A model training method and device, a bridge physical field determination method and device, equipment and a medium

Abstract

The application provides a model training method, a bridge physical field determination method, a device, equipment and a medium. According to an example of the application, the model training method can include: obtaining structure topology information of a bridge and sensing data collected by a sensor on the bridge; generating a feature vector for representing structure control information of the bridge based on the sensing data and the structure topology information; constructing a target evolution path from a random prior distribution to a target physical field distribution, and determining a conditional vector field corresponding to the target evolution path; training a prediction model by taking the feature vector as a conditional input and the conditional vector field as a supervision signal, so that the prediction model can learn an evolution rule from noise to a global bridge physical field under the constraint of the structure control information, and the global bridge physical field can be reconstructed with high fidelity from sparse local observation data through the prediction model.

Description

Technical Field

[0001] This application relates to the field of computer technology, and in particular to a method, apparatus, device and medium for model training and determination of bridge physics fields. Background Technology

[0002] During long-term service, bridges inevitably experience structural performance degradation due to environmental erosion, material aging, and other factors. Continuous and accurate condition assessment of bridge structures is crucial for ensuring traffic safety and structural integrity. Bridge structural health monitoring systems primarily rely on deploying discrete sensors at key cross-sections of the bridge to acquire local condition data.

[0003] However, due to limitations in economic costs and installation conditions, the number of sensors that can be deployed on bridges is relatively limited. They can usually only cover key sections or representative locations of the structure, making it difficult to reconstruct the physical field of the entire bridge from sparse local observation data. Summary of the Invention

[0004] To overcome the problems existing in related technologies, this application provides a model training, bridge physics field determination method, device, equipment and medium.

[0005] According to a first aspect of any embodiment of this application, a model training method is provided, the method comprising: Obtain the structural topology information of the bridge, as well as the sensing data collected by the sensors on the bridge; Based on the sensor data and the structural topology information, a feature vector is generated to characterize the structural control information of the bridge. Construct a target evolution path from a random prior distribution to a target physical field distribution, and determine the conditional vector field corresponding to the target evolution path; wherein, the target evolution path is the path of evolution from the random prior distribution to the target physical field distribution in the time dimension, and the conditional vector field is used to characterize the guiding information of the evolution from the random prior distribution to the target physical field distribution; The prediction model is trained using the feature vector as a conditional input and the conditional vector field as a supervision signal.

[0006] According to a second aspect of any embodiment of this application, a method for determining the physical field of a bridge is provided, the method comprising: Obtain the structural topology information of the bridge, as well as the sensing data collected by the sensors on the bridge; Based on the sensing data and the structural topology information, a feature vector is generated; Using the feature vector as a conditional constraint, a random noise vector is input into the prediction model trained using the method described in any embodiment; The evolution direction information output by the prediction model is integrated and extrapolated to obtain the bridge physical field.

[0007] According to a third aspect of any embodiment of this application, a model training apparatus is provided, the apparatus comprising: The first acquisition module acquires the structural topology information of the bridge and the sensing data collected by the sensors on the bridge. The first generation module is used to generate a feature vector representing the structural control information of the bridge based on the sensing data and the structural topology information. A determination module is used to construct a target evolution path from a random prior distribution to a target physical field distribution, and to determine the conditional vector field corresponding to the target evolution path; wherein, the target evolution path is a path that evolves from the random prior distribution to the target physical field distribution in the time dimension, and the conditional vector field is used to characterize the guiding information of the evolution from the random prior distribution to the target physical field distribution; The training module is used to train the prediction model using the feature vector as a conditional input and the conditional vector field as a supervision signal.

[0008] According to a fourth aspect of any embodiment of this application, a bridge physics field determination apparatus is provided, the apparatus comprising: The second acquisition module is used to acquire the structural topology information of the bridge and the sensing data collected by the sensors on the bridge. The second generation module is used to generate feature vectors based on the sensing data and the structural topology information; The input module is used to input a random noise vector into a prediction model trained using the method described in any embodiment, with the feature vector as a conditional constraint. The integration module is used to integrate and extrapolate the evolution direction information output by the prediction model to obtain the bridge physical field.

[0009] According to a fifth aspect of any embodiment of this application, a computer program product is provided, including a computer program / instructions that, when executed by a processor, implement the method described in any embodiment.

[0010] According to a sixth aspect of any embodiment of this application, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the method described in any embodiment.

