A bridge three-dimensional stiffness inversion and global state perception method and system

Abstract

The present application relates to the technical field of bridge structure health monitoring, in particular to a bridge three-dimensional stiffness inversion and global state sensing method and system. The method comprises the following steps: obtaining a prior data set containing spatial coordinates, load working condition information and corresponding displacement response; constructing a multi-branch physical information neural network, based on the prior data set and the measured displacement data set, using a composite loss function to train the multi-branch physical information neural network to simultaneously optimize the network parameters of the three-dimensional displacement field distribution function and the bridge stiffness field distribution function; extracting and solidifying the bridge stiffness field distribution function in the trained multi-branch physical information neural network to generate a bridge digital twin model; based on the bridge digital twin model, new known loads and new sparse displacement observation data, solving the full-field three-dimensional displacement continuous field under the corresponding working condition, and automatically differentiating the full-field three-dimensional displacement continuous field to analytically obtain the three-dimensional strain tensor and stress tensor of the whole bridge.

Description

Technical Field

[0001] This invention relates to the field of bridge structural health monitoring technology, specifically to a method and system for bridge three-dimensional stiffness inversion and global state perception. Background Technology

[0002] In modern transportation infrastructure management, accurate health monitoring and condition assessment of bridge structures are crucial. Traditional methods mainly rely on deploying sensor networks at key structural locations to acquire discrete monitoring data, or updating structural parameters through finite element model correction. Among these methods, physical information neural networks (PINNs) offer a new approach to structural condition perception. However, most existing PINN-based solutions are based on simplified mechanical models, such as simplifying bridges to models following one-dimensional beam element theory. While these methods can handle overall deformation, they cannot accurately reflect the complex three-dimensional mechanical behavior of structures such as long-span concrete box girders and rigid frame bridges, including localized cracking in the web, three-dimensional stress concentration in the anchorage zone, and distortion effects at variable cross-sections. Furthermore, existing stiffness inversion methods often couple the elastic modulus with geometric properties such as the moment of inertia of the cross section, failing to achieve independent and continuous localization of material stiffness degradation.

[0003] Another common approach relies on finite element model correction. This method matches observed data by adjusting stiffness parameters at the discrete element level. However, this method has inherent drawbacks: first, model correction depends on pre-defined meshes, which can easily lead to decreased computational accuracy in stress concentration regions due to mesh distortion or singularities; second, the updated stiffness field is piecewise discrete, failing to form a spatially continuous functional expression, which is not conducive to fine-grained damage localization; and third, the model correction process based on optimization algorithms is computationally intensive, making it difficult to meet the needs of real-time online monitoring and rapid condition assessment.

[0004] Existing technologies suffer from limitations such as the inability to perform refined three-dimensional solid mechanical analysis of bridges, the inability to invert spatially continuous stiffness fields, and the difficulty in balancing computational efficiency and accuracy. Solving the problem of how to achieve refined three-dimensional solid mechanical analysis of bridge structures and efficiently and accurately invert spatially continuous stiffness distribution fields based on sparse observation data to construct high-fidelity digital twin models to support full-field state perception is a pressing issue. Summary of the Invention

[0005] To address the shortcomings of existing methods and the needs of practical applications, this invention provides a method for bridge three-dimensional stiffness inversion and global state perception, comprising the following steps: Based on bridge design data, a priori dataset containing spatial coordinates, load condition information, and corresponding displacement responses is obtained. A multi-branch physical information neural network is constructed, with spatial coordinates and load condition parameters as inputs, and outputs including a three-dimensional displacement field distribution function and a bridge stiffness field distribution function. Based on the priori dataset and the measured displacement dataset, the multi-branch physical information neural network is trained using a composite loss function to simultaneously optimize the network parameters of the three-dimensional displacement field distribution function and the bridge stiffness field distribution function. The composite loss function includes at least an observation loss term based on the measured displacement dataset and a regularization constraint term based on the bridge stiffness field distribution function. The bridge stiffness field distribution function in the trained multi-branch physical information neural network is extracted and solidified to generate a bridge digital twin model. Based on the bridge digital twin model, new known loads, and new sparse displacement observation data, the full-field three-dimensional displacement continuous field under the corresponding load condition is solved, and the full-field three-dimensional displacement continuous field is automatically differentiated to analytically obtain the three-dimensional strain tensor and stress tensor of the entire bridge.

