Bridge digital twin field generation method and device

Abstract

The present disclosure provides a bridge digital twin field generation method and device, the method comprising: acquiring real-time monitoring data collected by at least one sensor deployed on a bridge; loading a pre-trained target neural network model, and based on the real-time monitoring data, performing online parameter adjustment on the target neural network; wherein the target neural network model has a hard constraint output structure constructed based on a spatial symbolic distance function, and the output result of the target neural network model satisfies the geometric boundary condition of the bridge; through forward propagation calculation of the target neural network model after parameter adjustment, outputting the continuous displacement field and stress field of the bridge to obtain the digital twin field of the bridge. The present disclosure overcomes the defects of traditional finite element transient solution that is time-consuming and difficult to meet high-frequency synchronization requirements, and conventional data-driven models that easily violate physical boundary conditions, effectively eliminating numerical penetration and physical distortion at the boundary.

Description

Technical Field

[0001] This specification relates to the field of civil engineering technology, and in particular to a method and apparatus for generating digital twin fields of bridges. Background Technology

[0002] As vital transportation infrastructure, the construction of high-fidelity digital twins of bridges is crucial for safety assessments throughout their service life. Currently, schemes for representing the dynamic response of bridges mainly fall into two categories: one is based on traditional computational mechanics finite element method (FEM) modeling, which solves high-dimensional elastic dynamic partial differential equations through implicit or explicit integration to simulate the stress field distribution of the structure under complex working conditions in a mechanism-driven manner. The other is based on purely data-driven deep learning proxy models, which directly establish an end-to-end mapping relationship between sensor monitoring data and structural response using architectures such as convolutional neural networks (CNN) and recurrent neural networks (RNN), attempting to bypass the cumbersome process of solving physical equations.

[0003] However, the above-mentioned solutions have significant drawbacks in terms of real-time performance and accuracy. First, the FEM-based mechanistic model has extremely high degrees of freedom, and the transient dynamics solution is time-consuming, making it difficult to meet the millisecond-level real-time synchronization requirements of high-frequency sensing data, resulting in a lag in the twin's state. Second, the purely data-driven model lacks physical interpretability, is susceptible to environmental noise interference, and often violates the law of conservation of energy when encountering unseen loads, producing physical illusions. In addition, the sparse deployment of field sensors and the presence of noise make traditional filtering algorithms prone to divergence when estimating the state in high-dimensional space, failing to accurately invert the continuous displacement and stress field of the entire bridge using local noisy data. The scheme for generating a digital twin of the bridge needs improvement. Summary of the Invention

[0004] In view of this, this specification provides a method and apparatus for generating digital twin fields of bridges.

[0005] According to a first aspect of the embodiments of this specification, a method for generating a bridge digital twin field is provided, the method comprising: Acquire real-time monitoring data from at least one sensor deployed on the bridge; A pre-trained target neural network model is loaded, and the parameters of the target neural network are adjusted online based on the real-time monitoring data; wherein, the target neural network model has a hard-constrained output structure constructed based on the spatial symbolic distance function, and the output of the target neural network model satisfies the bridge geometric boundary conditions; The continuous displacement field and stress field of the bridge are calculated by forward propagation of the target neural network model with adjusted parameters, so as to obtain the digital twin field of the bridge.

[0006] According to a second aspect of the embodiments of this specification, a bridge digital twin field generation apparatus is provided, the apparatus comprising: The acquisition module is used to acquire real-time monitoring data collected by at least one sensor deployed on the bridge; An adjustment module is used to load a pre-trained target neural network model and adjust the parameters of the neural network online based on the real-time monitoring data; wherein, the target neural network model has a hard-constrained output structure constructed based on the spatial symbolic distance function, and the output of the target neural network model satisfies the bridge geometric boundary conditions; The generation module is used to calculate the continuous displacement field and stress field of the bridge through forward propagation calculation of the target neural network model with adjusted parameters, so as to obtain the digital twin field of the bridge.

[0007] According to a third aspect of the embodiments of this specification, a bridge digital twin field generation apparatus is provided, the apparatus comprising: one or more processors; wherein the processors are configured to perform the steps of the method as described in any of the first aspects.

[0008] According to a fourth aspect of the embodiments of this specification, a computer-readable storage medium is provided that stores computer instructions thereon, which, when executed by a processor, implement the steps of the method as described in any of the first aspects.

[0009] According to a fifth aspect of the embodiments of this specification, a computer program product is provided, including a computer program / instructions that, when executed by a processor, implement the steps of the method as described in any of the first aspects.

[0010] The technical solutions provided in the embodiments of this specification may include the following beneficial effects: In this embodiment, by acquiring real-time bridge monitoring data and loading a pre-trained target neural network model, online parameter adjustment is performed using a hard-constraint output structure constructed based on the spatial symbolic distance function. This overcomes the shortcomings of traditional finite element transient solutions, which are time-consuming and unable to meet high-frequency synchronization requirements, and conventional data-driven models, which are prone to violating physical boundary conditions. The model output is mathematically forced to satisfy the geometric support boundary constraints of the bridge, effectively eliminating numerical penetration and physical distortion at the boundaries. Based on this, the parameter-adjusted model performs fast forward propagation calculations, directly generating a globally continuous displacement and stress field without repeatedly solving high-dimensional partial differential equations. This achieves real-time mapping of locally sparse measured data into a high-fidelity global physical response with extremely low computational cost, significantly improving the timeliness of state synchronization, the accuracy of global field reconstruction, and physical compliance of the bridge digital twin.

[0011] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this specification. Attached Figure Description

[0012] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this specification and, together with the description, serve to explain the principles of this specification.

[0013] Figure 1 This is a flowchart illustrating a method for generating a digital twin field of a bridge, provided in an exemplary embodiment.

