency of black-box models. This ensures that the reconstructed monitoring data not only statistically approximates the true values ​​but also strictly satisfies boundary conditions and the law of energy conservation, significantly improving the confidence and scientific rigor of bridge health assessment data. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the overall process of a method for reconstructing bridge displacement monitoring data in one embodiment of the present invention. Figure 2 This is a diagram of a spatiotemporal physical graph network architecture incorporating multidimensional physical constraints in one embodiment of the present invention; Figure 3 This is a schematic diagram of the collaborative deformation constraint of a single-section multi-measuring-point array sensor in one embodiment of the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0019] This embodiment provides a method for reconstructing bridge displacement monitoring data, taking a scenario of spatially adjacent highway bridge clusters as an example. This method utilizes the spatiotemporal consistency of vehicle load transfer among bridge groups to achieve high-precision reconstruction of bridges with missing data. It should be understood that although this embodiment uses highway bridges as an example, this method is also applicable to linear infrastructure clusters such as railway bridges and urban viaducts that bear moving loads and have spatial proximity. The implementation process is described in conjunction with a specific application scenario and existing bridge monitoring computing terminal equipment. The mathematical models, parameter calibration strategies, and data tensor transformation processes of key algorithm modules in the bridge displacement monitoring data reconstruction method are explained in detail. Figure 1-3 As shown, the implementation steps include: (1) Obtain displacement monitoring data of the first bridge and preprocess it to determine the time-varying delay of the monitoring data of the first bridge mapped to the time axis of the second bridge.

[0020] The main control service is started on the local computing terminal to establish a communication channel with the database and obtain the vertical displacement monitoring data of the first bridge. Then, a sliding buffer window is constructed in the terminal process memory using a double-ended queue, and the time window length is set. and sliding step size Discrete displacement signals are obtained by slicing and sampling the vertical displacement monitoring data. Then perform operations on the discrete displacement signal. Perform the following preprocessing procedure: (1.1) Extract the effective excitation time window of the load from the monitoring data of the first bridge.

[0021] First, the Teager-Kaiser energy operator is used for nonlinear envelope extraction to amplify the transient impact characteristics caused by vehicle load, thus obtaining the energy sequence. The calculation is expressed as:

[0022] Next, the absolute median difference is introduced to calculate the adaptive dynamic threshold. To eliminate the influence of ambient background noise drift, the calculation is expressed as follows:

[0023] In the formula, Energy sequence The mean, The absolute median difference of the energy sequence. The penalty coefficient is usually set to 2 to 3. The reason for using the absolute median instead of the standard deviation is that it is more robust to outliers and can still accurately determine the start and end times of load excitation even when the background noise is not Gaussian.

[0024] Finally, the intervals that continuously cross this threshold are selected as the effective bridge crossing time window for the load. .

[0025] (1.2) Tracking traffic flow wave velocity based on the effective excitation time window of the load.

[0026] The time interval between adjacent loads arriving at the first bridge is calculated, and then, under the condition of constant speed travel, it is converted into the instantaneous observed vehicle speed. Based on this, a one-dimensional Kalman filter is constructed, and through time updates and measurement updates, the optimal posterior estimate of the road segment vehicle flow wave velocity is output as the traffic flow wave velocity. Specifically, the state equation and observation equation are constructed as follows:

[0027] In the formula, express The real-time traffic flow wave speed , These are process noise and observation noise, respectively. The optimal posterior estimate of the vehicle flow wave velocity is output through updates based on time and monitoring data. , The instantaneous observed vehicle speed is calculated from the arrival time interval of adjacent loads. All the above parameters conform to a mean of 0 and a variance of . Gaussian distribution. Extracting bridge spacing. Calculate the time-varying delay of the vehicle arriving at the second bridge. .

[0028] This step analyzes the load response characteristics in the monitoring data of the first bridge to identify the effective time period for vehicles to cross the bridge. Combining this with the geographical distance between the two bridges and the real-time tracked vehicle flow wave speed, it dynamically calculates the time difference required for the load to be transferred to the second bridge. The accuracy of this time-varying delay calculation directly determines the accuracy of the bridge data alignment. Through precise spatiotemporal mapping, the response sequence of the first bridge can be shifted and aligned on the time axis to the response time of the second bridge, establishing a strong physical causal relationship between the two previously unrelated sets of data, providing a correct temporal reference for subsequent model inference.