[0006] Optionally, the step of obtaining a priori dataset containing spatial coordinates, load condition information, and corresponding displacement responses based on bridge design data includes: A baseline finite element model of the bridge was established based on the bridge design data. Multiple load conditions are applied to the reference finite element model for batch calculations, generating the prior dataset containing spatial coordinates, load condition information, and corresponding simulated displacement responses.

[0007] Optionally, the multi-branch physical information neural network includes: The input layer is used to receive spatial coordinates and operating parameters; Shared hidden layer network entity; The first output branch is used to output the three-dimensional displacement field; The second output branch is used to output a spatially continuous elastic modulus field.

[0008] Optionally, training the multi-branch physical information neural network using a composite loss function includes staged training: In the first stage, the multi-branch physical information neural network is pre-trained using the prior dataset to preliminarily determine the network parameters of the three-dimensional displacement field distribution function; In the second stage, the measured displacement dataset and the prior dataset are combined, and the composite loss function is used to jointly train the multi-branch physical information neural network to simultaneously optimize the network parameters of the three-dimensional displacement field distribution function and the bridge stiffness field distribution function.

[0009] Optionally, the composite loss function further includes a physical loss term based on the physical control equation, which is obtained by substituting the predicted values ​​of the three-dimensional displacement field distribution function and the bridge stiffness field distribution function into the static equilibrium control equation and calculating the equation residuals.

[0010] Optionally, the static equilibrium governing equations are three-dimensional Navier-Lamé equations, expressed as follows: in, It is a displacement vector. and To be related to the elastic modulus field Lamé constant related to Poisson's ratio Given the volume forces, For gradient operators, For the Laplace operator.

[0011] Optionally, the physical loss term is expressed in the three-dimensional domain of the bridge. Internally collected configuration point set The sum of squares of the residuals from the above equations is obtained, which satisfies: in, Represents the physical loss term. Indicates the number of configuration points. Indicates the first The residual of the point in the x-direction, Indicates the first The residual of the point in the y-direction, Indicates the first The residual of the point in the z-direction.

[0012] Optionally, the composite loss function further includes a boundary condition loss term, which includes at least one of geometric boundary condition loss and force boundary condition loss.

[0013] Optionally, after extracting and solidifying the bridge stiffness field distribution function in the multi-branch physical information neural network after training, the method further includes: Based on the sensitivity analysis of the pre-trained multi-branch physical information neural network to the spatial displacement field, the optimal location for deploying displacement sensors on the actual bridge is determined.

[0014] Secondly, to efficiently execute the bridge three-dimensional stiffness inversion and global state perception method provided by this invention, this invention also provides a bridge three-dimensional stiffness inversion and global state perception system, including: an input device, an output device, a processor, and a memory. The input device, output device, processor, and memory are interconnected. The memory stores program instructions used for the bridge three-dimensional stiffness inversion and global state perception method. This bridge three-dimensional stiffness inversion and global state perception system of this invention has a compact structure and stable performance, and can stably execute the bridge three-dimensional stiffness inversion and global state perception method provided by this invention, further improving the overall applicability and practical application capability of this invention.

[0015] Beneficial effects: First, since the neural network directly takes three-dimensional spatial coordinates as input and outputs a continuous function, its analysis is based on the three-dimensional Navier-Lamé governing equations. Therefore, it can perform refined mechanical analysis of bridges at the solid level, accurately reflecting the three-dimensional stress state of complex parts such as box girders and variable cross-sections, overcoming the limitations of traditional one-dimensional beam element models. Second, by inverting the elastic modulus field as an independent continuous function, it achieves direct and continuous localization of material stiffness degradation, avoiding coupling with cross-sectional geometric parameters and the singularity problems caused by finite element discrete meshes, thus improving the accuracy and interpretability of stiffness inversion. Third, the composite loss function incorporates physical equation constraints, boundary conditions, and prior regularization, ensuring that the inversion process strictly follows mechanical laws, enhancing the theoretical consistency and reliability of the results, and effectively preventing overfitting under sparse data. Finally, the trained digital twin model solidifies the stiffness field, requiring only an update to the displacement field when facing new working conditions. This computationally efficient model can rapidly deduce the full-field displacement, strain, and stress based on sparse real-time observation data, achieving real-time and accurate perception of the bridge's global state and meeting the needs of online monitoring and early warning. Attached Figure Description