[0011] According to a seventh aspect of any embodiment of this application, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the method described in any embodiment.

[0012] The technical solution provided in this application may include the following beneficial effects: As can be seen from the above embodiments, by acquiring the structural topology information of the bridge and the sensing data collected by sensors on the bridge, a feature vector is generated based on the sensing data and structural topology information. The feature vector carries the force transmission path and stiffness distribution information of the bridge structure, constructs the target evolution path from random prior distribution to target physical field distribution, and determines the conditional vector field corresponding to the target evolution path. The prediction model is trained with the feature vector as the conditional input and the conditional vector field as the supervision signal. This enables the prediction model to learn the evolution law from noise to the global bridge physical field under the constraint of structural control information. The prediction model can reconstruct the global bridge physical field with high fidelity from sparse local observation data.

[0013] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and do not limit this application. Attached Figure Description

[0014] The accompanying drawings, which are incorporated in and form part of this application, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0015] Figure 1 This is a flowchart illustrating a model training method according to an exemplary embodiment of this application.

[0016] Figure 2 This is a schematic diagram of the architecture of a model training system according to an exemplary embodiment of this application.

[0017] Figure 3 This is a flowchart illustrating another model training method according to an exemplary embodiment of this application.

[0018] Figure 4 This is a flowchart illustrating a method for determining the physical field of a bridge according to an exemplary embodiment of this application.

[0019] Figure 5 This is a flowchart illustrating another method for determining the physical field of a bridge according to an exemplary embodiment of this application.

[0020] Figure 6 This is a schematic diagram of the structure of an electronic device according to an exemplary embodiment of this application.

[0021] Figure 7 This is a block diagram illustrating a model training apparatus according to an exemplary embodiment of this application.

[0022] Figure 8This is a block diagram of a bridge physics field determination device according to an exemplary embodiment of this application. Detailed Implementation

[0023] 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 numbers 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 application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0024] The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The singular forms “a,” “the,” and “the” used in this application 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 or all possible combinations of one or more of the associated listed items.

[0025] It should be understood that although the terms first, second, third, etc., may be used in this application to describe various information, such 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 application, 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."

[0026] In related technologies, a physical inversion method based on finite element model updates is usually adopted. Sensor data is used as the objective function, and optimization algorithms are used to continuously adjust and invert the underlying parameters of the finite element mechanical model, such as the stiffness matrix, mass matrix, or boundary conditions, until the finite element forward calculation results match the measured data.

[0027] However, the inversion process based on the finite element model update is a highly nonlinear ill-conditioned inverse problem that requires extremely dense stiffness matrix recombination and iterative solution. A single state reconstruction takes a very long time, which cannot meet the real-time requirements of bridge physical field reconstruction. Furthermore, it depends on the initial model parameters, and the inversion results are prone to divergence when the model error is large.

[0028] To address the aforementioned problems, this application proposes a model training method, apparatus, equipment, and medium for determining the physical field of a bridge. The following embodiments are provided to further illustrate this application: Please see Figure 1 , Figure 1This is a flowchart illustrating a model training method according to an exemplary embodiment of this application. The method can be executed by electronic devices such as monitoring terminals and local industrial control computers, or by servers such as cloud servers and cluster servers, or by a combination of electronic devices and servers. This application does not impose any limitations on this method.

[0029] This method can be applied to scenarios such as bridge structural health monitoring, bridge digital twin global field simulation, and bridge damage status assessment. By fusing sensor data with bridge structural topology, constructing target evolution paths, and co-training feature vectors and condition vector fields, it can quickly and accurately output evolution direction information with only a small amount of sensor data, so as to reconstruct the physical field of the entire bridge that conforms to the laws of structural mechanics.

[0030] like Figure 1 As shown, the method may include the following steps: Step S101: Obtain the structural topology information of the bridge and the sensing data collected by the sensors on the bridge.

[0031] In this step, the structural topology information of the bridge is obtained by reading the bridge finite element model file, parsing the bridge's digital design drawings, and exporting the bridge's 3D scan model. The structural topology information reflects the mechanical connections of the bridge and can be a discrete finite element topology diagram of the entire bridge domain. This information may include all discrete mesh nodes in the bridge, the adjacency relationships formed by each node based on structural stiffness, the spatial coordinates of the nodes, and boundary constraints.