[0014] Figure 2 This is a flowchart illustrating another method for generating a bridge digital twin field, provided in an exemplary embodiment.

[0015] Figure 3 This is a schematic diagram of the training process of a target neural network model provided in an exemplary embodiment.

[0016] Figure 4 This is a schematic diagram of the architecture of a target neural network model provided in an exemplary embodiment.

[0017] Figure 5 This is a schematic diagram of a closed-loop process for applying a target neural network model, provided in an exemplary embodiment.

[0018] Figure 6 This is a schematic diagram of the structure of a bridge digital twin field generation device provided in an exemplary embodiment.

[0019] Figure 7 This is a schematic diagram of the structure of a bridge digital twin field generation system provided in an exemplary embodiment. Detailed Implementation

[0020] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this specification. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this specification as detailed in the appended claims.

[0021] The terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to be limiting of this specification. The singular forms “a,” “the,” and “the” as used in this specification and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any and all possible combinations of one or more of the associated listed items.

[0022] It should be understood that although the terms first, second, third, etc., may be used in this specification to describe various information, this information should not be limited to these terms. These terms are only used to distinguish information of the same type from one another. For example, without departing from the scope of this specification, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the word "if" as used herein may be interpreted as "when," "when," or "in response to determination."

[0023] The foregoing has described specific embodiments of this specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired result. In some embodiments, multitasking and parallel processing are possible or may be advantageous.

[0024] Among related technologies, the main schemes for bridge digital twins and global physical field reconstruction include: Option 1, based on traditional computational mechanics finite element (FEM) high-dimensional modeling: Relying on engineers to build a high-fidelity three-dimensional structural model, and solving the high-dimensional elastic dynamic partial differential equation (PDE) system through implicit or explicit integration, to characterize the dynamic response and stress field distribution of the bridge under complex working conditions in a mechanism-driven manner.

[0025] Option 2, based on a purely data-driven deep learning proxy model: With the development of artificial intelligence, deep learning architectures such as CNN, RNN, and self-attention feature extraction (Transformer) have been introduced into the field of health monitoring. This approach attempts to completely bypass the cumbersome solution of physical equations, directly relying on data collected by discrete sensors on-site, and establishing an end-to-end mapping relationship between monitoring state and structural response through training with massive amounts of data.

[0026] Option 3, Dynamic State Inversion Estimation Based on Traditional Filtering Algorithms: When faced with the problem of sparse field sensor deployment, a reduced-order mechanical mechanism model and traditional state estimation algorithms such as extended Kalman filtering are usually combined to perform online assimilation and parameter inversion of the full-bridge mechanical state using local noisy monitoring data.

[0027] As bridge digital twin technology advances towards real-time and precision, the above-mentioned solutions exhibit the following significant drawbacks: The computational bottleneck and lag of the mechanistic model based on the finite element method (FEM): The three-dimensional finite element model of a complex bridge contains millions of degrees of freedom. The implicit or explicit integral solution of transient dynamics is extremely time-consuming. It is impossible to achieve millisecond-level real-time synchronization and assimilation with the high-frequency (e.g., 100 Hz) sensing data of the real bridge, resulting in the twin model being in a state of lag for a long time.

[0028] The black-box nature and physical contradictions of purely data-driven artificial intelligence (AI): Existing deep learning models rely solely on limited discrete sensor data to fit surface relationships, ignoring the internal mechanical constitutive relationships of the structure. When encountering extreme conditions or out-of-distribution (OoD) loads, predictions often violate the laws of mass or energy conservation, creating dangerous physical illusions.

[0029] High-frequency noise contamination of state inversion under sparse observations: The number of sensors deployed on the bridge site is far lower than the spatial degrees of freedom (extremely sparse), and is accompanied by complex environmental noise. Traditional methods (such as extended Kalman filters) are prone to divergence when estimating state in high-dimensional space, and cannot accurately invert the continuous stress / strain field of the entire bridge using sparse and noisy local monitoring data.

[0030] To address the dimensionality curse and real-time issues in solving partial differential equations, resolve boundary condition penetration and physical uncontrollability problems, and achieve joint assimilation of sparse data and mechanistic equations, this disclosure provides the following method and apparatus for generating digital twin fields of bridges.

[0031] Figure 1 This is a schematic flowchart illustrating a method for generating a digital twin field of a bridge, provided in an exemplary embodiment. For example... Figure 1As shown, this method can be performed by a system for generating digital twins, and the method may include the following steps: Step S101: Obtain real-time monitoring data collected by at least one sensor deployed on the bridge.

[0032] In this embodiment of the disclosure, at least one sensor may be deployed at the location of a critical load-bearing component of the bridge, such as the mid-span of the main beam, the base of the bridge tower, the support node, and the anchorage area of ​​the hanger.

[0033] At least one of the sensors may be, for example, but not limited to, a fiber optic strain sensor, a piezoelectric accelerometer, a Global Navigation Satellite System (GNSS) displacement sensor, a laser deflection sensor, or a microelectromechanical tilt sensor, etc., and this disclosure does not limit it.

[0034] In this embodiment of the disclosure, the sensor described above can collect data and provide real-time monitoring data to the system.

[0035] The real-time monitoring data refers to the structural dynamic response observations collected by the aforementioned sensor array over a continuous time axis. Due to limitations in engineering deployment costs and installation feasibility, this real-time monitoring data exhibits typical sparsity in spatial distribution and high-frequency sampling characteristics in the temporal dimension. Furthermore, the raw signals are often superimposed with environmental wind vibration noise, temperature drift, or transmission packet loss. In practice, the bridge-side data acquisition gateway captures the raw electrical signals from each measuring point at a preset sampling frequency (e.g., 10Hz to 2000Hz). After analog-to-digital conversion, anti-aliasing filtering, and baseline correction, the standardized data stream is uploaded to the system via industrial Ethernet or a low-latency wireless protocol.