[0016] Figure 1 A flowchart of a bridge three-dimensional stiffness inversion and global state perception method provided in an embodiment of the present invention; Figure 2 A framework diagram of a bridge three-dimensional stiffness inversion and global state perception system provided in an embodiment of the present invention. Detailed Implementation

[0017] Specific embodiments of the present invention will now be described in detail. It should be noted that the embodiments described herein are for illustrative purposes only and are not intended to limit the invention. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be apparent to those skilled in the art that these specific details are not necessary to practice the invention. In other instances, well-known circuits, software, or methods have not been specifically described to avoid obscuring the invention.

[0018] Throughout this specification, references to "an embodiment," "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in connection with that embodiment or example is included in at least one embodiment of the invention. Therefore, the phrases "in an embodiment," "in an embodiment," "an example," or "an example" appearing in various places throughout the specification do not necessarily refer to the same embodiment or example. Furthermore, specific features, structures, or characteristics can be combined in one or more embodiments or examples in any suitable combination and / or sub-combination. Moreover, those skilled in the art will understand that the illustrations provided herein are for illustrative purposes and are not necessarily drawn to scale.

[0019] Please see Figure 1 This invention provides a method for three-dimensional stiffness inversion and global state perception of bridges. In one embodiment, the method includes the following steps: S1. Based on bridge design data, obtain a priori dataset containing spatial coordinates, load condition information and corresponding displacement response.

[0020] In this embodiment, a baseline finite element model of the bridge is established based on the bridge design data. Specifically, the processor reads bridge design drawings, inspection reports, and other data stored in the memory, and extracts the geometric dimensions and material design parameters (such as the design value of the elastic modulus) of the structure. Poisson's ratio Information such as cross-sectional properties and boundary conditions.

[0021] Based on this information, the processor calls the interface or built-in solver of finite element analysis software (such as ANSYS, ABAQUS) to establish a three-dimensional solid reference finite element model of the bridge.

[0022] Multiple load conditions are applied to the benchmark finite element model for batch calculations, generating a priori dataset containing spatial coordinates, load condition information and corresponding simulated displacement responses. Specifically, the processor automatically applies a series of preset load conditions to the established finite element model through script control, such as applying concentrated or distributed forces of varying magnitudes at different bridge span locations to simulate static load tests or typical operational loads.

[0023] For each working condition, the finite element solver calculates the displacement response of the bridge across the entire field. The processor then samples the data in batches from the finite element calculation results and records the three-dimensional spatial coordinates of the sampling points. Parameters of the current operating condition (such as the magnitude of the force) Location of action and the corresponding displacement components in the three directions. This results in a large prior dataset that reflects the mechanical behavior of the structure under design conditions, providing low-fidelity supervision signals for the subsequent pre-training of neural networks.

[0024] Through batch finite element analysis, input-output data pairs covering the entire spatial domain of the bridge and various load conditions were efficiently generated. This data, serving as prior knowledge, helps the neural network quickly learn the macroscopic mechanical mapping laws of the structure that conform to the design state during the initial training phase. This lays a solid initial foundation for subsequent refined inversion using measured data, avoiding convergence difficulties or instability issues that might occur when the model is trained from a random state.

[0025] The prior dataset may also include the coordinates of a large number of configuration points randomly scattered inside the structural domain for calculating physical loss, as well as the coordinates of boundary points collected at supports, loading surfaces, etc., and their corresponding known displacements or surface force values ​​for calculating boundary condition loss. These points and their corresponding physical information together constitute a more complete training sample set.

[0026] S2. Construct a multi-branch physical information neural network. The input of the multi-branch physical information neural network is spatial coordinates and working condition parameters, and the output includes a three-dimensional displacement field distribution function and a bridge stiffness field distribution function.

[0027] In this embodiment, the multi-branch physical information neural network includes an input layer, a shared hidden layer network body, a first output branch, and a second output branch.