[0032] Sensor data is continuously collected by various sensors, such as fiber optic strain gauges, accelerometers, and Global Positioning System (GPS) / Global Navigation Satellite System (GNSS), which are installed at stress locations such as the main beam, supports, anchorage zones, and piers of the bridge.

[0033] The acquired sensor data can include observation signals such as displacement observation data, acceleration data, temperature data, and strain data. The acquired sensor data can be stored in segments according to fixed time windows, with preprocessing operations such as noise filtering and normalization performed simultaneously to ensure data stability in subsequent feature extraction stages. The acquired structural topology information and the preprocessed multimodal sensor data can be stored in a cache storage unit as the data foundation for subsequent calculation processes.

[0034] Step S102: Based on the sensor data and structural topology information, generate a feature vector to characterize the structural control information of the bridge.

[0035] In this step, based on sensor data and structural topology information, a processing logic that integrates graph representation learning and temporal feature extraction can be used to complete the compressed mapping of global features. First, based on the structural topology information of the bridge, the spatial relationships of all nodes within the structural topology information are clarified. The spatial coupling and correlation features brought about by the location of the measuring points and the stiffness connection relationship of the bridge are then mined to obtain spatial features that can characterize the local spatial mechanical correlation of a single node.

[0036] We perform time-dimensional feature extraction processing on continuously acquired sensor time-series signals within a time window to explore the dynamic evolution of sensor data under external loads and environmental temperature changes, and extract time-series features that can characterize the dynamic response trend of the bridge. Then, based on spatial and time-series features, we obtain feature vectors that carry structural control information such as the overall stiffness distribution, boundary constraints, and external loads of the bridge, serving as the bridge's unique implicit structural fingerprint.

[0037] In one embodiment, for each node in the structural topology information, the features of the nodes and their neighboring nodes are aggregated by means of feature weighted aggregation, local convolution operation, etc., and the spatial coupling and correlation information between the nodes caused by the bridge section stiffness, support constraints, and component connection is fused to obtain the spatial features of the nodes.

[0038] In this context, nodes in the structural topology information are discretized positional units used to characterize the spatial discrete points and mechanical degrees of freedom of the bridge structure. The structural topology information can be pre-constructed as a finite element topology graph, where nodes correspond to a set of discrete nodes in the finite element model, including nodes with and without sensors. The adjacency relationships of nodes are determined by the structural stiffness connection relationships.

[0039] Neighborhood nodes are adjacent nodes that have a physical stiffness connection with the current node in the structural topology information. Neighborhood nodes are used to provide neighborhood information during the spatial feature aggregation process, enabling the current node to integrate the features of surrounding nodes with which it has a mechanical force transmission path, thereby capturing the coupling correlation of the local space.

[0040] Spatial features are feature vectors obtained by aggregating the features of each node and its corresponding neighboring nodes in the structural topology information. Spatial features are used to characterize the local mechanical environment of a node in a bridge structure, and can include stiffness transfer relationships between nodes and neighboring nodes, spatial positional relationships, and local boundary constraints.

[0041] For the continuous sensing data collected within a preset sliding time window, the dynamic change patterns of the sensing data caused by the reciprocating action of vehicle load, periodic changes in ambient temperature, and slow structural deformation are captured by multi-layer convolutional transformation and temporal nonlinear mapping, and the temporal characteristics of the sensing data are extracted.

[0042] Among them, temporal features are feature vectors that characterize the dynamic response change trend of bridges. Temporal features are used to characterize the dynamic response law of bridge structures under the influence of external loads, changes in ambient temperature, and other factors that evolve over time. They can include temporal information such as short-term impact fluctuations caused by vehicle loads, long-period slow drift caused by temperature changes, and the vibration characteristics of the structure itself.

[0043] After obtaining the spatial and temporal features corresponding to each node, the spatial and temporal features are fused by methods such as feature dimension concatenation and feature weighted fusion to obtain the feature vector.

[0044] As described above, spatial features are obtained by aggregating the features of neighboring nodes for each node in the structural topology information. At the same time, temporal features of the sensor data are extracted, and the spatial features and temporal features are fused to obtain a feature vector. Only a small amount of sensor data is needed to generate a feature vector that simultaneously contains the spatial coupling correlation information and dynamic response change trend information of the bridge structure. This achieves the collaborative representation of structural spatial information and load response information, and improves the completeness and accuracy of the feature vector in expressing the control information of the bridge structure.

