Bridge dynamic deformation monitoring method and system

Abstract

The invention relates to the technical field of bridge health monitoring, in particular to a bridge dynamic deformation monitoring method and system. The method comprises the following steps: establishing a space coordinate reference network model of a bridge; obtaining a space-time registration result of multi-source heterogeneous data based on the space coordinate reference network model; according to the time-space registration result, performing hybrid error compensation and obtaining a compensation result; obtaining a deformation diagnosis result of the bridge structure according to the compensation result; and realizing dynamic deformation monitoring of the bridge through the deformation diagnosis result. According to the invention, through unifying the space-time reference, high-precision fusion of multi-source data is realized and a global deformation field is constructed; an environment noise and system error cooperative compensation mechanism is combined, so that the tiny deformation identification capability is greatly improved; a physical mechanism and a data driving model are fused, so that the diagnosis interpretability is remarkably enhanced; based on a dynamic three-dimensional visualization and self-adaptive early warning strategy, real-time accurate response to the health state of the bridge structure is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge health monitoring, and in particular to a bridge dynamic deformation monitoring method and system. Background Art

[0002] With the rapid development of transportation infrastructure, bridges are key nodes, and their structural health is directly related to operational safety and service life. However, under the influence of long-term loads, environmental erosion and material aging, bridges are prone to cumulative deformation and even structural damage. If not monitored and warned in time, major safety accidents may occur. Traditional manual detection methods are inefficient and have long cycles, and it is difficult to meet the needs of real-time dynamic monitoring of modern bridges.

[0003] In the existing technology, bridge deformation data is mainly collected through GNSS, accelerometers or fiber optic sensors, or local monitoring is achieved by loosely combining multiple sensors. This method has the following defects: First, due to the lack of unified time and space benchmarks, the fusion accuracy of multi-source heterogeneous data is low, making it difficult to establish a global deformation field; second, there is a lack of joint compensation mechanism for environmental noise and system errors, which affects the ability to identify small deformations; third, the physical model is difficult to adapt to complex working conditions, and the pure data-driven method lacks mechanical mechanism constraints, resulting in poor interpretability of diagnostic results; fourth, deformation visualization and early warning strategies are static and cannot dynamically respond to changes in structural states. Therefore, the development of high-precision and intelligent bridge dynamic deformation monitoring technology has become a core issue that needs to be urgently addressed in the field of engineering safety.

[0004] At present, there is not enough research work on bridge dynamic deformation monitoring, and there is no specific multi-dimensional, multi-level, and multi-scale high-precision intelligent bridge dynamic deformation monitoring method. Summary of the invention

[0005] In view of the defects in the prior art, the present invention provides a bridge dynamic deformation monitoring method and system.

[0006] In a first aspect, a method for dynamically monitoring the deformation of a bridge provided by the present invention includes the following steps: establishing a spatial coordinate reference network model of the bridge; obtaining the spatio-temporal registration result of multi-source heterogeneous data based on the spatial coordinate reference network model; performing hybrid error compensation according to the spatio-temporal registration result and obtaining a compensation result; obtaining a deformation diagnosis result of the bridge structure based on the compensation result; and realizing the dynamic deformation monitoring of the bridge through the deformation diagnosis result. By establishing a spatial coordinate reference network model of the bridge, the present invention realizes the high-precision three-dimensional numerical representation of the bridge structure, providing a unified spatial reference framework for multi-source data fusion; by obtaining the spatio-temporal registration result of multi-source heterogeneous data, the problem of inconsistency of different sensor data in time and space scales is effectively solved, providing a spatio-temporally consistent data basis for bridge deformation monitoring and analysis; by using a hybrid error compensation method combining deep learning and physical models, combining the data-driven characteristics of deep learning with the mechanism constraints of physical models, the influence of environmental interference and system errors is significantly reduced, and the accuracy and robustness of deformation monitoring are greatly improved; by obtaining the deformation diagnosis result of the bridge structure, the intelligent parsing from raw data to the structural health state is realized, providing a quantitative basis for evaluating the deformation state of the bridge structure.

[0007] Optionally, the establishment of the spatial coordinate reference network model of the bridge includes: deploying a plurality of sensor nodes at key parts of the bridge, the key parts including main girders, bridge piers and bearings, and the sensor nodes including a global navigation satellite system, an accelerometer array, an inertial measurement unit, an edge computing unit and a temperature and pressure sensor; measuring the initial distances between the sensor nodes by using a laser rangefinder; establishing a spatial coordinate reference network model according to the initial distances, the spatial coordinate reference network model being used to provide a spatial coordinate reference for the data of the sensor nodes; collecting multi-source heterogeneous data based on the spatial coordinate reference network model, the multi-source heterogeneous data including the timestamps and spatial coordinate data of the global navigation satellite system, the accelerometer array and the inertial measurement unit; designing a non-linear optimization objective function according to the multi-source heterogeneous data; and optimizing the spatial coordinate reference network model through the non-linear optimization objective function to obtain an optimized spatial coordinate reference network model. By deploying multi-type sensor nodes at key parts of the bridge, the present invention constructs an all-round and multi-dimensional monitoring network, realizing the holographic perception and data collaborative acquisition of the dynamic response of the bridge structure; by using a laser rangefinder to accurately measure the initial distances between sensor nodes and establishing a spatial coordinate reference network model, a unified high-precision spatial coordinate reference is provided for multi-source heterogeneous data, solving the positioning error problem caused by inconsistent coordinate systems in existing monitoring methods; by designing a non-linear optimization objective function to dynamically optimize the spatial coordinate reference network model, it is beneficial to the adaptive fusion and calibration of multi-source heterogeneous data in the spatio-temporal dimension.