[0028] The input layer is used to receive spatial coordinates input from the processor. and operating parameters ,For example These input parameters are concatenated into a vector.

[0029] The shared hidden layer network typically consists of multiple fully connected layers, with activation functions (such as Tanh, Swish, etc.) set between layers to extract and fuse high-dimensional features from the input.

[0030] The first output branch is connected after the shared hidden layer and is used to output a three-dimensional vector, namely the three-dimensional displacement field distribution function. This function provides a displacement prediction for any spatial point under a given load.

[0031] The second output branch is also connected after the shared hidden layer, and is used to output a scalar, namely a spatially continuous elastic modulus field. The field function is independent of the load condition and is only related to the spatial location. It characterizes the distribution of material stiffness inside the bridge. The network parameters (i.e., all weights and biases) are optimized by the processor during training. The network architecture decouples the displacement field (related to the load) and the stiffness field (unrelated to the load but spatially variable), making it possible to directly infer the independent material stiffness distribution.

[0032] Understandably, the constructed multi-branch network is the core of this invention's functionality. Its first branch directly parameterizes the displacement field, and the second branch directly parameterizes the stiffness field. This design makes the stiffness inversion objective clear and independent. As a universal function approximator, the neural network can express complex displacement and stiffness distributions in the form of continuous functions, overcoming the limitations of piecewise discretization of the stiffness field in traditional finite element methods. This achieves true spatial continuous inversion, which is beneficial for precise damage localization and visualization.

[0033] S3. Based on the prior dataset and the measured displacement dataset, the multi-branch physical information neural network is trained using a composite loss function to simultaneously optimize the network parameters of the three-dimensional displacement field distribution function and the bridge stiffness field distribution function. The composite loss function includes at least an observation loss term based on the measured displacement dataset and a regularization constraint term based on the bridge stiffness field distribution function.

[0034] In this embodiment, the training process may employ a phased strategy, specifically including a first phase and a second phase.

[0035] Phase 1: Pre-training the multi-branch physical information neural network using a prior dataset to initially determine the network parameters of the 3D displacement field distribution function. In this phase, the stiffness field branch can be temporarily frozen or simply initialized. The main optimization objective is to make the network output displacement field fit the simulated displacement data in the prior dataset. The loss function used can be limited to the observation loss term. This involves calculating the mean square error between the network-predicted displacement and the finite element simulation displacement at corresponding points. Through this pre-training, the network can learn the basic mapping relationship between load, coordinates, and displacement under the design stiffness, thus obtaining reasonable initial parameters.

[0036] The second stage involves combining the measured displacement dataset with the prior dataset and using a composite loss function to jointly train a multi-branch physical information neural network, thereby simultaneously optimizing the network parameters of the three-dimensional displacement field distribution function and the bridge stiffness field distribution function.

[0037] The measured displacement dataset comes from load tests or monitoring systems of actual bridges, and is typically sparse. At this stage, the composite loss function is fully utilized, and the processor calculates the total loss: , in, It is the observation loss term based on the measured displacement dataset. It is the physical loss term based on the physical governing equations. It is the boundary condition loss term. It is a regularization constraint term (i.e., stiffness regularization loss) based on the bridge stiffness field distribution function. It is the prior data loss term. These are the weighting coefficients for each loss term.

[0038] The processor calculates the gradient of the total loss with respect to all network parameters (including displacement and stiffness branches) using the backpropagation algorithm, and updates the parameters using an optimizer (such as Adam) so that the network simultaneously satisfies the requirements of fitting sparse measured data, conforming to the physical governing equations, satisfying boundary conditions, and approximating the stiffness prior.

[0039] The first stage utilizes sufficient but low-fidelity prior data to enable the network to quickly converge to a reasonable solution space, avoiding the problems of getting trapped in local optima or overfitting that can easily occur when training directly with sparse measured data. The second stage introduces high-fidelity but sparse measured data and fine-tunes it under the strong physical constraints of the composite loss function. This allows the network to effectively correct and inversely derive a stiffness field that more closely resembles the actual structure based on a small amount of real information, while ensuring the physical rationality of the solution.