[0029] (2) Project the monitoring data of the first bridge onto the modal feature space to obtain the modal features of the first bridge.

[0030] To reduce data dimensionality and extract features with clear physical meaning, it is necessary to transform the high-dimensional displacement field to a low-order modal coordinate system. This projection process relies on a high-precision mode shape matrix, but actual monitoring data often contains noise and spurious modes. Therefore, the mode shape matrix in this step is obtained as follows: First, obtain complete historical displacement monitoring data for both bridges. The initial state space model is calculated using the random subspace method to obtain the included frequencies. Damping ratio And mode matrix The initial set of modal parameters is used as the initial estimate for iteration, where This indicates the modal order. Calculate the initial mode shape matrix. generalized inverse matrix and displacement monitoring data Projecting onto the modal feature space yields the initial modal coordinate matrix. , where + denotes the generalized inverse of the corresponding matrix.

[0031] The Bayesian inference framework assumes that the true modal coordinates follow a Laplace sparse prior distribution, transforming the modal coordinate solution into a regularized sparse optimization problem. This allows for the automatic identification and removal of noise components from a statistically optimal perspective. The Modal Confidence Criterion (MAC) is used to test the orthogonality of each mode shape. When the MAC values ​​of two modes exceed a preset threshold (e.g., 0.95), they are identified as spurious repeating modes and removed. The mode shape matrix obtained through this iterative denoising mechanism has high fidelity, ensuring the physical accuracy of subsequent modal projections and avoiding the accumulation of reconstruction errors caused by basis vector distortion.

[0032] (3) Based on structural dynamics constraints, macroscopic energy constraints and historical deformation mode constraints, a loss function of the graph neural network model is constructed to update the model parameters; the graph neural network model is configured to learn the lateral coupling relationship between the spatial measurement points of the second bridge.

[0033] In terms of model structure design, each spatial measurement point within the cross-section of the second bridge is instantiated as a graph node. The graph neural network model adaptively generates connection weights between graph nodes to implicitly learn the lateral coupling relationships between the spatial measurement points of the second bridge. During the inference phase, the modal features of the first bridge are used as input to the graph neural network model. Information is transmitted and aggregated between graph nodes through graph convolutional layers, outputting the predicted modal features of the second bridge. Regarding the construction of the loss function, to overcome the shortcomings of purely data-driven models, such as overfitting under underdetermined conditions and generating non-physical solutions, this embodiment constructs a loss function that integrates multi-dimensional physical constraints to update model parameters. The loss function is composed of data fitting loss, structural dynamics constraints, macroscopic energy constraints, and historical deformation mode constraints. Structural dynamics constraints: Predictive modal characteristics are extracted within the vehicle departure time window. Automatic differentiation techniques are used to obtain the modal velocities and accelerations of each order. These modal velocities and accelerations are then substituted into the free decay vibration differential equations composed of pre-identified modal parameters. The physical residuals are used as structural dynamics constraints. This constraint forces the displacement response output by the model to satisfy the bridge structure's own dynamic equations during the free vibration stage after vehicle departure, ensuring the correctness of the reconstruction results in terms of micromechanical mechanisms.

[0034] Macroscopic energy constraint: Within the effective excitation time window of the load, the measured displacement of the first bridge and the reconstructed displacement of the second bridge are discretely integrated at squares. An energy mapping ratio coefficient calibrated by complete historical data is introduced to constrain the integral ratio between the measured displacement and the reconstructed displacement, serving as a macroscopic energy constraint. This constraint, based on the Rayleigh energy method principle, ensures the conservation of energy transfer during the bridge reconstruction process and prevents the model from generating non-physical responses with abnormal amplitudes or energy divergence.

[0035] Historical Deformation Pattern Constraint: Using historical intact data of the second bridge, principal component analysis was performed on the mid-span section displacement to extract statistical basis vectors representing the dominant lateral deformation patterns. The reconstructed displacements were projected onto these statistical basis vectors, constraining the reconstructed displacements to maintain consistency with the statistical characteristics of the historical intact data, thus serving as the historical deformation pattern constraint. This constraint utilizes the stable deformation patterns formed by the bridge's long-term evolution as a regularization term, effectively suppressing abnormal spatial distribution patterns caused by local sensor failures or random noise interference, ensuring that the reconstructed lateral deformation patterns conform to the historical statistical patterns of the bridge.