[0008] Optionally, the spatial coordinate reference network model satisfies the following expression: Wherein, is the actual initial distance measurement value between node and node ; is the temperature difference between node and node ; is the reference temperature; is the initial measurement noise; is the influence coefficient of environmental temperature on distance measurement; and are the environmental temperatures of node and node respectively; is the influence coefficient of instrument pressure on distance measurement; and are the environmental pressures of node and node respectively; and are the spatial coordinates of node and node respectively; The non - linear optimization objective function is as follows: Wherein, is the GNSS measurement coordinate of node ; is the displacement measured by the accelerometer of node ; is the initial coordinate of node . By establishing an expression of the spatial coordinate reference network model containing multi - variable compensation terms such as temperature difference, environmental pressure, and measurement noise, the present invention realizes the dynamic environmental error correction of the measurement value of the laser rangefinder, significantly improves the initial distance measurement accuracy, and reduces the interference of temperature and pressure fluctuations on the reference network; by designing a multi - constraint non - linear optimization objective function, the absolute positioning, relative displacement, and initial reference are unified into the optimization framework, realizing the collaborative calibration of multi - source sensor data and the adaptive optimization of the spatial reference network; by simultaneously considering the distance residual between nodes and the single - node positioning consistency in the objective function, a global - local joint optimization mechanism is constructed, enabling the spatial coordinate reference network model to have both overall stability and local dynamic adjustment capabilities, providing a highly reliable coordinate reference for subsequent deformation monitoring.

[0009] Optionally, obtaining the spatio-temporal registration result of multi-source heterogeneous data based on the spatial reference network includes: constructing a spatio-temporal registration objective function based on the spatial reference network, and the spatio-temporal registration objective function is as follows: Wherein, is the timestamp function of the th sensor, is the reference time function, is the spatial coordinate function of the th sensor, is the reference space function, is the spatio-temporal transformation matrix of the th data source, represents the spatio-temporal second-order mixed partial derivative constraint term, , , are weight coefficients, and are both the total number of sensors, and , is the total number of data sources, is time, is the spatial domain variable; using the Lie group Lie algebra optimization method to solve the spatio-temporal registration objective function to obtain the spatio-temporal sequence of the registered multi-source heterogeneous data; adopting adaptive Kalman filtering to smooth the spatio-temporal sequence and obtain the smoothing result. By constructing a weighted objective function including the timestamp difference term, the spatial coordinate difference term and the spatio-temporal transformation smoothing term, the present invention realizes the unified constraint optimization of multi-source sensor data in the spatio-temporal dimension, significantly improves the spatio-temporal alignment accuracy of multi-source heterogeneous data; by using the Lie group Lie algebra method to solve the spatio-temporal registration objective function, it fully utilizes the smooth characteristics of the Lie group manifold and the linearization advantage of the Lie algebra, and effectively solves the singularity and non-linear convergence problems of the existing optimization methods when dealing with the spatio-temporal transformation matrix; by introducing adaptive Kalman filtering to smooth the registered spatio-temporal sequence, dynamically adjusting the process noise covariance and the observation noise covariance, while retaining the true deformation characteristics, effectively suppressing the double interference of sensor noise and registration residuals, and providing high-quality spatio-temporal alignment data for subsequent depth-physical hybrid error compensation.

[0010] Optionally, performing hybrid error compensation according to the spatio-temporal registration result and obtaining the compensation result includes: establishing a physical error model according to the spatio-temporal registration result, and the physical error model satisfies the following expression: Wherein, is the output of the physical error model, is the bridge displacement field function, , , represents the weight coefficient, represents the spatial position, is the time, is the attenuation coefficient; Based on the physical error model, a deep learning compensation network is constructed, and the loss function of the deep learning compensation network is as follows: where, is the function value of the loss function, is the true deformation value, is the predicted output of the physical error model, is the output value of the deep learning compensation network, , , are the weight coefficients, represents the th feature dimension of the input feature, are the network parameters; According to the deep learning compensation network, a multi-scale feature fusion architecture is built; Based on the multi-scale feature fusion architecture, depth-physical hybrid error compensation is performed and a compensation result is obtained. The present invention constructs a physical prior model that can not only reflect the mechanical mechanism of the bridge but also adapt to the time-varying environment by fusing the bridge structure stiffness, velocity effect, and displacement field, and introducing an exponential decay term to simulate the time-varying characteristics of environmental interference; By designing a composite loss function, the collaborative optimization of data-driven and physical constraints is realized, enabling the deep learning compensation network to conform to the basic laws of solid mechanics while maintaining the non-linear fitting ability; By building a multi-scale feature fusion architecture, multi-scale error compensation from millimeter-level high-frequency vibration to centimeter-level overall deformation is realized.

[0011] Optionally, the performing depth-physical hybrid error compensation and obtaining a compensation result based on the multi-scale feature fusion architecture includes: Based on the multi-scale feature fusion architecture, a residual attention mechanism is designed; According to the residual attention mechanism, a hybrid training strategy is designed; Through the hybrid training strategy, data compensation for the fusion of the deep learning compensation network and the physical error model is performed and a compensation result is obtained. The present invention realizes the adaptive fusion of local deformation characteristics and global mechanical responses of the bridge by designing a residual attention mechanism, significantly improving the robustness of error compensation; By designing a hybrid training strategy, the depth-physical hybrid model not only maintains the constraint of physical laws but also has the adaptability of data-driven.

[0012] Optionally, the obtaining the deformation diagnosis result of the bridge structure according to the compensation result includes: According to the compensation result, a bridge deformation feature extraction model is established, and the expression of the bridge deformation feature extraction model is as follows: Among them, is the characteristic extraction value of the overall deformation state of the bridge, , is the curvature weight coefficient, is the weight of the th key point, is the deformation amount of the current deformation mode at the position , is the deformation amount of the reference deformation mode at , is the total number of monitoring points, is the bridge displacement field function, represents the spatial position; Based on the bridge deformation feature extraction model, a dynamic Bayesian diagnostic network is constructed, and the dynamic Bayesian diagnostic network includes a state transition probability and an observation likelihood function; Through the dynamic Bayesian diagnostic network, a deformation diagnosis result of the bridge structure is obtained. The present invention realizes multi-dimensional quantitative characterization of the overall stiffness degradation and local damage characteristics of the bridge by establishing a bridge deformation feature extraction model, and the extracted deformation feature values can simultaneously reflect the degradation degree of the overall structural performance and the abnormal deformation of key parts; By constructing a dynamic Bayesian diagnostic network, probabilistic reasoning from time-series deformation data to structural health status is realized.