[0045] In one embodiment, when aggregating the features of a node and its neighboring nodes, a multi-head attention mechanism can be used to perform weighted fusion calculations of neighborhood information. First, multiple attention heads are set up using multiple independent attention mapping networks and feature transformation branches. Each attention head can independently perform linear transformation operations on the features of the node and the features of its neighboring nodes, respectively solving for the degree of association and matching between the node and its corresponding neighboring nodes, thereby determining the attention weights between each group of nodes and their neighboring nodes. These attention weights quantify the proportion of influence of different neighboring nodes on the spatial mechanical state of the current node.

[0046] For example, the structural topology information of a bridge can be a finite element topology diagram. ,in, It is a set containing all discrete nodes of the finite element method. Adjacent edges are connected based on structural physical stiffness. For the normalized adjacency matrix, Let be the number of nodes in the finite element topology graph. For any node in the finite element topology graph... During the time window The historical observation sequence and its spatial coordinate combination within the range form the initial feature tensor. , The number of feature dimensions of the node.

[0047] Based on Formula 1, and combining the structural topological connections between nodes and their neighboring nodes, as well as the relative position codes between nodes reflecting changes in the local structural stiffness of the bridge, the scoring values ​​are comprehensively calculated and normalized to determine the nodes under a single attention focus. With neighboring nodes Attention weights between : Formula 1 in, Represents the current network layer number. Used to identify the attention head corresponding to the current calculation; For the first A linear transformation weight matrix for each attention head is used to perform a unified dimensional mapping on the original features of the nodes; , They are nodes With neighboring nodes In the network layer Features; For feature concatenation operators; For nodes With neighboring nodes Relative position encoding between them; Assign an attention scoring vector; It is a nonlinear unit activation function; Representative node The set of all first-order neighbor nodes and nodes It normalizes the score value to a weight coefficient in the interval [0,1].

[0048] After obtaining all attention weights, the features of the current node and the features of all neighboring nodes can be weighted and aggregated using methods such as weighted multiplication and feature summation, with the attention weights corresponding to each attention head as the weighting coefficients. After the above aggregation operation, the spatial features corresponding to each attention head can be obtained.

[0049] For example, according to Formula 2 below, the attention weights obtained from the current attention head can be used as weighting coefficients to weight and aggregate the features of the node and the features of each neighboring node after linear transformation. A non-linear activation function is then introduced to complete the feature mapping, resulting in the... Spatial characteristics of the attention head output: Formula 2 in, Represents the current network layer number. Represents the next layer of the network; For the first Each node outputs attention. exist Spatial characteristics of layers; It is a non-linear activation function; Representative node The set of all first-order neighbor nodes and nodes itself; Attention weights; Let be the linear transformation matrix of the attention head; For the first Layer nodes Its characteristics.

[0050] After acquiring the spatial features corresponding to each of the attention heads, the spatial features corresponding to multiple attention heads are spliced ​​together and integrated into the same feature tensor by splicing along the feature dimension and stacking features in series. This integrates the spatial coupling information of different scales and different correlation dimensions captured by multiple attention branches, and finally obtains spatial features that integrate complete neighborhood interaction relationships.

[0051] For example, the spatial features corresponding to multiple attention heads can be concatenated along the feature dimension according to the following formula 3 to obtain the concatenated spatial features: Formula 3 in, The total number of attention heads set for a multi-head attention mechanism; Represents the concatenation operation of feature dimensions; For nodes exist Spatial features after layer fusion of all attention head information.

[0052] As described above, attention weights between nodes and their neighboring nodes are determined by multiple attention heads. Based on these attention weights, spatial features of each attention head are obtained through weighted aggregation. The spatial features of multiple attention heads are then concatenated, enabling the model to capture the association patterns between nodes from multiple different feature subspaces. Different attention heads can focus on different mechanical transmission patterns such as bending and torsion, thereby comprehensively reflecting the complex spatial mechanical characteristics of the bridge structure and improving the accuracy of spatial feature extraction.