[0036] The system performs sliding window truncation and outlier interpolation on the received data stream to construct a real-time monitoring tensor containing the spatial coordinates of the measurement points, timestamps, and measured physical quantities. This tensor serves as the real physical anchor point for subsequent model assimilation, and its high-frequency sparsity directly determines whether the digital twin field can achieve millisecond-level responses to transient loads or local damage evolution in the structure. This step provides a high-fidelity, low-latency data source input for subsequent physical field reconstruction through standardized hardware interfaces and an edge preprocessing pipeline.

[0037] Step S102: Load the pre-trained target neural network model and adjust the parameters of the target neural network online based on the real-time monitoring data.

[0038] The target neural network model has a hard-constrained output structure based on the spatial symbolic distance function, and the output of the target neural network model satisfies the geometric boundary conditions of the bridge.

[0039] In this embodiment of the disclosure, the target neural network model refers to a physical information neural network (PINN) with fixed weights after offline pre-training based on massive historical working conditions or high-fidelity numerical simulation data.

[0040] The Signed Distance Function (SDF) is an implicit geometric representation tool used to quantify the shortest directed distance from any point in 3D space to the geometric surface of a bridge entity. Its mathematical properties include strictly zero values ​​at the bridge's geometric support boundaries (such as fixed ends, hinge points, or free surfaces), positive values ​​inside the structural entity, and negative values ​​outside. Its gradient direction is naturally perpendicular to the boundary surface. The system can extract the SDF distance field based on the 3D solid model of the bridge, denoted as... The field is at the physical support boundary. Strictly meet Satisfy within the structural domain .

[0041] The hard-constraint output structure refers to a network topology simulation layer that forcibly couples the original output of the target neural network with the boundary conditions through analytical mathematical construction. Unlike traditional soft constraints that rely on weighted penalties based on loss functions, this structure cuts off the possibility of boundary violations from the underlying computational graph, ensuring that the model absolutely obeys the physical support boundary under any input conditions, and completely eliminating boundary penetration, support reaction force distortion, and numerical oscillations.

[0042] Online parameter adjustment refers to the process of using a very small amount of real-time sparse observation data during the inference phase to fine-tune the weights of the pre-trained model in a few steps through a fast curvature optimization algorithm, thereby achieving the instantaneous diffusion of local measured information to the global physical field.

[0043] In practice, this step can deeply integrate architectural constraints and dynamic assimilation mechanisms. At the architectural mapping level, the target neural network is not a direct stacking of standard multilayer perceptrons; its output is cascaded with a nonlinear topology simulation layer based on SDF.

[0044] At the dynamic assimilation level, after the system loads the pre-trained base, it parses the real-time monitoring data from step S101 into local assimilation constraint boundaries. Then, it calls a curvature search optimizer, preferably an L-BFGS or quasi-Newton method, to perform online iterative adjustments to the model weight parameters. Since the residuals of the three-dimensional elastic dynamics partial differential equations are hard-coded within the model, this optimization is not simply data curve fitting. Instead, it utilizes the curvature information provided by the second-order Hessian matrix approximation to quickly anchor local sparse measurement point observations and simultaneously correct weights within a very small number of iterations, typically 10-50 steps. The embedded PDE physical conservation law acts as a strong regularization term in this process, automatically spreading the local correction effect along the stress wave propagation path to the global region without sensors, effectively filtering out high-frequency environmental noise and suppressing overfitting.

[0045] This step enables the model to achieve real-time synchronization of dynamic conditions such as sudden traffic loads, material degradation, or extreme temperature changes with extremely low computing power while maintaining the global physical evolution laws, completely breaking through the time bottleneck of traditional finite element restart solutions.

[0046] The training process of the target neural network model will be described in subsequent embodiments and will not be described here.

[0047] Step S103: Through forward propagation calculation of the target neural network model with adjusted parameters, the continuous displacement field and stress field of the bridge are output to obtain the digital twin field of the bridge.

[0048] In this embodiment, forward propagation computation refers to inputting the dense spatiotemporal grid coordinates to be queried into the target neural network model that has undergone online parameter adjustment, either in one go or in a streaming manner. It then relies on the automatic computation graph of the deep learning framework to perform a single tensor multiplication and nonlinear activation transfer. This process completely eliminates the expensive iterative operations of traditional numerical methods, such as stiffness matrix assembly, lower-upper triangular decomposition inversion, or explicit / implicit time-step integration.

[0049] Among them, the continuous displacement field and stress field refer to the tensors of structural deformation state and internal force distribution output with arbitrary spatial resolution (such as millimeter-level voxel grid or continuous analytical function) within the entire spatiotemporal range of the bridge. In essence, they are gapless digital mappings of the real physical service state.

[0050] The digital twin field is a multi-dimensional dynamic data cube that integrates geometric topology, real-time physical response, material constitutive model and historical evolution trajectory, which can directly drive three-dimensional visualization rendering, fatigue life prediction or structural safety early warning.

[0051] In practice, the compute nodes generate a target query coordinate set covering the entire region of interest (ROI) of the bridge. The data is then batch-injected into the target neural network model that has undergone fine-tuning in step S102. The target neural network model directly outputs a continuous displacement field after a single forward propagation. To synchronously reconstruct the stress field, the system can invoke the built-in Auto-Differentiation engine in the computation graph to perform spatial first-order partial derivative operations on the output displacement field, directly obtaining the geometric strain tensor ε. Subsequently, it substitutes this tensor with the constitutive relation of the generalized Hooke's law for instantaneous mapping to obtain the full-field stress tensor. .