[0013] Optionally, the obtaining the deformation diagnosis result of the bridge structure through the dynamic Bayesian diagnostic network includes: Through the dynamic Bayesian diagnostic network, a bridge structural health diagnosis model is established, and the bridge structural health diagnosis model satisfies the following expression: Among them, is the bridge structural health index, is the basic health offset, is the sensitivity coefficient of the th damage index, is the time-varying function of the th damage index, is the total number of damage indices, is the total time, is a time variable; through the bridge structure health diagnosis model, the deformation diagnosis result of the bridge structure is obtained. By establishing a bridge structure health diagnosis model, the present invention non-linearly correlates the cumulative effect of the time-varying function of the damage index with the health index, realizing the dynamic quantitative evaluation of the long-term performance degradation of the bridge; by introducing a damage sensitivity coefficient to perform weighted fusion on different damage indexes, combining time-domain integral operation to capture the damage accumulation process, a comprehensive diagnosis system that can simultaneously reflect sudden damage and progressive deterioration is constructed; by setting the basic health offset in the health diagnosis model, the contribution degrees of the initial construction defects of the bridge and the newly added damage during the operation period are effectively distinguished, and the output deformation diagnosis result not only includes the current health state, but also can warn of potential accelerated deterioration risks.

[0014] Optionally, the realization of the dynamic deformation monitoring of the bridge through the deformation diagnosis result includes: through the deformation diagnosis result, a digital twin model is constructed, and the expression of the digital twin model is as follows: Wherein, is the bridge deformation field, is the diffusion coefficient, is the dynamic feedback force of the th sensor node, is the Dirac function, represents the spatial position, represents the position of the th sensor, is the time, represents the total number of sensor nodes; based on the digital twin model, an adaptive early warning strategy is designed; according to the adaptive early warning strategy, a rendering equation is established; according to the rendering equation, a three-dimensional deformation field visualization result is generated; through the three-dimensional deformation field visualization result, the dynamic deformation monitoring of the bridge is realized. By constructing a digital twin model, the present invention realizes the dynamic coupling of physical mechanisms and real-time monitoring data, which can not only reflect the structural mechanics propagation characteristics but also accurately reproduce the deformation response of actual measurement points; by designing an adaptive early warning strategy and dynamically adjusting the early warning threshold, the intelligent transformation from uniform early warning to hierarchical early warning in key areas is realized; by establishing a color rendering equation, the visualization of the bridge structure deformation is realized, which is beneficial to identifying high-risk areas and force flow transmission paths of the bridge and greatly improving the judgment efficiency of complex deformation modes.

[0015] In a second aspect, a bridge dynamic deformation monitoring system provided by the present invention includes an input device, a processor, an output device, and a memory. The input device, the processor, the output device, and the memory are interconnected. Among them, the memory is used to store a computer program, the computer program includes program instructions, the processor is configured to call the program instructions, and the system uses the described bridge dynamic deformation monitoring method. The system provided by the present invention has a high degree of integration, and the information transmission between each component is smooth. Through the full-chain monitoring system of the spatial reference network model - deep physical compensation - dynamic Bayesian diagnosis, multi-source heterogeneous sensor data is deeply fused and error-compensated under a unified spatio-temporal reference, realizing full-scale high-precision monitoring from millimeter-level micro-deformation to centimeter-level overall displacement; by adopting a depth-physical hybrid modeling method, the system has both physical interpretability and data adaptability; through a three-dimensional visualization warning platform driven by digital twins, the real-time deformation field is dynamically associated with the health diagnosis index to generate a heat map, realizing the closed-loop management of monitoring - diagnosis - warning - visualization. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a flowchart of a bridge dynamic deformation monitoring method according to an embodiment of the present invention; Figure 2 It is a flowchart of obtaining the spatio-temporal registration result of multi-source heterogeneous data based on the spatial reference network model according to an embodiment of the present invention; Figure 3 It is a schematic structural diagram of a bridge dynamic deformation monitoring system according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0017] The specific embodiments of the present invention will be described in detail below. It should be noted that the embodiments described here are only for illustrative purposes and are not used to limit the present invention. In the following description, in order to provide a thorough understanding of the present invention, a large number of specific details are set forth. However, it is obvious to those of ordinary skill in the art that the present invention does not have to be implemented with these specific details. In other instances, well-known circuits, software, or methods are not specifically described to avoid obscuring the present invention.

[0018] Throughout the specification, references to "one embodiment", "an embodiment", "one example" or "an example" mean that a particular feature, structure, or characteristic described in connection with the embodiment or example is included in at least one embodiment of the present invention. Thus, the phrases "in one embodiment", "in an embodiment", "one example" or "an example" appearing throughout the specification do not necessarily all refer to the same embodiment or example. In addition, the particular features, structures, or characteristics may be combined in any suitable combination and / or sub-combination in one or more embodiments or examples. Further, those of ordinary skill in the art should understand that the diagrams provided herein are for illustrative purposes only and are not necessarily drawn to scale.

[0019] Please refer to Figure 1 , an embodiment of the present invention provides a method for monitoring the dynamic deformation of a bridge, the method comprising the following steps: S1. Establish a spatial reference network for bridge sensors.

[0020] In one embodiment, first deploy sensor nodes at key parts of the bridge to ensure coverage of the main stress areas of the bridge, and the key parts include the main girder, piers and bearings. Each sensor node includes a dual-frequency GNSS receiver, a MEMS accelerometer array, a force-axis MEMS-IMU, an edge computing unit and a temperature and pressure sensor; the dual-frequency GNSS receiver is a receiving device capable of simultaneously receiving and processing signals of two different frequencies of the Global Navigation Satellite System (GNSS), capable of providing millimeter-level positioning and anti-multipath effects; the MEMS accelerometer array is a sensor array composed of multiple micro-electromechanical system (MEMS) accelerometers for measuring three-dimensional vibration and improving the signal-to-noise ratio; the force-axis MEMS-IMU is an inertial measurement unit based on micro-electromechanical system (MEMS) technology for monitoring inclination, angular velocity and compensating for GNSS dynamic errors; the edge computing unit is used for real-time data fusion and optimization calculation; the temperature and pressure sensor is used for measuring the ambient temperature and pressure.

[0021] Further, use a high-precision laser rangefinder to measure the initial distances between all sensor nodes, and record the ambient temperature and instrument pressure for correcting measurement errors. The instrument pressure refers to the air pressure of the surrounding environment when the laser rangefinder is measuring, and the air pressure has a certain influence on the measurement accuracy of the laser rangefinder because the change in air pressure will affect the air refractive index, thereby affecting the propagation speed of the laser and the ranging result.