[0040] In the embodiments, the specific implementation of each term in the composite loss function can be further refined, including the physical loss term. By substituting the predicted values ​​of the three-dimensional displacement field distribution function and the bridge stiffness field distribution function into the static equilibrium governing equations and calculating the equation residuals, the static equilibrium governing equations can be obtained using the three-dimensional Navier-Lamé equations: in, It is a displacement vector. and To be related to the elastic modulus field Lamé constant related to Poisson's ratio Given the volume forces, For gradient operators, For the Laplace operator.

[0041] Lamé constant and Through the elastic modulus field and the preset Poisson ratio From the formula , Calculated.

[0042] Physical loss item Through the three-dimensional domain of bridge A large set of configuration points randomly sampled within the interior The sum of squares of the residuals from the above equations is obtained, which satisfies: in, Represents the physical loss term. Indicates the number of configuration points. Indicates the first The residual of the point in the x-direction, Indicates the first The residual of the point in the y-direction, Indicates the first The residual of the point in the z-direction.

[0043] In the embodiment, the boundary condition loss term This may include geometric boundary condition loss. Force boundary condition loss .

[0044] Calculate the error between the network-predicted displacement and the zero displacement (or other known displacement) on displacement-constrained boundaries (such as fixed supports). At the boundary where surface forces are known to act The above calculation specifically predicts surface forces. With known surface forces The sum of squares of the differences: , Among them, the predicted surface force , The Cauchy stress tensor is calculated using the generalized Hooke's law from strain (the first derivative of displacement) and the stiffness field. It is the outer normal vector of the boundary.

[0045] Stiffness regularization loss The expression is: , in This is a reference value for the elastic modulus determined based on design or testing data. This constraint prevents the stiffness field from exhibiting physically meaningless drastic fluctuations in regions lacking data, guiding the inversion results towards engineering experience.

[0046] In actual training, the weight coefficients of each loss term It can be dynamically adjusted according to the training phase, for example, focusing on the pre-training phase. In the early stages of joint training, balance all aspects and increase [efforts] in the later stages. and Weights are added to improve accuracy.

[0047] S4. Extract and solidify the bridge stiffness field distribution function in the multi-branch physical information neural network after training to generate a bridge digital twin model.

[0048] Once the model training converges, the processor reads and saves the second output branch (i.e., the elastic modulus field). All network parameters (weights and biases) define a continuous function with respect to spatial coordinates. Fixing this function means that these parameters will remain fixed in subsequent calculations and will no longer participate in training updates. This fixed stiffness field function, combined with the network's main architecture, constitutes a three-dimensional digital twin model of the specific bridge, reflecting its current true stiffness state. This model encapsulates the structure's physical properties (stiffness) in a computable form.

[0049] It should be understood that the generated digital twin model is key to the shift from "training inversion" to "application awareness," as it captures the bridge's most fundamental and time-invariant mechanical property—stiffness distribution. Once obtained, when facing new and unknown load conditions, there is no need to repeat the complex inversion optimization process, greatly improving the real-time performance of state awareness.

[0050] In another embodiment, after extracting and solidifying the bridge stiffness field distribution function in the trained multi-branch physical information neural network, an additional step may be included: Based on the sensitivity analysis of the spatial displacement field by the pre-trained multi-branch physical information neural network, the optimal location for deploying displacement sensors on actual bridges is determined.

[0051] Specifically, after pre-training, the network has learned the dependence of the displacement field on spatial position under design conditions. The processor can automatically differentiate to calculate the gradient of the network output displacement with respect to the input spatial coordinates under typical load conditions, or analyze the effect of changing the sensor position on the loss function (especially...). The influence of the item) indicates that areas that are sensitive to displacement changes or contribute significantly to the overall state inference can be identified as optimal locations for sensor deployment. This provides theoretical guidance for the design of low-cost and high-efficiency monitoring systems in practical engineering.

[0052] S5. Based on the bridge digital twin model, new known loads, and new sparse displacement observation data, solve for the full-field three-dimensional displacement continuous field under the corresponding working condition, and automatically differentiate the full-field three-dimensional displacement continuous field to analytically obtain the three-dimensional strain tensor and stress tensor of the entire bridge.