[0036] More specifically, in this embodiment, the initial modal coordinate matrix in step (2) above is... Iteration loop, number In this iteration, the mode shape matrix from the previous round is first used. (Modal parameters) and the previous modal coordinate matrix Displacement response of reconstructed bridge ; Calculate the residuals: ; And estimate the noise standard deviation: ,in It is a function for calculating the standard deviation.

[0037] Furthermore, by introducing a Bayesian inference framework and assuming that the true modal coordinates follow a Laplace sparse prior distribution, the solution for the modal coordinates is transformed into... Regularized sparse optimization problem.

[0038] With uncertainty Based on the current modal coordinate matrix Element-wise threshold filtering is performed to obtain the sparse purified modal coordinate matrix. :

[0039] In the formula, To and The relevant adaptive threshold parameters. This operation enables the separation of noise and spurious modes from a statistically optimal perspective.

[0040] Using the purified modal coordinate matrix and the current mode matrix The response is updated and reconstructed through modal superposition, and the mode vectors of each order are re-identified.

[0041] Furthermore, the modal confidence criterion values ​​between each vibration mode are calculated:

[0042] If the MAC value of any two mode shapes is higher than a preset threshold (e.g., 0.95), they are identified as false repeating modes and removed. The remaining modes form a new mode shape matrix. .

[0043] Use the updated modal parameters as prior input for the next iteration, and repeat the above steps until the changes in modal frequency and damping ratio between two adjacent iterations are lower than the preset convergence tolerance. Outputs the final converged high-fidelity steady-state modal parameters, including frequencies. Damping ratio And mode matrix It is serialized and saved locally for hot reloading by the main program.

[0044] Furthermore, the mode shape matrix of the first bridge (labeled with A as a subscript in the mathematical expression) is read. Calculate its Moore-Penrose generalized inverse The measured displacement matrix of the first bridge By projecting the modal coordinates of the first bridge to a lower-order modal coordinate system, the modal coordinates are obtained: .

[0045] M displacement measurement points within the cross-section of the second bridge (denoted by B as a subscript in the mathematical expression) are instantiated as graph nodes. The assumption of rigid lateral connection is abandoned; the connection weight matrix between nodes is generated entirely by data, enabling the graph network to adaptively learn the lateral displacement relationships of the bridge. Based on the graph neural network model, the input is the modal coordinate sequence of the first bridge. By implicitly learning the mapping of the lateral force transmission mechanism of the two bridges through graph convolutional layers, the predicted modal coordinate matrix of the second bridge is output. .

[0046] In the backpropagation weight optimization stage, adaptive weights are introduced. , , Construct a total loss function that includes data fitting and a multidimensional physical-history feature penalty term:

[0047] The definitions of each loss term are as follows: 1) Data fitting loss During the offline training phase, using intact historical data from both bridges, the displacement of the second bridge is projected to obtain the true modal coordinates, resulting in: .

[0048] Calculate the mean square error between the predicted modal coordinates and the true values: .

[0049] 2) Structural dynamic constraints Extracting the prediction mode coordinate matrix During the vehicle departure time window The segment within. The modal velocities of each order are obtained using computational graph automatic differentiation techniques. With modal acceleration Substituting the modal parameters identified in step two into the free decay vibration differential equation (i.e., the equation of motion for the free vibration of the structure after the vehicle leaves), we construct the physical residual:

[0050] in, , For the second bridge First-order modal damping ratio and circular frequency, This represents the number of sampling points within the time window.

[0051] 3) Macroscopic energy constraints (macroscopic physical constraints based on the Rayleigh energy method) : During the load-excited vibration time window Inside, the measured displacement matrix of the first bridge is respectively... Reconstructed displacement matrix of the second bridge Perform a squared discrete integral and introduce an energy mapping scaling factor calibrated from complete historical data. To constrain the energy ratio between the two and avoid abnormal trends, the calculation is expressed as follows:

[0052] Reconstruction displacement of the second bridge The predicted modal coordinates are obtained in real time using the following formula: .