[0022] Furthermore, a spatial coordinate reference network model is established. Its purpose is to construct a unified geometric reference framework, provide a spatial coordinate reference for all sensor data, and ensure the fusion of multi-source data in the same coordinate system; and eliminate the influence of sensor installation position errors or local coordinate system differences on data consistency. The spatial coordinate reference network model satisfies the following expression: where, is the measured actual distance value between node and node ; is the temperature difference between node and node ; is the reference temperature; is the initial measurement noise; is the influence coefficient of environmental temperature on distance measurement; and are the environmental temperatures of node and node respectively; is the influence coefficient of instrument pressure on distance measurement; and are the environmental pressures of node and node respectively; and are the spatial coordinates of node and node respectively.

[0023] Furthermore, synchronous data acquisition is carried out. Among them, GNSS provides absolute coordinates , the MEMS accelerometer array provides high-frequency vibration displacements , the laser rangefinder provides relative distance constraints, and the force-axis MEMS-IMU provides dynamic attitude compensation to ensure that the measurement data of GNSS, the accelerometer array, and the laser rangefinder are accurate in a unified attitude reference system, thereby improving the measurement accuracy.

[0024] Furthermore, a non-linear optimization objective function is designed. The non-linear optimization objective function minimizes the following three errors: The first item: the error between the laser range measurement and the coordinate calculation distance; The second item: the error between the GNSS coordinates and the optimized coordinates, where the optimized coordinates are understood as the coordinates to be optimized; The third item: the error between the accelerometer displacement and the coordinate change.

[0025] The non-linear optimization objective function is as follows: Among them, is the GNSS measurement coordinate of node , is the accelerometer measurement displacement of node , is the initial coordinate of node .

[0026] Furthermore, the Levenberg-Marquardt algorithm is adopted for iterative optimization to obtain the optimal coordinate .

[0027] Furthermore, using the optimal coordinate, the spatial coordinate reference network model is dynamically updated to correct and update the distance measurement value to adapt to the bridge deformation.

[0028] It should be noted that the spatial reference network is the basis for the spatio-temporal alignment of subsequent multi-source data, and its accuracy directly affects the reliability of the registration result.

[0029] The advantage of this method is that regardless of whether it is in a high-temperature, low-temperature, high-pressure or low-pressure environment, the distance measurement value can be corrected according to the actual environmental parameters to ensure the stability and reliability of the network in various complex environments.

[0030] S2. Based on the spatial reference network model, obtain the spatio-temporal registration result of multi-source heterogeneous data.

[0031] Please refer to Figure 2 , in one embodiment, first based on the spatial reference network model, collect multi-source heterogeneous data, including the timestamps and spatial coordinate data of GNSS, accelerometers, and inertial measurement units.

[0032] Furthermore, initialize the reference time function and the reference space function .

[0033] Furthermore, calculate the timestamp error and spatial coordinate error according to the sensor data.

[0034] Furthermore, set the weight coefficients , , to balance the time registration, spatial registration, and spatio-temporal smoothness.

[0035] Furthermore, construct a spatio-temporal registration objective function, and the spatio-temporal registration objective function is defined as follows: Among them, is the The timestamp function of a sensor, is the reference time function, is the spatial coordinate function of the th sensor, is the reference space function, is the spatio-temporal transformation matrix of the th data source, represents the spatio-temporal second-order mixed partial derivative constraint term, , are the weight coefficients, and are both the total number of sensors, and , is the total number of data sources, is time, is the spatial domain variable, used to describe the position distribution of sensors on the bridge structure.

[0036] It should be noted that in the spatio-temporal registration objective function, represents the difference between the spatial coordinates of the th sensor and the reference space function . The optimization objective is to align the spatial data of all sensors to a unified reference, that is, to unify the sensor data with different sampling frequencies and different spatio-temporal resolutions into the same timestamp and spatial coordinate system, solve the problems of data asynchrony and coordinate system mismatch, and provide consistent input for subsequent analysis.

[0037] Furthermore, the Lie group Lie algebra optimization method is adopted to solve the spatio-temporal registration objective function.

[0038] Specifically, the spatio-temporal transformation matrix is represented as a Lie group element.

[0039] Furthermore, the Lie algebra is used to linearly approximate the spatio-temporal registration objective function.

[0040] Furthermore, the Gauss-Newton method is used to solve the optimal transformation matrix to obtain the spatio-temporal sequence of the registered multi-source data.

[0041] Furthermore, it is verified whether the spatio-temporal sequence of the registered multi-source data meets the accuracy requirements.

[0042] Furthermore, the adaptive Kalman filter is adopted to smooth the registered spatio-temporal sequence. The adaptive Kalman filter model is as follows: where, is the th state variable, is the A state variable, including displacement, velocity, and acceleration, is the state transition matrix, is the noise driving matrix, is the system noise, is the observation vector, is the observation matrix, is the observation noise, and its covariance matrix is: Among them, represents the observation noise variance of GNSS, reflecting the positioning accuracy of GNSS; represents the measurement noise variance of the accelerometer, characterizing the credibility of acceleration data; represents the noise variance of the inertial measurement unit; represents the dynamic adjustment coefficient, which is used to compensate for unmodeled noise or sudden disturbances, such as GNSS signal loss and instantaneous sensor failure; represents the identity matrix, ensuring that the adaptive adjustment acts on all observation dimensions and preventing the covariance matrix from losing positive definiteness.

[0043] The advantage of this method is that it can effectively suppress noise interference, stabilize data fluctuations, promote the coordination of multi-source data, thereby comprehensively improving data quality, optimizing the signal-to-noise ratio, enhancing system robustness, and laying a solid foundation for subsequent accurate analysis and reliable prediction of bridge deformation.

[0044] Regarding the process of smoothing, specifically, first, initialize the state vector and the covariance matrix .

[0045] Furthermore, calculate the prior state estimate and covariance.

[0046] Furthermore, update the state estimate and covariance according to the observation data.

[0047] Furthermore, adaptively adjust the observation noise covariance , to improve the robustness of the filter.

[0048] Furthermore, output the smoothed spatio-temporal sequence data.

[0049] This method has the following effects: One is to propose a joint optimization objective function that includes time alignment terms, space alignment terms, and spatio-temporal smoothing terms. The advantage is that it introduces spatio-temporal second-order mixed partial derivative constraints in bridge monitoring, enforces the continuity and smoothness of spatio-temporal transformation, and avoids sudden changes in the registered data.