[0052] Ultimately, the system reconstructs the physical quantities of discrete query points into a continuous high-dimensional spatiotemporal tensor flow, which is then pushed to the twin visualization engine or health assessment module. This process leverages the generalization properties of neural networks—one-time inference and global mapping—to achieve instantaneous reconstruction from sparse measured anchor points to a high-fidelity continuous physical field within millisecond latency, thus fully constructing a bridge digital twin field with self-synchronization and self-evolution capabilities.

[0053] In the above embodiments, by acquiring real-time monitoring data of the bridge and loading a pre-trained target neural network model, online parameter adjustment is performed using a hard-constraint output structure constructed based on the spatial symbolic distance function. This overcomes the shortcomings of traditional finite element transient solutions, which are time-consuming and unable to meet high-frequency synchronization requirements, and conventional data-driven models, which are prone to violating physical boundary conditions. The model output is mathematically forced to satisfy the geometric support boundary constraints of the bridge, effectively eliminating numerical penetration and physical distortion at the boundaries. Based on this, the model with adjusted parameters performs fast forward propagation calculations, directly generating a globally continuous displacement and stress field without repeatedly solving high-dimensional partial differential equations. This achieves real-time mapping of locally sparse measured data into a high-fidelity global physical response with extremely low computational cost, significantly improving the timeliness of state synchronization, the accuracy of global field reconstruction, and physical compliance of the bridge digital twin.

[0054] Figure 2 This is a flowchart illustrating another method for generating a bridge digital twin field, provided in an exemplary embodiment. For example... Figure 2 As shown in Figure 1, this method mainly introduces the training process of the target neural network model, which may include the following steps: Step S201: Construct the joint loss functional of the initial neural network model.

[0055] In this embodiment of the disclosure, the joint loss functional At least by the first loss function Second loss function constitute.

[0056] Among them, the joint loss functional It refers to a multi-objective optimization scalar field that integrates data-driven assimilation objectives with physical law constraints, used to guide neural networks in finding the optimal weight configuration in the parameter space that simultaneously satisfies measured observations and the law of conservation of mechanics.

[0057] Wherein, the first loss function This is used to characterize the data assimilation loss between the real-time measurement data acquired by the sensor and the predicted values ​​of the initial neural network model. First loss function It can measure the deviation between the predicted output and the actual measurement at a known sensor location, and is used to anchor the model's local data fitting ability.

[0058] Wherein, the second loss function This is used to characterize the physical residual loss of self-supervised partial differential equations (PDEs). Second loss function. It can measure the degree to which the output field of the model satisfies the partial differential equations of three-dimensional elastic dynamics in a continuous spatiotemporal domain, and is used to ensure the physical interpretability and generalization extrapolation ability of the model.

[0059] Among them, the hard constraint output structure refers to the analytical mapping layer embedded at the end of the model, which forces the network output to automatically meet the support conditions at the geometric boundary through the spatial symbolic distance function, thereby eliminating the boundary penetration error from the topology level.

[0060] Automatic differentiation is a core computational technique in deep learning frameworks, used to accurately and efficiently solve for higher-order derivatives of the displacement field with respect to spatial coordinates and time in the computation graph, avoiding the truncation error and grid dependence of traditional finite difference methods.

[0061] In terms of specific implementation, firstly, it can perform high-dimensional implicit representation and automatic differential derivation of the partial differential equations (PDEs) of the elastic dynamics of complex spatial structures of bridges, thereby constructing a mechanical law constraint space with complete physical knowledge reserves for deep neural networks.

[0062] In this embodiment, the bridge as a whole can be considered as a three-dimensional continuous medium, whose spatiotemporal evolution is strictly governed by the Navier-Cauchy elastic dynamics equations. For the bridge spatial domain... and time domain Set the boundary conditions as follows (Corresponding to the Dirichlet boundary with known displacement and the Neumann boundary with known surface force, respectively).

[0063] Global displacement field of a structure under external dynamic loads (such as wind and traffic flow) The following set of three-dimensional elastic dynamics partial differential equations with damped dissipation terms can satisfy Equation 1: Formula 1 in, For the spatial density distribution of structural materials, For external volume force field, For the generalized Rayleigh damping operator. Stress tensor. With strain tensor The mapping between them is determined by the generalized Hooke's law (isotropic linear elastic constitutive model), as shown in Equations 2 and 3, respectively: Formula 2 in, and The spatially dependent Lamé constant, It is a second-order unit tensor. The system uses a multilayer perceptron (MLP) as the target neural network model. Replaces traditional finite element method nodal shape function interpolation. Total strain tensor Instead of discrete differentiation, it utilizes the Automatic Differentiation (AD) technique of deep learning frameworks to accurately obtain the derivative in the computational graph: Formula 3 To avoid gradient explosion and non-convex optimization failure caused by inconsistencies in the dimensions of multiple physical quantities during the training process of neural networks, the system first performs automatic minimax normalization and affine dimensionless transformation on the spatiotemporal coordinates and state variables in the above PDE group to extract the dimensionless feature tensors of high-dimensional state quantities.

[0064] Furthermore, the system can deeply embed the governing equations and boundary conditions into the aforementioned multilayer perceptron architecture based on absolute hard-constrained topological mapping and joint functional optimization using the spatial symbolic distance function (SDF), thereby generating a twin model that fully complies with physical laws.

[0065] Traditional PINN loss functions treat boundary conditions as soft penalties, which can easily lead to physically unacceptable non-zero displacement seepage at the fixed or simply supported ends of the bridge. To overcome this limitation, this method constructs a hard-constrained nonlinear physical simulation (Ansatz) using the spatial symbolic distance function (SDF). The system extracts the SDF distance field based on the 3D solid model of the bridge, denoted as... The field is at the physical support boundary. Strictly meet Satisfy within the structural domain .