[0053] The generated digital twin model is loaded into the processor. For a new operating load condition (the load magnitude and location are known or partially known), the processor inputs the new load parameters and any spatial coordinate points of interest within the entire bridge domain into the network. At this point, the stiffness field branch parameters of the network are fixed.

[0054] Simultaneously, displacement observation data from several sparse measuring points under this working condition, acquired by the actual monitoring system, are used as new constraints. Then, the processor reconfigures a simplified composite loss function, which typically includes force boundary condition losses for the new load. and observation loss for new observation data Physical loss and stiffness regularization loss It is still retained, but the stiffness field is not updated.

[0055] Using this loss function as the objective, the parameters of only the first output branch (displacement field branch) of the network are optimized (or used as trainable variables) to quickly solve for the full-field three-dimensional displacement continuum that satisfies the new load and new observation data. .

[0056] Since the network is a continuous function, the displacement field is also spatially continuous. Then, the processor uses automatic differentiation to perform an analysis of the displacement field. Calculate the first-order partial derivative in space and directly analyze the Cauchy strain tensor. The components: Finally, based on the solidified stiffness field and the calculated strain tensor Through the generalized Hooke's law (in To and and (related stiffness tensor), the processor can analytically calculate the three-dimensional Cauchy stress tensor at any point on the entire bridge. .

[0057] This invention adapts to new sparse observation data by fixing the stiffness field and optimizing only the displacement field. The computational load is much smaller than that of a complete inversion process, making it possible to quickly deduce the strain and stress state of the bridge across the entire field based on real-time monitoring data. This enables real-time perception from sparse local information to a global refined state, providing a direct basis for structural safety early warning and assessment.

[0058] This invention first generates a priori dataset of displacement response covering various load conditions based on design data. Then, it constructs a multi-branch physical information neural network that takes spatial coordinates and load parameters as input and outputs a three-dimensional displacement field and a continuous stiffness field. Next, using a composite loss function incorporating observation, regularization, and physical equation constraints, the network is trained with both the prior and measured displacement datasets to simultaneously optimize the displacement and stiffness distribution functions. After training, the stiffness field distribution function representing the actual structural state is solidified, generating a digital twin model of the bridge. Finally, for new load conditions, based on this digital twin model and sparse new observation data, the full-field three-dimensional displacement continuous field can be quickly solved, and the strain and stress tensors of the entire bridge can be directly analyzed analytically through automatic differentiation.

[0059] This method transforms the complex problem of solving partial differential equations and parameter inversion into an optimizable learning problem through neural networks. It uses automatic differentiation to accurately calculate higher-order derivatives in physical equations and uses a composite loss function to ensure that the solution achieves a balance in terms of data fitting, adherence to physical laws, and prior knowledge constraints, thereby realizing three-dimensional refined global state perception based on sparse observations.

[0060] It should be noted that the specific implementation methods described above, such as image processing, numerical simulation, and the construction and training of machine learning models, can all be accomplished by the processor by calling the corresponding computer program instructions stored in memory. Those skilled in the art can implement the above functions using algorithms and tools known in the prior art, according to actual needs.

[0061] Please see Figure 2 In an embodiment, to efficiently execute the bridge three-dimensional stiffness inversion and global state perception method provided by the present invention, the present invention also provides a bridge three-dimensional stiffness inversion and global state perception system, including: an input device 1, an output device 2, a processor 3, and a memory 4. The input device 1, output device 2, processor 3, and memory 4 are interconnected. The memory 4 stores program instructions for executing the steps of the bridge three-dimensional stiffness inversion and global state perception method. The bridge three-dimensional stiffness inversion and global state perception system of the present invention has a compact structure and stable performance, and can stably execute the bridge three-dimensional stiffness inversion and global state perception method of the present invention, further improving the overall applicability and practical application capability of the present invention.

[0062] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the present invention.