[0053] In one embodiment, when extracting the temporal features of the sensing data, convolution processing can be performed along the time dimension to extract the temporal features. The acquired sensing data is a one-dimensional temporal sequence arranged along the time axis. Multi-scale one-dimensional convolutional kernels can be used to traverse the temporal signal along a time sliding window. Small-sized convolutional kernels capture short-term fluctuation features such as instantaneous load impacts and vibration abrupt changes, while large-sized expanded convolutional kernels expand the temporal receptive field to uncover long-period evolution patterns such as periodic temperature changes and long-term structural creep. Multi-layer convolution stacking achieves hierarchical temporal feature extraction, with shallow layers capturing local details and deep layers fusing long-distance temporal correlations.

[0054] Gating mechanisms can also be introduced to collaboratively extract temporal features. For example, after each one-dimensional convolution operation, a gating unit can be set up to form a gated temporal convolution module. The gating mechanism can generate control gate signals through the gating weight matrix to adaptively filter and adjust the amplitude of the original temporal features output by the convolution.

[0055] When invalid timing information such as environmental noise or outliers is detected, the gating signal reduces the weight of the corresponding feature channel to suppress the transmission of irrelevant interference information. When mechanical response signals such as load changes or structural deformation are identified, the gating signal amplifies the weight of the corresponding timing feature to retain timing evolution information that reflects the true state of the bridge.

[0056] The features output by convolution are adaptively filtered through a gating mechanism, then connected to a nonlinear activation function to complete feature mapping, and finally compressed using temporal pooling. One-dimensional convolutional temporal extraction with a gating mechanism is performed independently on the temporal signals from multiple sensors. The temporal features from each output are aligned and fused to obtain temporal features that include short-term abrupt changes, long-period gradual variations, and filtered-out redundant noise.

[0057] For example, according to Equation 4 below, a one-dimensional temporal convolutional network with a gating mechanism can be introduced to extract dynamic response features along the time dimension. By expanding the receptive field through convolution, the temporal features of the sensor data can be extracted: Formula 4 in, node In the time dimension Temporal features output by the gated convolution module; For the node passed to the upper layer of the network Features; , There are two independent one-dimensional convolutional weight matrices, corresponding to the candidate feature branch and the gated weight branch, respectively. This represents a one-dimensional temporal convolution operation; , These are the bias terms corresponding to the two sets of convolutional branches; This is the hyperbolic tangent activation function, used to generate candidate temporal features to be screened; It is a non-linear activation function that outputs gate weights in the range [0,1]. The Hadamard product (element-wise multiplication) applies gating weights to candidate features to achieve adaptive selection.

[0058] After obtaining the spatial and temporal features corresponding to each node, the spatial and temporal features of individual nodes are aligned and stitched together to form node fusion features. After extracting and fusing the temporal and spatial features of all nodes, the global feature vector can be obtained by aggregating the feature vectors of all nodes according to the following formula 5: Formula 5 in, The feature vectors are from global fusion. This is a global feature aggregation mapping function used to perform normalization aggregation operations on feature vectors of multiple nodes; The number of nodes; For the first The node fusion features corresponding to each node; This is a node weight coefficient matrix, used to assign differentiated weights to sensors at different locations. Nodes in key stress areas can be assigned higher weights. This is a mean aggregation operation used to globally normalize the weighted fused features of all nodes.

[0059] As mentioned above, by performing convolution processing on the sensor data along the time dimension to extract temporal features, it is possible to capture the dynamic evolution of the sensor data caused by external loads and environmental temperature changes. This allows for the extraction of more stable temporal representations with fewer parameters, thereby improving the model's ability to capture long-term evolution patterns.

[0060] Step S103: Construct the target evolution path from the random prior distribution to the target physical field distribution, and determine the conditional vector field corresponding to the target evolution path.

[0061] In this step, the mathematical logic of the continuous evolution from random noise to the physical field of the real bridge can be built based on the optimal transmission theory, and the analytical derivation of the target evolution path and the conditional vector field can be completed.

[0062] First, a random prior distribution satisfying a Gaussian distribution is obtained, which is used to provide initial random samples for evolution. Then, the target physical field distribution is obtained, which is the probability distribution of the target global physical field of the bridge. The target physical field can be constructed by finite element simulation, aggregation of bridge measured global data, etc.

[0063] Samples are drawn from the random prior distribution and the target physical field distribution using methods such as random sampling and batch stratified sampling to form sample pairs. Based on the optimal transport theory, the optimal coupling matching relationship between each sample pair is determined. Weighted combination calculations are performed at any time point in the time dimension using linear interpolation rules to obtain all intermediate states in the evolution process. The intermediate states corresponding to all time points are concatenated to form a smooth target evolution path without curvature deviation.