[0066] Let the basic deep multilayer perceptron be The inputs include, but are not limited to, physical properties, boundary constraints, loads, etc. In this embodiment of the disclosure, the final predicted output of the physical displacement field is... Perform topology construction, as shown in Equation 4: Formula 4 In the formula, To satisfy the analytic basis functions of the known Dirichlet boundary, This is a scaling factor to control the decay rate. This construction analytically guarantees that the exponential term tends to [value] as the coordinates approach the boundary. The prediction degrees of freedom of the MLP network are forcibly reset to zero, and the output of the system absolutely satisfies the physical boundary constraints.

[0067] Subsequently, the system collected a small amount of sensor observation data. This can also be referred to as real-time measurement data. The physical conservation residuals of the network prediction field are calculated using the aforementioned formula. For example, as shown in Formula 5: Formula 5 Joint loss functional for training PINN model From the first loss function Second loss function Combined structures, as shown in Formula 6: Formula 6 in and These are the first weight value and the second weight value, respectively. This refers to the number of collocation points.

[0068] Here, collocation points can refer to the set of spatiotemporal coordinates that are discretely sampled within the physical computation domain. These coordinates are used to directly substitute into the control equations during neural network training to calculate the physical residuals, thereby driving the model parameters to optimize in a direction that satisfies the physical conservation laws.

[0069] Step S202: Iteratively update the weight parameters of the initial neural network model according to the joint loss functional. When the joint loss functional decreases to a preset convergence threshold, stop training and output the target neural network model.

[0070] In this embodiment of the disclosure, iterative update refers to using gradient descent or curvature optimization algorithms to gradually adjust the network weights along the negative gradient direction or curvature minimum direction of the joint loss functional, so that the model evolves from a random initialization state to an equilibrium state that is physically compliant and highly fitted to the data.

[0071] Among them, the collocation set refers to the set of discrete coordinate points used for sampling and calculating physical residuals within the spatiotemporal computation domain of the bridge, and its distribution quality directly determines the global coverage of PDE constraints.

[0072] The candidate coordinate pool refers to a large-scale set of spare coordinates that are randomly generated in advance for adaptive resampling, used to dynamically discover high-error regions during training.

[0073] The resampling probability density function refers to a probability distribution model constructed based on the physical residual energy norm, which is used to guide newly added collocation points to concentrate in regions of drastic residual changes.

[0074] Among them, the sharpening index is an amplification control parameter in the probability distribution, which is used to exponentially widen the sampling weight difference between the high residual region and the low residual region, thereby enhancing the ability to capture local abrupt changes (such as stress concentration and crack initiation).

[0075] The convergence threshold is a preset critical value for the joint loss functional to stop decreasing, used to determine whether the model has reached the optimal fit between the physical laws and the observed data.

[0076] In practice, the system first determines the set of collocation points corresponding to the current iteration cycle. If it is the first training cycle, a specified number of coordinates are randomly and uniformly sampled from the candidate collocation point pool generated based on the bridge's spatiotemporal domain as the initial set of collocation points. If it is not the first iteration cycle, new collocation points corresponding to the current iteration cycle are determined and merged into the set of collocation points corresponding to the previous iteration cycle to obtain the set of collocation points corresponding to the current iteration cycle.

[0077] Specifically, in non-first iteration cycles, the system triggers a residual-based adaptive refinement (RAR) mechanism: In each training iteration cycle The system first randomly generates a large pool of candidate points across the entire spatiotemporal domain of the bridge. And calculate the posterior physical error index at each point, namely the energy norm residual. Subsequently, a probability density function based on residual intensity is constructed. For example, as shown in Formula 7: Formula 7 in To amplify the sharpening index in the extreme value region, a new round of collocation distribution is determined based on this probability distribution, and the newly added collocation points are... The training set is dynamically updated by focusing on residual extreme value regions (i.e., potential microcracks or stress concentration areas). .in, This is the set of collocation points corresponding to the previous iteration cycle. This is the set of collocation points corresponding to the current iteration cycle.

[0078] In this embodiment, when a very small amount of high-frequency fiber strain or acceleration measurement data is continuously received at the bridge site, the pre-trained PINN base, using second-order optimizers such as L-BFGS, only needs to perform a very small number of gradient fine-tuning steps to diffuse the local scattered data to the global scale through the internalized physical laws of partial differential equations, directly outputting a continuous digital twin field of the entire bridge. .

[0079] In the above embodiments, the finite element mesh dependency can be eliminated, achieving millisecond-level real-time twinning. Utilizing the meshless and automatic differentiation characteristics of PINN, complex solid mesh generation and large matrix inversion are avoided. Once the model is trained, physical quantity queries at any point in space and time are calculated via forward propagation, improving efficiency by hundreds or thousands of times compared to traditional mechanics software. Eliminating the physical illusions of traditional AI algorithms, the SDF hard constraint mechanism and PDE loss-forced surrogate model output strictly adhere to first principles such as mass and momentum conservation. The digital twin model possesses transparent engineering mechanics interpretability and can be directly and safely used for bridge fatigue life prediction and ultimate bearing capacity assessment. Global physical field derivation under sparse sensing data, using physical equations as strong regularization conditions, can still resist high-frequency environmental noise and accurately deduce the continuous physical field in areas without sensor deployment, even under extremely sparse sensing constraints.