[0053] 4) Constraints of historical deformation patterns (This item is based on PCA-dominant deformation mode constraints): Using historical intact data of the second bridge, principal component analysis is performed on the mid-span section displacement to extract the previous deformation mode. Statistical basis vectors representing the dominant lateral deformation modes The reconstructed displacements are projected onto these historical dominant patterns, constraining them to conform to historical statistical characteristics to avoid generating anomalous lateral deformation patterns.

[0054] After training with multidimensional physical and historical features, the graph neural network model yields the predicted modal coordinate matrix of the second bridge. By combining the principle of modal superposition, the reconstruction result is obtained: .

[0055] (4) Using the updated graph neural network model, based on the modal features of the first bridge and the time-varying delay, output the predicted modal features of the second bridge, and reconstruct the monitoring data of the second bridge based on the predicted modal features.

[0056] This step involves using the graph neural network model, optimized with multidimensional physical constraints, for actual inference after model training. The modal features of the first bridge are input into the model, and time-series alignment is performed using a determined time-varying delay. The model then outputs the predicted modal features of the second bridge at the current moment. Finally, using the identified mode shape matrix of the second bridge, the predicted modal features are reconstructed into the displacement response in physical space through the principle of modal superposition, thus obtaining the reconstructed monitoring data of the second bridge.

[0057] (5) Terminal deployment and real-time computing.

[0058] After the graph neural network model is trained, node fusion and tensor quantization are performed on the graph neural network model containing weight information, and it is deployed on the computing terminal. The main inference thread extracts slice data in real time, calls the underlying computing engine to complete the inference, and obtains the missing bridge reconstruction displacement data. The reconstructed data with timestamps is then inserted into the database through an interface to fill in the missing data, realizing a closed loop for the reconstruction of partial bridge missing monitoring data.

[0059] Example 2: This example provides a bridge monitoring data reconstruction device. This device serves as a modular implementation of the method described in the preceding examples, aiming to support component-level protection and flexible deployment of software products through a functionally decoupled architecture. The device includes a data acquisition module, a latency determination module, a feature projection module, a model acquisition module, and a data reconstruction module. These modules interact and collaborate via an internal data bus or shared memory mechanism.

[0060] The data acquisition module is used to acquire monitoring data from the first bridge. This module is configured to establish a communication connection with the database or sensor acquisition terminal of the bridge health monitoring system, and to retrieve or receive the displacement response sequence of the first bridge in real time. In practical engineering applications, the data acquisition module typically integrates a sliding buffer window unit for slicing and preprocessing the continuous data stream to meet the batch processing or streaming computing needs of subsequent modules.

[0061] The time delay determination module is used to determine the time-varying delay of the monitoring data of the first bridge mapped to the time axis of the second bridge based on the spatiotemporal transmission characteristics of the same excitation. This module internally encapsulates a nonlinear envelope extraction unit and a traffic flow wave velocity tracking unit. The nonlinear envelope extraction unit is configured to perform Teager-Kaiser energy operator operations and combine them with an adaptive absolute median threshold to accurately extract the effective excitation time window of the load from the monitoring data. The traffic flow wave velocity tracking unit is configured to construct a one-dimensional Kalman filter and output a smooth optimal posterior estimate of the traffic flow wave velocity based on the instantaneous vehicle speed observations within the time window.

[0062] The feature projection module projects the monitoring data of the first bridge onto the modal feature space to obtain the modal features of the first bridge. This module stores or dynamically loads the pre-identified mode shape matrix of the first bridge and is configured to perform generalized matrix inverse operations, converting the displacement vectors in the high-dimensional physical space into low-dimensional modal coordinates. The core function of this module is data dimensionality reduction and noise removal; the mode shape matrix it internally calls is a high-fidelity basis vector based on Bayesian inference and iterative denoising using modal confidence criteria.

[0063] The model acquisition module is used to acquire a graph neural network model. This model is obtained by constructing a loss function and updating parameters based on structural dynamic constraints, macroscopic energy constraints, and historical deformation mode constraints. It is configured to learn the lateral coupling relationships between spatial measurement points of the second bridge. During the training phase, this module is configured to construct a multi-dimensional physical constraint loss function that includes free decay residuals, energy integral ratios, and PCA projections, and update the network weights through backpropagation to force the model to comply with structural mechanics boundary conditions. During the inference phase, this module is configured to load the model parameters that have converged during training and implicitly capture the lateral force transmission paths between measurement points within the cross-section of the second bridge using an adaptive adjacency matrix generation mechanism.