[0050] Second, the spatio-temporal transformation matrix is modeled as a Lie group element, and the local linearization property of Lie algebra is used for efficient optimization. The advantage is that the Lie group method can strictly maintain the rigidity of the transformation matrix, such as the orthogonality of rotation and translation, avoid the distortion of the bridge geometric structure after registration, and support the global optimal registration of multi-source heterogeneous data, especially suitable for the deformation monitoring of large-scale bridges, such as cable-stayed bridges and suspension bridges.

[0051] Third, a dynamic adjustment strategy for the noise covariance matrix is proposed. The advantage is that by fusing the noise characteristics of multi-source sensors, the filtering robustness is improved.

[0052] S3. According to the spatio-temporal registration result, perform depth-physical hybrid error compensation and obtain the compensation result.

[0053] In one embodiment, first, based on the spatio-temporal registration result in step S2, collect bridge displacement field data .

[0054] Furthermore, calculate the second-order spatial derivative of the displacement field and the time derivative .

[0055] Furthermore, establish a physical error model, and the expression of the physical error model is as follows: where is the output of the physical error model, representing the part of the bridge deformation error dominated by physical laws, is the bridge displacement field function, describing the deformation displacement of the bridge at the spatial position and time , , , represent weight coefficients, is the attenuation coefficient.

[0056] Furthermore, use the physical error model to output the physical error for subsequent compensation.

[0057] Furthermore, design a deep learning compensation network, which is used to correct the complex non-linear errors that cannot be captured by the physical error model; the deep learning compensation network includes an output layer, a loss function, and a network structure.

[0058] Specifically, for the deep learning compensation network, the input is the bridge displacement field data, time series data, and other relevant feature data, including environmental temperature data; the output is the final predicted value obtained by adding the deep learning compensation value and the output value of the physical error model.

[0059] Furthermore, for the deep learning compensation network, the loss function is as follows: where is the function value of the loss function, is the true deformation value, is the predicted output of the physical error model, is the output value of the deep learning compensation network, , , are hyperparameters that respectively control the weights of the three losses; is used to balance the importance of the prediction error term, is used to control the strength of weight regularization, is used to adjust the contribution of the gradient penalty term, represents the th feature dimension of the input features, are network parameters.

[0060] Furthermore, for the deep learning compensation network, a suitable network structure is selected according to the dimension of the input data. The network structure includes a multi-layer perceptron and a convolutional neural network. The multi-layer perceptron is suitable for processing low-dimensional data and performs feature extraction and prediction through multiple fully connected layers; the convolutional neural network is suitable for processing high-dimensional data and performs feature extraction through convolutional layers and pooling layers.

[0061] It should be noted that the network structure is a network structure that combines a multi-layer perceptron and a convolutional neural network. The hidden layer of the multi-layer perceptron part contains multiple fully connected layers, and the number of neurons in each layer can be adjusted according to the specific task. The output of each layer undergoes a non-linear transformation through an activation function. The convolutional layer of the convolutional neural network part uses multiple convolutional kernels to perform convolutional operations on the input data to extract local features; the pooling layer of the convolutional neural network part performs downsampling on the output of the convolutional layer to reduce the data dimension while retaining important features.

[0062] The advantage of this method is that it can effectively correct the errors of the physical model, improve the accuracy of prediction, and is suitable for processing input data with complex features.

[0063] Furthermore, based on the deep learning compensation network, a multi-scale feature fusion architecture is built, and its goal is to capture local details, extract global features, and enhance the feature expression ability; the local details include cracks and local stress concentrations, the global features include the overall displacement trend and low-frequency vibration modes, and the feature expression ability includes accuracy and robustness.

[0064] Specifically, first, a feature extraction formula is designed, and the feature extraction formula is as follows: Among them, is the feature of the layer, represents input feature concatenation, represents a pooling operation, represents the feature of the layer, represents the feature of the layer, represents the feature of the layer weight matrix, represents the bias of the layer, represents an activation function.

[0065] Furthermore, design the network hierarchy, which includes a shallow network (layers 1 - 3), a middle network (layers 4 - 6), and a deep network (more than 6 layers). The shallow network corresponds to high - frequency detailed features and is used to detect local deformations of the bridge, including cracks and texture changes; the middle network corresponds to medium - frequency transition features and is used to connect local and global information; the deep network corresponds to low - frequency global features and is used to analyze the overall displacement trend of the bridge, including bridge subsidence and tilt.

[0066] Furthermore, perform cross - layer connections. Directly transfer shallow features to the deep layer to avoid information loss; merge feature maps of different levels in the channel dimension; assign learnable weights to features of different levels.

[0067] Furthermore, design a pooling strategy.

[0068] Specifically, first divide the pooling methods into max - pooling, average - pooling, and learnable pooling. Max - pooling is suitable for local deformation detection, which is beneficial to retaining significant features but may lose some details; average - pooling is suitable for global trend analysis, which is beneficial to smoothing noise but may weaken key features; learnable pooling is suitable for adaptive feature extraction, which is beneficial to automatically optimizing pooling but has a higher computational cost.

[0069] Furthermore, input the feature maps into three parallel branches respectively, and each branch corresponds to a pooling method, namely the max - pooling, the average - pooling branch, and the learnable pooling. It should be noted that combining these three pooling methods together can perform feature extraction on the input data from different perspectives. The fused features contain significant features, global information, and adaptively extracted features, which are more comprehensive and rich, and help to improve the model's ability to capture various types of features.

[0070] The advantage of this method is that through cross - layer connections, feature concatenation, and pooling strategies, it realizes the joint analysis of local and global bridge deformations, greatly improving the detection efficiency and accuracy.

[0071] Furthermore, based on the multi-scale feature fusion architecture, a residual attention mechanism is introduced. The residual attention mechanism is used to dynamically weight physical features and deep learning features, enhancing the model's attention to key information, including attention weight calculation and residual connection.

[0072] Specifically, the calculation formula for the attention weight is as follows: where, is the attention weight matrix, representing the importance of different features, is the query matrix, is the key matrix, is the transpose operation of the matrix, is the value matrix of physical features, feature dimension, represents converting the input into a probability distribution to ensure the non-negativity and normalization of the attention weight.

[0073] Furthermore, a residual connection is performed, that is, adding the attention-weighted physical features to the original deep learning features, aiming to retain the information of the original deep learning features and avoid information loss; introducing constraints on physical features to enhance the interpretability and generalization ability of the model.