[0080] In this embodiment of the disclosure, a training process for a target neural network model is also provided, such as... Figure 3 As shown. This process is driven by multi-source heterogeneous measurement point data and spatiotemporal coordinates. Through closed-loop iteration of two core modules—PINN network and topology hard constraint engine, and differential differentiation and adaptive resampling (Physics & RAR)—it ultimately outputs a high-fidelity twin base that satisfies physical boundary conditions and has convergent residuals. The specific execution process is as follows: First, the system receives input spatiotemporal coordinates and multi-source heterogeneous measurement data (such as sparse displacement observations, strain gauge readings, or acceleration time history data), which are then fed into the PINN network and topological hard constraint module. To eliminate optimization non-convexity caused by dimensional differences and numerical spans among multiple physical quantities, the system performs spatiotemporal normalization and affine transformation on the spatiotemporal coordinates and corresponding physical state variables, mapping them to a unified dimensionless feature space, thus providing a numerically stable computational basis for subsequent network training.

[0081] The normalized feature tensor is fed into a multilayer perceptron (MLP) for nonlinear feature mapping and function approximation. To overcome the shortcomings of traditional PINN loss function-dependent weighted penalties (soft constraints) which easily lead to boundary penetration and numerical oscillations, the system simultaneously extracts the spatial symbolic distance field (SDF) of the bridge's three-dimensional geometric model and constructs an analytical boundary distance function. Subsequently, a nonlinear topology fitting (Ansatz) layer is used to deterministically algebraically couple the original unconstrained output of the MLP, the analytical basis functions satisfying the Dirichlet conditions, and the SDF field, forcing the network's final output... The mathematical structure is strictly convergent to the physical support boundary, achieving hard locking of the boundary conditions.

[0082] After completing the hard constraint mapping, the process enters the differentiation and adaptive resampling module. The system calls the automatic differentiation (AD) technique built into the deep learning framework to perform displacement field calculations on the static computation graph. Accurate first- and second-order spatial / temporal partial derivative calculations are performed to directly map the full-field strain and stress tensors. Based on this, the stress tensor, material constitutive parameters, and external loads are substituted into the three-dimensional elastic dynamics governing equations to calculate the physical residuals of the partial differential equations (PDEs). Simultaneously, the measured data at the sensor deployment coordinates are compared with the model predictions to calculate the data assimilation error. After weighted fusion using preset weighting coefficients, a joint loss functional is constructed.

[0083] The system continuously evaluates whether the current joint loss is below a preset convergence threshold. If the convergence condition is not met (determined as no), an adaptive collocation resampling (RAR) strategy based on PDE residuals is triggered: the system traverses the current computational domain, calculates the physical residual energy norm at each candidate point, constructs a resampling probability density function accordingly, and introduces a sharpening exponent to exponentially amplify the sampling weights of high residual regions (such as stress concentration areas, geometric abrupt angles, or crack initiation zones). The system dynamically extracts new collocations based on this probability distribution, feeds them back to the network input, and merges them with the original training set. The model continues to perform forward propagation and gradient backward updates based on the updated collocation distribution, forming an adaptive iterative closed loop of residual evaluation-dynamic encryption-weight correction.

[0084] When the joint loss steadily decreases after multiple iterations and reaches the convergence threshold (determined as yes), the system terminates the training process, indicating that the PINN model training is complete. At this point, the output target neural network model has deeply integrated local measured data anchoring with global physical conservation laws, possessing strong physical extrapolation robustness and millisecond-level forward inference capabilities. It can be directly loaded into the online fine-tuning module for real-time generation of bridge digital twin fields, global field reconstruction, and dynamic inference of structural health status.

[0085] In this disclosure embodiment, a model architecture diagram is also provided, for example... Figure 4 As shown, the architecture is divided into five functional layers from top to bottom, realizing a closed-loop process from spatiotemporal parameter input to physical compliance field output and multi-objective joint optimization. A detailed description follows: 1. Multidimensional time-varying excitation and spatiotemporal parameterization layer: As the input end of the network, the system receives spatial coordinate input (x, y, z) and time dimension input t, and places the bridge structure in a continuous four-dimensional spatiotemporal domain for parameterized modeling, providing independent variable benchmarks for subsequent reconstruction of the physical field.

[0086] 2. Neural Network Proxy Layer: Spatiotemporal parameterized data is fed into the Multilayer Perceptron (MLP) module. This layer acts as a high-dimensional nonlinear function approximator, utilizing the representational capabilities of deep networks to perform preliminary fitting of the complex spatial gradient and temporal evolution characteristics of the displacement field, outputting the original displacement characteristics without physical constraints.

[0087] 3. Topological Hard Constraint Mapping Layer (SDF): This layer aims to solve the boundary condition satisfaction problem. The system first extracts the global distance field from the geometric model through Rvachev Boolean operations. (i.e., the spatial symbolic distance field SDF), quantifying the directed distance between a spatial point and its geometric boundary. Subsequently, using the Ansatz technique (nonlinear topological fitting), the... The analytical basis functions satisfying the Dirichlet boundary conditions are deterministically algebraically coupled with the original output of the MLP. This operation forces the network's final output to automatically converge to the true boundary conditions at the geometric boundaries, thereby outputting a physically compliant displacement field and fundamentally eliminating boundary penetration errors.

[0088] 4. Partial Differential Equation Physical Solution Layer (AD&PDE): Based on the physically compliant displacement field, the system uses automatic differentiation (AD) technology to accurately solve the first-order partial derivatives in the computational graph to obtain the strain tensor ε. Then, the strain is mapped to the stress tensor σ through the generalized Hooke's law. Finally, the displacement, stress, material constitutive parameters and external loads are substituted into the three-dimensional elastic dynamics control equations to calculate the equation residuals in order to evaluate the degree of deviation of the model output from the mechanical conservation laws.

[0089] 5. Multi-objective functional joint optimization layer: This layer constructs the optimization objective function of the model. The system generates the joint loss functional. For example, as shown in Formula 6, by jointly adjusting the first and second weight values, the model simultaneously optimizes the data fitting accuracy and physical law constraints during training, thereby achieving high-fidelity digital twin field reconstruction.