[0064] Among them, the target evolution path is the path of evolution from random prior distribution to target physical field distribution in the time dimension. The starting point of the time dimension corresponds to the random prior distribution, and the ending point corresponds to the target physical field distribution. The target evolution path can reflect the complete change trajectory of random noise evolving into the real bridge's full-domain physical field.

[0065] For the constructed target evolution path, the conditional vector field corresponding to the evolution path can be obtained by differentiating the path function with respect to continuous-time variables and performing differential analytical operations. The conditional vector field represents the instantaneous change guidance information of the evolution process, used to characterize the guidance information for the evolution from a random prior distribution to the target physical field distribution. It can characterize the direction and rate of change of the intermediate state of the target evolution path at any given time point.

[0066] In one embodiment, a mathematical path can be established to evolve from a random prior distribution to the physical field of the entire bridge, modeling the generation process of the bridge's global state as a continuous-time variable. Internally, from the prior Gaussian noise distribution Smooth evolution to target physical field distribution The forward push process.

[0067] First, determine the constraints that the target evolution path must satisfy. The target evolution path that satisfies the continuity equation in passive fluid dynamics can be determined according to Equation 6 below. : Formula 6 in, The evolution from a random prior distribution to the target physical field distribution is obtained Probability density distribution at time points; A conditional vector field that drives the evolution of the distribution; It is a divergence operator; For continuous time points The partial derivative operator.

[0068] Obtain a first sample from a random prior distribution and a second sample from the target physical field distribution. The first sample is the starting point of the target evolution path, and the second sample is the preset ending point of the target evolution path.

[0069] According to optimal transport theory, the optimal matching relationship between the first and second samples is determined with the goal of minimizing transport cost. Optimal transport theory seeks the coupling scheme that minimizes the total cost of transporting probability mass from a random prior distribution to a target physical field distribution, i.e., minimizing the 2-Wasserstein distance between them.

[0070] For example, the optimal matching relationship between the first sample and the second sample can be determined according to the following formula 7: Formula 7 in, Random prior distribution With the target physical field distribution The 2-Wasserstein distance between them; For all feasible probability coupling sets Find the minimum value within the inner quadrant; This is the first sample obtained from a random prior distribution; This is the second sample obtained from the target physical field distribution; The distance is L2 Euclidean distance; This is the probability measure corresponding to the optimal coupling scheme.

[0071] The first and second samples are weighted and combined based on their matching relationships to determine the intermediate states of the target evolution path. For example, the target evolution path from the first sample to the second sample can be constructed based on the probabilistic flow displacement interpolation theory in optimal transport theory, given that the optimal matching relationship between the first and second samples has been determined.

[0072] Among them, the time points of the target evolution path in the time dimension are used to characterize the relative progress of the evolution process, and the value range of the time points is [0,1]. The starting point of the corresponding target evolution path is the random prior distribution. The endpoint of the target's evolution path, i.e., the target's physical field distribution. The value within corresponds to the middle position on the target evolution path.

[0073] During the training phase, random sampling at different time points enables the prediction model to learn the evolutionary direction information at each position along the entire evolutionary path. The weight of the first sample is negatively correlated with the time point of the target evolutionary path, while the weight of the second sample is positively correlated with the time point.

[0074] At any point in time along the target evolution path, the intermediate state is determined by a weighted combination of the first and second samples. When When the intermediate state is equal to the first sample, the weight of the first sample is 1, and the weight of the second sample is 0; when When the intermediate state equals the second sample, the weight of the first sample is 0, and the weight of the second sample is 1; when At this point, the intermediate state is the linear interpolation result of the first and second samples. As the time point increases, the contribution of the first sample gradually decreases, while the contribution of the second sample gradually increases. By concatenating the intermediate states corresponding to all time points, a smooth, curvature-free target evolution path is formed from the first sample to the second sample.

[0075] At any point in time along the target evolution path, the intermediate state of the target evolution path can be determined by a weighted combination of the first and second samples according to the following formula 8: Formula 8 in, for The intermediate state corresponding to a given time point; for Evolutionary mapping function corresponding to a given time point; For normalized continuous-time variables, the value range is [0,1]; The first sample The corresponding weights, over time Increases and decreases; For the second sample The corresponding weights, over time It increases and grows.