[0074] This method dynamically adjusts the weights of physical features and deep learning features through the attention mechanism to highlight key information; by introducing the value matrix of physical features, the model is constrained by physical laws during training; through residual connection, it ensures that the original features are not completely covered, improving the stability and performance of the model.

[0075] Furthermore, a hybrid training strategy is designed. The hybrid training strategy combines the optimization objectives of deep learning and physical error models to ensure that the model not only fits the data but also conforms to physical laws. The core of the hybrid training strategy is to balance the data-driven deep learning loss and the loss constrained by physical laws, enabling the model to learn complex features from the data and follow physical laws. By dynamically adjusting the mixing coefficient, the weights of the two in training are flexibly controlled, ultimately improving the generalization ability and interpretability of the model.

[0076] Specifically, the hybrid training process is as follows: pre-train the physical model and initialize the parameters , , and ; fix the physical model and train the deep learning compensation network; jointly fine-tune and optimize the overall model through the hybrid strategy.

[0077] It should be noted that for joint fine-tuning, first adjust the mixing coefficient , and then use the hybrid gradient to update the model parameters : where represents the parameter vector of the model at the -th step of training, represents the parameter vector of the model at the -th step of training, represents the learning rate, represents the mixing coefficient, represents the data-driven loss, which is the loss function calculated by the deep learning compensation network on the training data, and measures the difference between the network prediction output and the true target value, is the model parameter, representing the set of all trainable parameters, including weight and bias parameters, which determines the mapping relationship, represents the physical constraint loss, which is the output by the physical error model and the physical constraint loss based on the mean square error form, and it satisfies the following relational expression: where represents the number of samples, is the output of the physical error model corresponding to the -th sample.

[0078] Furthermore, by the above deep-physical hybrid parameter update model, update the physical error model and the deep learning compensation network parameters, so as to optimize the overall model.

[0079] Furthermore, through the optimized overall model, obtain the compensation result, and the compensation result includes adding the output by the physical error model and the output of the deep learning compensation network to get the data.

[0080] Furthermore, verify the compensation effect through the measured data, and adjust the model parameters and network structure.

[0081] The advantages of this method are as follows: By deeply integrating the physical model with the deep learning compensation network, it realizes the collaborative optimization of data-driven methods and physical laws in bridge displacement field analysis. It not only retains the interpretability and stability of the physical model but also uses neural networks to capture complex non-linear features that are difficult to describe by traditional models, significantly improving the prediction accuracy. By adopting the design that combines the multi-scale feature fusion architecture with the residual attention mechanism, it simultaneously processes the macroscopic overall displacement and microscopic local deformation features of bridge deformation. The attention mechanism is used to dynamically weight the importance of different-scale features, solving the deficiency of traditional methods in cross-scale feature fusion. The proposed hybrid training strategy ensures the physical rationality of the model while avoiding the gradient conflict problem that easily occurs in traditional training, making the model have both high accuracy and strong generalization ability.

[0082] S4. Obtain the deformation diagnosis result of the bridge structure according to the compensation result.

[0083] In one embodiment, first, according to the compensation result, establish a bridge deformation feature extraction model, and the bridge deformation feature extraction model satisfies the following relationship: where is the feature extraction value of the overall deformation state of the bridge, which synthesizes the local deformation gradient and the global deformation difference and is used to quantify the overall deformation state of the bridge. and are the curvature weight coefficients, which respectively control the contributions of the first derivative (slope) and the second derivative (curvature). is the key point weight, indicating the importance of the deviation between the deformation of the th monitoring point (spatial position) and the reference deformation. is the deformation amount of the current deformation mode at the position ; is the deformation amount of the reference deformation mode (initial healthy state) at ; is the total number of monitoring points; is the bridge displacement field function; represents the spatial position.

[0084] The advantage of this method is that by calculating the bridge deformation feature extraction value, it comprehensively quantifies the local and global deformation differences and comprehensively and accurately evaluates the dynamic deformation state of the bridge.

[0085] Furthermore, based on the bridge deformation feature extraction model, construct a dynamic Bayesian diagnosis network. The dynamic Bayesian diagnosis network includes a state transition probability and an observation likelihood function. The state transition probability is: where represents the transition from the bridge state Probability of evolving to the bridge state , where \(t\) represents time, \(A\) represents the state transition constraint matrix, \(Q\) is the process noise variance; the observation likelihood function is: wherein, \(p(z_t|x_t)\) represents the likelihood probability of observing the mode \(z_t\) given the bridge state \(x_t\), \(z_t\) is the \(t\)-th observed mode, including strain, displacement, and vibration data, \(H\) is the \(t\)-th observed mode, including strain, displacement, and vibration data, \(H\) is the observation mapping matrix that maps the state \(x_t\) to the observation space, \(x_t\) \(t\) represents time, \(N\) is the total number of observed modes, \(R\) is the observation noise covariance, \(\mathcal{N}\) is the multivariate normal distribution. This likelihood function is used in Bayesian inference to calculate the posterior observation likelihood probability by combining the prior state transition probability, thereby diagnosing the real-time state of the bridge.

[0086] The advantage of this method is that it obtains the posterior probability distribution through Bayesian inference and diagnoses the deformation state of the bridge in real time, including normal, slightly damaged, and severely damaged states.

[0087] Furthermore, based on the dynamic Bayesian diagnosis network, a bridge structural health diagnosis model is established. The bridge structural health diagnosis model satisfies the following relationship: wherein, \(SHI\) is the bridge structural health index, , the larger the value, the more severe the damage, \(BHO\) is the basic health offset, \(s_i\) is the sensitivity coefficient of the \(i\)-th damage index, including crack propagation rate and frequency change, \(f_i(t)\) is the time-varying function of the \(i\)-th damage index, including strain accumulation and vibration mode change rate, \(n\) is the total number of damage indices, \(T\) is the total time, \(t\) is the time variable.

[0088] Furthermore, according to the bridge structural health index output by the bridge structural health diagnosis model, combined with the bridge design standard and historical data, three-level health discrimination thresholds , , are set.

[0089] Furthermore, a health discrimination function is established based on the bridge structure health index and the three - level warning threshold. The health discrimination function is as follows: where, represents the health level and is used to measure the degree of bridge deformation.

[0090] When the bridge structure is normal, with no visible deformation or only extremely small elastic deformation, including the deflection under normal load; When the bridge structure has slight deformation, with minor cracks appearing, the width of which is less than 0.2 mm, and local concrete spalling; When the bridge structure has moderate deformation, with visible structural deformation appearing, including the beam deflection exceeding the design limit, the pier inclination angle less than 3 degrees, and the crack propagation width ranging from 0.2 mm to 1 mm.