[0090] In this embodiment of the disclosure, a closed-loop flowchart for model application deduction is also provided, for example... Figure 5 As shown. This process is driven by real-time sparse monitoring data, relies on a pre-trained Physical Information Neural Network (PINN) foundation, and achieves high-fidelity reconstruction of all physical quantities across the field through rapid online fine-tuning, further completing structural safety status assessment and dynamic evolution. The specific execution logic is as follows: First, the system initiates a full-time and spatiotemporal digital twin simulation, acquiring sparse sensor data streams in real time. This data stream originates from sensor arrays deployed at key stress-bearing locations on the bridge (such as the mid-span of the main girder, the base of the towers, and the anchorage zone of the hangers), typically containing high-frequency sampled displacement, strain, or acceleration time-series signals. Although the data exhibits sparse spatial distribution, it provides realistic local physical observation anchor points for the digital twin model.

[0091] Subsequently, the process enters the rapid online fine-tuning and full-field mapping stage (L-BFGS Engine). The system first loads the pre-trained PINN base model, which, during offline training, has fully internalized the bridge's three-dimensional geometric topology, spatial symbolic distance field (SDF) hard constraint boundary conditions, and material physical stiffness mapping laws through a joint loss functional. Based on the real-time input sparse measurement point data, the system calls the L-BFGS (Limited-memory Broyden-Fletcher-Goldfarb-Shanno) second-order optimizer for a few-step fine-tuning. Leveraging the second-order optimizer's sensitivity to the curvature information of the loss function and its superlinear convergence characteristics, the model requires only a very small number of iterations to accurately anchor to the local measured data and synchronously correct the network weight parameters. By using the elastic dynamic partial differential equation (PDE) embedded in the model as a strong physical regularization constraint, the corrected local observation information can be rapidly diffused along the stress wave propagation path to the global region where no sensors are deployed, directly diffused and output the full-bridge continuous field, and instantly reconstructed the high-resolution transient displacement field and high-fidelity stress field, completely overcoming the computational bottleneck of traditional numerical methods in transient dynamic analysis that requires repeated assembly of stiffness matrices and time steps.

[0092] After the full-field physical field reconstruction is completed, the system enters the engineering state assessment and dynamic evolution stage (DigitalTwin). The system automatically extracts the response characteristics of key sections and calculates the Von Mises equivalent stress in real time based on the output full-field stress tensor to comprehensively assess the material yield risk under complex multiaxial stress states. The system compares the calculated local equivalent stress with the preset material yield limit in real time: if the judgment result is yes (i.e., local equivalent stress > yield limit), it indicates that the structure has entered the plastic deformation or microcrack initiation stage, and the system will immediately trigger a structural damage warning and dynamically update the remaining fatigue life state based on the current stress amplitude, cycle frequency, and material SN curve characteristics; if the judgment result is no, it indicates that the structure is in the elastic safe operating range, and the system maintains normal simulation cycle.

[0093] Ultimately, the system integrates and encapsulates the reconstructed full-field physical data, safety assessment conclusions, and life evolution status, outputting the bridge's digital generation results. This completes a closed-loop simulation from physical perception and full-field mapping to engineering early warning and life management, providing high-timeliness and high-precision digital foundation support for bridge maintenance decisions, intervention timing judgments, and long-term performance evaluations.

[0094] Figure 6 This is a schematic diagram of the structure of a bridge digital twin field generation device provided in an exemplary embodiment. (See diagram below.) Figure 6 As shown, it includes the following modules: The acquisition module 601 is used to acquire real-time monitoring data collected by at least one sensor deployed on the bridge; The adjustment module 602 is used to load a pre-trained target neural network model and adjust the parameters of the neural network online based on the real-time monitoring data; wherein, the target neural network model has a hard-constrained output structure constructed based on the spatial symbolic distance function, and the output result of the target neural network model satisfies the bridge geometric boundary conditions; The generation module 603 is used to calculate the continuous displacement field and stress field of the bridge through the forward propagation calculation of the target neural network model with adjusted parameters, so as to obtain the digital twin field of the bridge.

[0095] In some embodiments, this specification also provides a bridge digital twin field generation apparatus, which may include: one or more processors; wherein the processors are configured to perform the steps of the method as described in any of the preceding embodiments.

[0096] Figure 7 This is a schematic structural diagram of a bridge digital twin field generation system provided in an exemplary embodiment. Please refer to... Figure 7 At the hardware level, the system includes a processor 702, an internal bus 704, a network interface 706, memory 708, and non-volatile memory 710, and may also include other hardware required for its functions. One or more embodiments of this specification can be implemented in software, whereby the processor 702 reads the corresponding computer program from the non-volatile memory 710 into the memory 708 and then runs it. Of course, in addition to software implementation, one or more embodiments of this specification do not exclude other implementation methods, such as logic devices or a combination of hardware and software, etc. That is to say, the execution subject of the following processing flow is not limited to each logic unit, but can also be hardware or logic devices.

[0097] Based on the same concept as the methods described above, this specification also provides a computer-readable storage medium having computer instructions stored thereon that, when executed by a processor, implement the steps of the methods as described in any of the above embodiments.

[0098] Based on the same concept as the methods described above, this specification also provides a computer program product, including a computer program / instructions that, when executed by a processor, implement the steps of the methods as described in any of the above embodiments.

[0099] In addition, this disclosure also provides a system that can perform the steps of the methods described in any of the above embodiments.

[0100] Other embodiments of this specification will readily occur to those skilled in the art upon consideration of the specification and practice of the invention claimed herein. This specification is intended to cover any variations, uses, or adaptations that follow the general principles of this specification and include common knowledge or customary techniques in the art not claimed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this specification are indicated by the following claims.

[0101] It should be understood that this specification is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this specification is limited only by the appended claims.