[0064] The data reconstruction module utilizes a graph neural network model to output predicted modal features of the second bridge based on the modal features and time-varying delay of the first bridge, and reconstructs the monitoring data of the second bridge based on these predicted modal features. This module is configured to receive the first bridge modal features from the feature projection module and the time-varying delay parameters from the delay determination module, inputting them into the graph neural network model provided by the model acquisition module to obtain the predicted modal coordinates of the second bridge. Subsequently, this module is further configured to use the mode shape matrix of the second bridge to restore the predicted modal coordinates to the displacement response in physical space through the modal superposition principle, and write the timestamped reconstructed data into the target database to fill in missing segments. This module achieves the inverse mapping from abstract features to physical data, completing the closed loop of data reconstruction.

[0065] Through the modular architecture described above, this invention not only achieves high-precision reconstruction of bridge monitoring data, but also provides clear boundaries for the functional expansion and maintenance of the system. For example, when it is necessary to introduce new physical constraints or change the graph network architecture, only the model acquisition module needs to be updated without affecting the operation of other modules, which greatly enhances the feasibility and engineering adaptability of the technical solution.

[0066] Example 3: This example provides a computer device as the hardware execution carrier of the bridge displacement monitoring data reconstruction method described in the foregoing examples. The aim is to establish the subject of infringement determination for the technical solution in the manufacturing, sales, and use stages through a specific physical entity. Specifically, the computer device includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the bridge monitoring data reconstruction method as described in Example 1.

[0067] In this embodiment, the memory can be volatile memory or non-volatile memory, or a combination of both. The non-volatile memory can be read-only memory, programmable read-only memory, erasable programmable read-only memory, electrically erasable programmable read-only memory, or flash memory; the volatile memory can be random access memory, used as an external cache. The processor can be a central processing unit, network processor, graphics processing unit, or field-programmable gate array (FPGA) or other chip with data processing capabilities. The memory and processor are connected via a system bus or other communication interface, enabling the processor to read computer program instructions from the memory and execute corresponding operations. When the processor executes these instructions, its internal logic circuits are configured to sequentially or in parallel perform steps such as data acquisition, time-varying delay determination, modal feature projection, graph neural network model inference, and data reconstruction, thereby transforming the abstract algorithm flow into a concrete electrical signal processing procedure.

Claims

1. A method for reconstructing bridge displacement monitoring data, characterized in that, include: The displacement monitoring data of the first bridge is acquired and preprocessed to determine the time-varying delay of the monitoring data of the first bridge mapped to the time axis of the second bridge. The monitoring data of the first bridge is projected into the modal feature space to obtain the modal features of the first bridge; Based on structural dynamics constraints, macroscopic energy constraints, and historical deformation mode constraints, a loss function for a graph neural network model is constructed to update the model parameters; the graph neural network model is configured to learn the lateral coupling relationship between spatial measurement points of the second bridge. Using the updated graph neural network model, based on the modal features of the first bridge and the time-varying delay, the predicted modal features of the second bridge are output, and the monitoring data of the second bridge are reconstructed based on the predicted modal features.

2. The method for reconstructing bridge displacement monitoring data according to claim 1, characterized in that, The process of determining the time-varying delay includes: Extract the effective excitation time window of the load from the monitoring data of the first bridge; Traffic flow wave velocity is tracked based on the effective excitation time window of the load. The time-varying delay of vehicles arriving at the second bridge is calculated based on traffic flow wave velocity and bridge spacing.

3. The method for reconstructing bridge displacement monitoring data according to claim 2, characterized in that, The process of extracting the effective excitation time window of the load includes: The Teager-Kaiser energy operator was used to extract the nonlinear envelope from the monitoring data of the first bridge to obtain the energy sequence; An adaptive dynamic threshold is calculated by introducing the absolute median difference, and the time interval of continuously crossing the adaptive dynamic threshold is truncated as the effective excitation time window of the load. Based on the effective excitation time window of the load, the traffic flow wave velocity is tracked, including calculating the time interval between adjacent loads arriving at the first bridge and converting it into instantaneous vehicle speed, constructing a one-dimensional Kalman filter, and outputting the optimal posterior estimate of the road segment vehicle flow wave velocity as the traffic flow wave velocity through time update and measurement update.