[0091] When the bridge structure has severe deformation, with serious structural damage appearing, including beam fracture, obvious settlement of the pier or inclination with an inclination angle greater than 3 degrees, and cracks with a width greater than 1 mm, penetrating key components.

[0092] S5. Implement dynamic deformation monitoring and warning of the bridge based on the deformation diagnosis result.

[0093] In one embodiment, based on step S4, a digital twin model is constructed. The expression of the digital twin model is as follows: where, is the bridge deformation field, is the diffusion coefficient, reflecting the transmission rate of deformation in the structure, is the dynamic feedback force of the th sensor node, calculated from the measured data and the model prediction residual, is the Dirac function, indicating that the force acts on the node , represents the spatial position, represents the position of the th sensor, is the time, represents the total number of sensor nodes.

[0094] The advantage of this method is that by dynamically updating the bridge deformation field , the digital twin model is updated in real - time, synchronously reflecting the actual deformation state of the bridge.

[0095] Further, a sensitivity adjustment formula is established to implement an adaptive early warning strategy, and the sensitivity adjustment formula is as follows: Wherein, represents the sensitivity at time , represents the reference sensitivity, represents the maximum sensitivity, is the bridge structure health index in step S4, is the critical value of the bridge structure health index, is the adjustment rate, which controls the steepness of the change of sensitivity with the health index.

[0096] Further, the three-level threshold mentioned in step S4 is updated through the sensitivity, and its update formula is as follows: Wherein, represents the -th threshold at time , represents the initial threshold of the -th threshold, that is, the initial value of the three-level health discrimination threshold mentioned in step S4, represents the adjustment coefficient, represents the sensitivity at time represents the maximum sensitivity, represents the reference sensitivity.

[0097] It should be noted that based on step S4, when the three-level threshold changes, the corresponding relationship between the bridge structure health index and the health level will change, and thus the early warning strategy is updated in real time. The early warning results are as follows: When , no early warning is triggered; When , a mild early warning is triggered; When , a moderate early warning is triggered; When , a severe early warning is triggered.

[0098] The advantage of this method is that by outputting an adaptive threshold to replace the fixed threshold, the response ability to sudden damage is improved.

[0099] Further, a rendering equation is established to realize the visualization of the three-dimensional deformation field, and the rendering equation is as follows: Wherein, Indicates the color intensity value of the output image at the pixel point Combining the deformation contributions of all nodes, Indicates the total number of monitoring nodes, Is the amplitude coefficient, controlling the Visualization intensity of the deformation data of the -th monitoring node, Indicates the -th monitoring node's coordinate position projected on the two-dimensional plane, Indicates the Gaussian kernel smoothing parameter, which determines the diffusion range of the deformation influence in space, Indicates the -th node's deformation amount, Indicates the deformation-color mapping function, which converts the deformation amount into a color value.

[0100] The advantage of this method is that it combines the theoretical model, real-time monitoring, and visualization to form a complete closed-loop for bridge health management.

[0101] Please refer to Figure 3 which is Figure 3 the structural schematic diagram of the bridge dynamic deformation monitoring system in the embodiment of the present invention. The system includes an input device, a processor, an output device, and a memory. The input device, the processor, the output device, and the memory are interconnected. Among them, the memory is used to store computer programs, and the computer programs include program instructions. The processor is configured to call the program instructions, and the system uses the bridge dynamic deformation monitoring method described above.

[0102] In this embodiment, the input device includes a data acquisition module and an edge computing node; Specifically, the data acquisition module includes a GNSS receiver, an accelerometer array, an inertial measurement unit, a laser rangefinder, and a temperature and pressure sensor, which are used to collect bridge data in real time, including displacement, vibration, attitude, temperature, and pressure data. The edge computing node is deployed at key parts of the bridge, including the main girder, bridge pier, and bearing, and is used for data preprocessing and preliminary spatio-temporal alignment.

[0103] The processor includes a high-performance computing unit, a spatio-temporal registration module, an error compensation module, and a dynamic diagnosis engine; Specifically, the high-performance computing unit is used to run a depth-physics hybrid model, a Bayesian network model, and a digital twin model. The spatio-temporal registration module incorporates a multi-source data fusion algorithm. The error compensation module combines physical model and deep learning error compensation algorithms to compensate for system errors. The dynamic diagnosis engine is used to update the bridge structure health index and predict the deterioration trend.

[0104] The output device includes a three-dimensional visualization terminal, a multi-level early warning terminal, and a report generation module; Specifically, the three-dimensional visualization terminal is used to output a deformed heat map rendered in a red, yellow, and green color gradient; the multi-level early warning terminal includes an audible and visual alarm for early warning broadcasts of bridge deformation damage; the report generation module is used to automatically generate an analysis report on the bridge deformation trend.

[0105] The memory uses a high-speed solid-state drive, which features fast read and write speeds, large capacity, and high reliability, and can meet the needs of storing large amounts of data. It is mainly used to store the data input by the input device and the data processed by the processor.

[0106] In summary, the present invention solves the problem of inconsistent coordinate systems in multi-sensor data fusion by establishing a high-precision three-dimensional spatial reference network; by integrating physical mechanisms and deep learning, it takes into account both environmental interference suppression and mechanical law constraints in error compensation; by quantifying the damage accumulation effect through a dynamic Bayesian network, it realizes probabilistic inference from deformation data to health status; and by generating an adaptive early warning and a visualized three-dimensional deformation field through a digital twin model, it greatly improves the monitoring reliability and decision-making efficiency under complex working conditions.

[0107] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the various embodiments of the present invention, and they should all be covered within the scope of the claims and the description of the present invention.

Claims

1. A bridge dynamic deformation monitoring method, characterized in that: The method comprises the following steps: Establish a spatial coordinate reference network model of the bridge; Based on the spatial coordinate reference network model, obtaining the spatiotemporal registration result of multi-source heterogeneous data; According to the spatiotemporal registration result, performing mixed error compensation and obtaining a compensation result; Obtaining deformation diagnosis results of the bridge structure according to the compensation results; The dynamic deformation monitoring of the bridge is realized through the deformation diagnosis result.