[0102] The above description is merely a preferred embodiment of this specification and is not intended to limit this specification. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this specification should be included within the scope of protection of this specification.

Claims

1. A method for generating a digital twin field of a bridge, characterized in that, The method includes: Acquire real-time monitoring data from at least one sensor deployed on the bridge; A pre-trained target neural network model is loaded, and the parameters of the target neural network are adjusted online based on the real-time monitoring data; wherein, the target neural network model has a hard-constrained output structure constructed based on the spatial symbolic distance function, and the output of the target neural network model satisfies the bridge geometric boundary conditions; The continuous displacement field and stress field of the bridge are calculated by forward propagation of the target neural network model with adjusted parameters, so as to obtain the digital twin field of the bridge.

2. The method according to claim 1, characterized in that, The online parameter adjustment of the target neural network model based on the real-time monitoring data includes: The pre-trained target neural network model is used as the deduction base to initialize the physical stiffness mapping and topological constraint laws of the target neural network model; The local measurement point observations in the real-time monitoring data are used as assimilation constraints. The weight parameters of the target neural network model are iteratively adjusted using a curvature search optimizer, the local measurement point observations are anchored using a curvature search algorithm, and the model parameters of the target neural network model are synchronously corrected. Based on the corrected model parameters, the local observation constraints are diffused to the global spatiotemporal domain without sensors by using the embedded physical partial differential equations, thus completing the online parameter adjustment.

3. The method according to claim 1, characterized in that, The target neural network model is trained in the following manner: A joint loss functional is constructed for an initial neural network model, wherein the joint loss functional is composed of at least a first loss function and a second loss function. The first loss function is used to characterize the data assimilation loss between the real-time measurement data collected by the sensor and the predicted value of the initial neural network model. The second loss function is used to characterize the physical residual loss of the self-supervised partial differential equation (PDE). The self-supervised PDE physical residual loss is obtained by using the displacement field output by the initial neural network model, obtaining the strain and stress tensors through automatic differentiation, and substituting them into the elastic dynamics partial differential equation to calculate the residual norm. The weight parameters of the initial neural network model are iteratively updated according to the joint loss functional. When the joint loss functional decreases to a preset convergence threshold, training is stopped and the target neural network model is output.

4. The method according to claim 3, characterized in that, The method further includes: Acquire measured observation data collected by the sensor at the spatiotemporal coordinate point corresponding to its deployment location; Input the spatiotemporal coordinates into the initial neural network model to obtain the prediction data output by the initial neural network model; Calculate the error norm between the measured observation data and the model prediction data, and determine the first loss function based on the error norm and the first weight value.

5. The method according to claim 4, characterized in that, The method further includes: Extract the spatial symbolic distance field of the bridge geometric model, wherein the spatial symbolic distance field is used to characterize the distance from the spatial coordinates to the boundary of the bridge geometric support; Construct analytical basis functions that satisfy the aforementioned bridge geometric support boundary conditions; The original output of the initial neural network model, the analytical basis function, and the spatial symbolic distance field are combined through an exponential decay term to construct a nonlinear topological fit, thereby obtaining the predicted data that satisfies the boundary support conditions.

6. The method according to claim 3, characterized in that, The method further includes: The displacement field output by the initial neural network model is spatially and temporally differentiated using automatic differentiation techniques to obtain the strain tensor and acceleration terms. Based on the generalized Hooke's law, the stress tensor is calculated from the strain tensor. Substitute the stress tensor, structural material density distribution, damping operator, and external volume force into the three-dimensional elastic dynamics partial differential equation and calculate the residual values ​​on both sides of the equation. The energy norm of the residual value is calculated, and the second loss function is obtained based on the energy norm and the second weight value.

7. The method according to claim 3, characterized in that, The iterative update of the weight parameters of the initial neural network model according to the joint loss functional includes: Determine the set of collocation points corresponding to the current iteration cycle; Based on the set of collocations corresponding to the current iteration cycle, the joint loss functional is calculated, and the weight parameters of the initial neural network model are iteratively updated according to the calculated joint loss functional.

8. The method according to claim 7, characterized in that, Determining the set of collocation points corresponding to the current iteration cycle includes: Based on the spatiotemporal domain of the bridge, a pool of candidate points is randomly generated. If the current iteration cycle is the first iteration cycle, then at least one configuration is randomly selected from the candidate configuration pool to obtain the configuration set corresponding to the current iteration cycle; If the current iteration cycle is not the first iteration cycle, then the newly added collocation points corresponding to the current iteration cycle are determined, and the newly added collocation points are merged into the collocation point set corresponding to the previous iteration cycle to obtain the collocation point set corresponding to the current iteration cycle.

9. The method according to claim 8, characterized in that, The process of determining the new collocation points corresponding to the current iteration cycle includes: Calculate the energy norm of the physical residual of the partial differential equation at each candidate point in the candidate collocation pool; A resampling probability density function is constructed based on the physical residual energy norm to extract the new coordinate point from the candidate coordinate point pool. The probability density function is used to indicate the probability weight of each candidate coordinate point in the candidate coordinate point pool, and the probability weight is positively correlated with the physical residual energy norm.

10. A bridge digital twin field generation device, characterized in that, The device includes: The acquisition module is used to acquire real-time monitoring data collected by at least one sensor deployed on the bridge; An adjustment module is used to load a pre-trained target neural network model and adjust the parameters of the neural network online based on the real-time monitoring data; wherein, the target neural network model has a hard-constrained output structure constructed based on the spatial symbolic distance function, and the output of the target neural network model satisfies the bridge geometric boundary conditions; The generation module is used to calculate the continuous displacement field and stress field of the bridge through forward propagation calculation of the target neural network model with adjusted parameters, so as to obtain the digital twin field of the bridge.

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