[0076] As described above, by sampling the first and second samples from the random prior distribution and the target physical field distribution, the matching relationship between the first and second samples is determined based on the optimal transport theory. The first and second samples are then weighted and combined according to the matching relationship to determine the intermediate state, thus constructing a linear path from the random prior distribution to the target physical field distribution. This ensures that the evolution direction of any point on the path remains constant, avoiding the accumulation of truncation errors caused by the high curvature of the path in the diffusion model, and providing a foundation for subsequent large-step integral derivation.

[0077] In one embodiment, when determining the conditional vector field corresponding to the target evolution path, the intermediate states of the target evolution path can be differentiated in time to obtain the conditional vector field. The conditional vector field can indicate the instantaneous change direction and rate of change of the intermediate states along the target evolution path.

[0078] For example, the conditional vector field on the target evolution path can be obtained by taking the real-field partial derivative of the determined intermediate state with respect to time according to the following formula 9: Formula 9 in, Let the conditional vector field be the field of conditions, and the values ​​of the conditional vector field can be determined by the second sample. Compared with the first sample The differences are determined.

[0079] As described above, by taking the time derivative of the intermediate states of the target evolution path, the conditional vector field is obtained, which can accurately characterize the instantaneous change direction and rate of change of the intermediate states along the target evolution path, providing a stable optimization target for the training of the prediction model.

[0080] In one embodiment, when determining the conditional vector field corresponding to the target evolution path, multiple conditional vector fields corresponding to multiple matching relationships can be obtained. A weighted average of these multiple conditional vector fields is then performed to obtain the weighted averaged conditional vector field.

[0081] Each matching relationship corresponds to a pair of first and second samples, and each conditional vector field is obtained by differentiating the intermediate states with respect to time from the corresponding pair of first and second samples. A weighted average conditional vector field is obtained by performing a probability-weighted average of multiple conditional vector fields. This weighted average conditional vector field is used to characterize the overall evolutionary trend of the target evolutionary path, integrating the different evolutionary directions corresponding to multiple different sample pairs into a unified evolutionary direction.

[0082] For example, the globally weighted averaged conditional vector field can be obtained by performing expected marginalization on the joint distribution of the conditional vector field according to the following formula 10: Formula 10 in, The conditional vector field after global weighted averaging; This is the conditional vector field corresponding to a single pair of samples; A sample pair consisting of the first sample and the second sample exist Conditional probability density at time points; For sample pairs The joint distribution; for Marginal probability density at a given time point; It is an integral measure of the sample space.

[0083] As described above, by acquiring multiple conditional vector fields corresponding to multiple matching relationships and performing weighted averaging, a weighted averaged conditional vector field is obtained. This allows the conditional vector field to integrate the evolutionary direction information of multiple different sample pairs, reflecting the overall evolutionary trend of the target evolutionary path. It can eliminate the random bias introduced by a single sample pair, making the supervision signal smoother and more stable, and further improving the training stability of the prediction model.

[0084] Step S104: Train the prediction model using the feature vector as the conditional input and the conditional vector field as the supervision signal.

[0085] In this step, the feature vector output in step S102 is used as the conditional input of the model, and the conditional vector field obtained by parsing in step S103 is used as the supervision signal for model training. The training process of the prediction model is completed through backpropagation of loss and iterative optimization.

[0086] The prediction model is a parameterized deep neural network. Its output is the evolutionary direction information of the noise transforming into the real physical field, which can be represented as an instantaneous velocity vector field. During training, feature vectors are embedded into the model's input layer as fixed constraints. A random noise vector from a random prior distribution is input to the model, and the model forward-deduces and outputs the predicted evolutionary direction information.

[0087] The deviation between the predicted evolution direction of the model output and the conditional vector field, which serves as the supervision signal, can be determined by methods such as difference calculation and Euclidean distance measurement. Based on the deviation value, a data reconstruction loss is constructed. The model parameters are then initially adjusted iteratively according to the data reconstruction loss, so that the evolution direction of the model output gradually conforms to the target evolution path obtained by the optimal transmission theory.

[0088] The training process of the prediction model is completed by iteratively executing sample input, forward inference, loss calculation, and parameter update until the loss converges to the preset threshold and the model output accuracy meets the preset accuracy.

[0089] The trained prediction model can continuously output evolution direction information at each time step during the inference phase. Then, combined with the ordinary differential equation solver, the evolution direction information is integrated and deduced to obtain the global bridge physical field that conforms to the laws of mechanics.