2. A bridge dynamic deformation monitoring method according to claim 1, characterized in that: The spatial coordinate reference network model for establishing the bridge includes: Deploy multiple sensor nodes at key locations of the bridge, including the main beam, piers, and supports, and the sensor nodes include a global navigation satellite system, an accelerometer array, an inertial measurement unit, an edge computing unit, and a temperature and pressure sensor; Using a laser rangefinder, measuring the initial distance between the sensor nodes; According to the initial distance, a spatial coordinate reference network model is established, wherein the spatial coordinate reference network model is used to provide a spatial coordinate reference for the data of the sensor node; Based on the spatial coordinate reference network model, multi-source heterogeneous data is collected, wherein the multi-source heterogeneous data includes timestamps and spatial coordinate data of the global navigation satellite system, the accelerometer array, and the inertial measurement unit; Designing a nonlinear optimization objective function based on the multi-source heterogeneous data; The spatial coordinate reference network model is optimized through the nonlinear optimization objective function to obtain an optimized spatial coordinate reference network model.

3. A bridge dynamic deformation monitoring method according to claim 2, characterized in that: The spatial coordinate reference network model satisfies the following expression: in, For Node and nodes The actual initial distance measurement between For Node and nodes The temperature difference between is the reference temperature, is the initial measurement noise, is the influence coefficient of ambient temperature on distance measurement, and Node and nodes The ambient temperature, is the influence coefficient of instrument pressure on distance measurement, and Node and nodes environmental pressure, and Node and nodes The spatial coordinates of the nonlinear optimization objective function are as follows: in, For Node GNSS measurement coordinates, For Node The accelerometer measures displacement, For Node The initial coordinates of .

4. A bridge dynamic deformation monitoring method according to claim 1, characterized in that: The obtaining of the spatiotemporal registration result of multi-source heterogeneous data based on the spatial reference network includes: Based on the spatial reference network, a spatiotemporal registration objective function is constructed, and the spatiotemporal registration objective function is as follows: in, For the The timestamp function of each sensor, is the base time function, For the The spatial coordinate function of the sensor, is the base space function, For the The spatiotemporal transformation matrix of the data source, represents the space-time second-order mixed partial derivative constraint term, , , is the weight coefficient, and are the total number of sensors, and , is the total number of data sources, For time, is the spatial domain variable; The space-time registration objective function is solved by using the Lie group and Lie algebra optimization method to obtain the space-time sequence of the multi-source heterogeneous data after registration; Adaptive Kalman filtering is used to smooth the space-time series and obtain a smoothing result.

5. A bridge dynamic deformation monitoring method according to claim 1, characterized in that: The performing mixed error compensation and obtaining a compensation result according to the spatiotemporal registration result comprises: According to the spatiotemporal registration result, a physical error model is established, and the physical error model satisfies the following expression: in, is the output of the physical error model, is the bridge displacement field function, , , represents the weight coefficient, Indicates the spatial position, For time, is the attenuation coefficient; Based on the physical error model, a deep learning compensation network is constructed, and the loss function of the deep learning compensation network is as follows: in, is the function value of the loss function, is the true deformation value, is the predicted output of the physical error model, is the output value of the deep learning compensation network, , , is the weight coefficient, The first feature dimensions, is the network parameter; Based on the deep learning compensation network, a multi-scale feature fusion architecture is built; Based on the multi-scale feature fusion architecture, depth-physical hybrid error compensation is performed and a compensation result is obtained.

6. A bridge dynamic deformation monitoring method according to claim 5, characterized in that: The performing depth-physical mixed error compensation and obtaining the compensation result based on the multi-scale feature fusion architecture includes: Based on the multi-scale feature fusion architecture, a residual attention mechanism is designed; Based on the residual attention mechanism, a hybrid training strategy is designed; Through the hybrid training strategy, data compensation is performed by integrating the deep learning compensation network with the physical error model and a compensation result is obtained.

7. A bridge dynamic deformation monitoring method according to claim 1, characterized in that: The step of obtaining a deformation diagnosis result of the bridge structure according to the compensation result includes: According to the compensation result, a bridge deformation feature extraction model is established, and the expression of the bridge deformation feature extraction model is as follows: in, is the feature extraction value of the overall deformation state of the bridge, , is the curvature weight coefficient, For the Key point weights, For the current deformation mode at position The deformation amount, For the reference deformation mode The deformation amount, is the total number of monitoring points, is the bridge displacement field function, Indicates spatial location; Based on the bridge deformation feature extraction model, a dynamic Bayesian diagnosis network is constructed, wherein the dynamic Bayesian diagnosis network includes a state transition probability and an observation likelihood function; The deformation diagnosis result of the bridge structure is obtained through the dynamic Bayesian diagnosis network.

8. A bridge dynamic deformation monitoring method according to claim 7, characterized in that: The method of obtaining the deformation diagnosis result of the bridge structure through the dynamic Bayesian diagnosis network includes: A bridge structure health diagnosis model is established through the dynamic Bayesian diagnosis network, and the bridge structure health diagnosis model satisfies the following expression: in, is the bridge structure health index, is the basic health offset, For the The sensitivity coefficient of the damage index is For the The time-varying function of the damage index is is the total number of damage indicators, is the total time, is the time variable; The deformation diagnosis result of the bridge structure is obtained through the bridge structure health diagnosis model.

9. A bridge dynamic deformation monitoring method according to claim 1, characterized in that: The method of realizing dynamic deformation monitoring of the bridge through the deformation diagnosis result includes: A digital twin model is constructed based on the deformation diagnosis results. The expression of the digital twin model is as follows: in, is the bridge deformation field, is the diffusion coefficient, For the The dynamic feedback force of sensor nodes, is the Dirac function, Indicates the spatial position, Indicates The location of the sensor, For time, represents the total number of sensor nodes; Designing an adaptive early warning strategy based on the digital twin model; According to the adaptive early warning strategy, a rendering equation is established; Generate a three-dimensional deformation field visualization result according to the rendering equation; The dynamic deformation monitoring of the bridge is realized through the three-dimensional deformation field visualization result.

10. A bridge dynamic deformation monitoring system, the system using a bridge dynamic deformation monitoring method according to any one of claims 1 to 9, characterized in that: The system includes an input device, a processor, an output device and a memory, wherein the input device, the processor, the output device and the memory are connected to each other, wherein the memory is used to store a computer program, the computer program includes program instructions, and the processor is configured to call the program instructions.

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