4. The method for reconstructing bridge displacement monitoring data according to claim 1, characterized in that, The learning and configuration process of the graph neural network model for the lateral coupling relationship between the spatial measurement points of the second bridge includes: Instantiate each spatial measuring point within the cross section of the second bridge as a graph node; The graph neural network model adaptively generates connection weights between graph nodes to implicitly learn the lateral coupling relationship between spatial measurement points of the second bridge. The step of using the graph neural network model to output the predicted modal features of the second bridge based on the modal features of the first bridge and the time-varying delay includes: The first bridge modal features are used as input to the graph neural network model. Information is transmitted and aggregated between graph nodes through graph convolutional layers to output the predicted modal features of the second bridge.

5. The method for reconstructing bridge displacement monitoring data according to claim 1, characterized in that, The construction process of the graph neural network model includes: The structural dynamic constraints are determined based on the residuals of the differential equations of free decaying vibrations; The macroscopic energy constraint is determined based on the ratio of the square discrete integral of the measured displacement and the reconstructed displacement within the effective excitation time window of the load. The historical deformation mode constraint is determined based on the projection of the historical dominant deformation mode; Based on the structural dynamics constraints, the macroscopic energy constraints, the historical deformation mode constraints, and the data fitting loss, the loss function is constructed to update the parameters of the graph neural network model.

6. The method for reconstructing bridge displacement monitoring data according to claim 5, characterized in that, The structural dynamic constraints are determined based on the residuals of the differential equations of free decaying vibrations, specifically including: Extract the predicted modal features within the vehicle departure time window; Automatic differentiation techniques are used to obtain the modal velocities and modal accelerations of each order. Substitute the modal velocities and modal accelerations into the free decay vibration differential equation composed of pre-identified modal parameters, and use the physical residuals as the structural dynamics constraints.

7. The method for reconstructing bridge displacement monitoring data according to claim 5, characterized in that, The macroscopic energy constraint is determined based on the ratio of the square discrete integral of the measured displacement and the reconstructed displacement within the effective excitation time window of the load, including: Within the effective excitation time window of the load, the measured displacement of the first bridge and the reconstructed displacement of the second bridge are respectively subjected to square discrete integrals. An energy mapping ratio coefficient calibrated from complete historical data is introduced to constrain the integral ratio relationship between the measured displacement and the reconstructed displacement, serving as the macroscopic energy constraint. The historical deformation mode constraints are determined based on the projection of the historical dominant deformation mode, including: Using historical intact data of the second bridge, principal component analysis was performed on the mid-span section displacement to extract statistical basis vectors representing the dominant lateral deformation mode; The reconstructed displacement is projected onto the statistical basis vector, and the reconstructed displacement is constrained to maintain consistency with the statistical characteristics of the historical intact data, serving as the constraint for the historical deformation pattern.

8. The method for reconstructing bridge displacement monitoring data according to claim 1, characterized in that, The processing of the first bridge modal characteristics includes: Based on the mode shape matrix, the monitoring data of the first bridge is projected onto the modal feature space; The mode shape matrix is ​​obtained by: constructing an iterative denoising model that integrates Bayesian inference and modal confidence criteria based on the historical intact data of the first bridge and the second bridge; and extracting the modal frequencies, damping ratios, and mode shape matrices of the first bridge and the second bridge based on the iterative denoising model after removing false modes.

9. A device for reconstructing bridge displacement monitoring data, characterized in that, include: The data acquisition module is used to acquire monitoring data of the first bridge; The delay determination module is used to determine the time-varying delay of the monitoring data of the first bridge to the time axis of the second bridge based on the spatiotemporal transmission characteristics of the same source excitation. The feature projection module is used to project the monitoring data of the first bridge onto the modal feature space to obtain the modal features of the first bridge. The model acquisition module is used to acquire a graph neural network model. The graph neural network model is obtained by constructing a loss function to update parameters based on structural dynamic constraints, macroscopic energy constraints and historical deformation mode constraints, and is configured to learn the lateral coupling relationship between the spatial measurement points of the second bridge. The data reconstruction module is used to utilize the graph neural network model to output the predicted modal features of the second bridge based on the modal features of the first bridge and the time-varying delay, and to reconstruct the monitoring data of the second bridge based on the predicted modal features.

10. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the bridge displacement monitoring data reconstruction method according to any one of claims 1 to 8.

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