Claims

1. A method for three-dimensional stiffness inversion and global state perception of bridges, characterized in that, Includes the following steps: Based on bridge design data, a priori dataset containing spatial coordinates, load condition information and corresponding displacement response is obtained. A multi-branch physical information neural network is constructed. The input of the multi-branch physical information neural network is spatial coordinates and working condition parameters, and the output includes a three-dimensional displacement field distribution function and a bridge stiffness field distribution function. Based on the prior dataset and the measured displacement dataset, the multi-branch physical information neural network is trained using a composite loss function to simultaneously optimize the network parameters of the three-dimensional displacement field distribution function and the bridge stiffness field distribution function. The composite loss function includes at least an observation loss term based on the measured displacement dataset and a regularization constraint term based on the bridge stiffness field distribution function. The bridge stiffness field distribution function in the multi-branch physical information neural network after training is extracted and solidified to generate a bridge digital twin model; Based on the bridge digital twin model, new known loads, and new sparse displacement observation data, the full-field three-dimensional displacement continuous field under the corresponding working conditions is obtained by solving the problem. The full-field three-dimensional displacement continuous field is automatically differentiated and the three-dimensional strain tensor and stress tensor of the entire bridge are analytically obtained.

2. The bridge three-dimensional stiffness inversion and global state perception method according to claim 1, characterized in that, The prior data set obtained based on bridge design data, which includes spatial coordinates, load condition information, and corresponding displacement responses, includes: A baseline finite element model of the bridge was established based on the bridge design data. Multiple load conditions are applied to the reference finite element model for batch calculations, generating the prior dataset containing spatial coordinates, load condition information, and corresponding simulated displacement responses.

3. The bridge three-dimensional stiffness inversion and global state perception method according to claim 1, characterized in that, The multi-branch physical information neural network includes: The input layer is used to receive spatial coordinates and operating parameters; Shared hidden layer network entity; The first output branch is used to output the three-dimensional displacement field; The second output branch is used to output a spatially continuous elastic modulus field.

4. The bridge three-dimensional stiffness inversion and global state perception method according to claim 1, characterized in that, The training of the multi-branch physical information neural network using a composite loss function includes staged training: In the first stage, the multi-branch physical information neural network is pre-trained using the prior dataset to preliminarily determine the network parameters of the three-dimensional displacement field distribution function; In the second stage, the measured displacement dataset and the prior dataset are combined, and the composite loss function is used to jointly train the multi-branch physical information neural network to simultaneously optimize the network parameters of the three-dimensional displacement field distribution function and the bridge stiffness field distribution function.

5. The bridge three-dimensional stiffness inversion and global state perception method according to claim 1, characterized in that, The composite loss function also includes a physical loss term based on the physical control equation. The physical loss term is obtained by substituting the predicted values ​​of the three-dimensional displacement field distribution function and the bridge stiffness field distribution function into the static equilibrium control equation and calculating the equation residuals.

6. The method according to claim 5, characterized in that, The static equilibrium governing equations are three-dimensional Navier-Lamé equations, and their expression is as follows: in, It is a displacement vector. and To be related to the elastic modulus field Lamé constant related to Poisson's ratio Given the volume forces, For gradient operators, For the Laplace operator.

7. The method according to claim 5, characterized in that, The physical loss term is passed through the three-dimensional domain of the bridge. Internally collected configuration point set The sum of squares of the residuals from the above equations is obtained, which satisfies: in, Represents the physical loss term. Indicates the number of configuration points. Indicates the first The residual of the point in the x-direction, Indicates the first The residual of the point in the y-direction, Indicates the first The residual of the point in the z-direction.

8. The bridge three-dimensional stiffness inversion and global state perception method according to claim 1, characterized in that, The composite loss function further includes a boundary condition loss term, which includes at least one of geometric boundary condition loss and force boundary condition loss.

9. The bridge three-dimensional stiffness inversion and global state perception method according to claim 1, characterized in that, Following the extraction and solidification of the bridge stiffness field distribution function in the multi-branch physical information neural network after training, the method further includes: Based on the sensitivity analysis of the pre-trained multi-branch physical information neural network to the spatial displacement field, the optimal location for deploying displacement sensors on the actual bridge is determined.

10. A bridge three-dimensional stiffness inversion and global state perception system, characterized in that, The bridge three-dimensional stiffness inversion and global state perception system includes: an input device, an output device, a processor, and a memory. The input device, output device, processor, and memory are interconnected. The memory stores program instructions, which are used to execute the bridge three-dimensional stiffness inversion and global state perception method according to any one of claims 1-9.

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