[0090] The bridge physical field refers to the spatial distribution of physical quantities across the entire bridge structure under specific load and environmental conditions, which may include displacement field, stress field, strain field, etc. The displacement field is used to characterize the three-dimensional deformation of each node across the entire bridge, the strain field is used to characterize the degree of deformation of each infinitesimal element across the entire bridge, and the stress field is used to characterize the stress state of each infinitesimal element across the entire bridge.

[0091] During the training phase, the target physical field distribution corresponds to the numerical distribution of the real bridge physical field. The conditional vector field guides the prediction model to learn the evolution law from the random prior distribution to this physical field distribution. During the inference phase, the evolution direction information output by the prediction model is integrated and extrapolated to obtain the global bridge physical field. The bridge physical field can fully reflect the mechanical behavior of the bridge structure under service conditions and serves as the data foundation for subsequent bridge structural safety assessments, damage identification, and digital twin applications.

[0092] The model training method in this embodiment acquires the structural topology information of the bridge and the sensing data collected by sensors on the bridge. Based on the sensing data and structural topology information, a feature vector is generated, which carries the force transmission path and stiffness distribution information of the bridge structure. A target evolution path from random prior distribution to target physical field distribution is constructed, and the conditional vector field corresponding to the target evolution path is determined. The prediction model is trained with the feature vector as the conditional input and the conditional vector field as the supervision signal. This allows the prediction model to learn the evolution law from noise to the global bridge physical field under the constraint of structural control information. The prediction model can reconstruct the global bridge physical field with high fidelity from sparse local observation data.

[0093] Furthermore, by constructing a linear evolution path from a random prior distribution to the target physical field distribution, the evolution direction at any point on the path is constant and the curvature is zero. This provides a foundation for subsequent large-step integral deduction to achieve rapid global bridge physical field reconstruction, enabling the reconstruction of the bridge physical field to be completed with only a few integration steps during the inference stage.

[0094] In the foregoing embodiments, a feature vector was generated by fusing sensor data with structural topology information. This feature vector carries information about the force transmission path and stiffness distribution of the bridge structure, constructing a target evolution path and determining a conditional vector field. The prediction model was trained using the feature vector as conditional input and the conditional vector field as a supervisory signal. This enabled the prediction model to learn the evolution law from noise to the overall bridge physical field under the constraints of structural control information. The following embodiments will describe the training process of the prediction model in more detail and can be applied to any of the above embodiments.

[0095] In one embodiment, when training the prediction model, the intermediate states of the target evolution path, the current time point, and the feature vector can be input into the prediction model to obtain the evolution direction information at the current time point output by the prediction model. The evolution direction information can reflect the direction and rate of change of the state variables in order to evolve along the target evolution path towards the target physical field distribution in the intermediate state at the current time point.

[0096] The output evolution direction information is compared with the conditional vector field to determine the difference between them. The conditional vector field is the standard evolution direction derived analytically from the optimal transmission path, and the evolution direction information output by the prediction model is a prediction of the standard evolution direction. The difference between the evolution direction information and the conditional vector field reflects the accuracy of the prediction model's prediction of the evolution direction.

[0097] The data reconstruction loss is determined based on the difference between the evolution direction information and the conditional vector field, using methods such as difference calculation and Euclidean distance measurement. The data reconstruction loss measures the degree to which the predicted evolution direction deviates from the optimal transmission path. By minimizing the data reconstruction loss, the prediction model can learn the optimal transmission path for the evolution from the random prior distribution to the target physical field distribution.

[0098] At any given time point, the evolution direction information output by the prediction model should approximate the conditional vector field as closely as possible, enabling the model to learn the optimal transmission path from the random prior distribution to the target physical field distribution. By calculating the difference between the evolution direction information and the conditional vector field for all time points and all sample pairs, the prediction accuracy of the model along the entire evolution path can be comprehensively evaluated.

[0099] For example, the data reconstruction loss can be calculated according to the following formula 11: Formula 11 in, These are the network parameters for the prediction model; Indicates time Random sampling is performed from a uniform distribution in the interval [0,1]. This indicates that the first sample was drawn from a random prior distribution; This indicates that the second sample was sampled from the target physical field distribution; This is an intermediate state; This is the evolutionary direction information output by the prediction model; Conditional vector field; The square of the Euclidean distance represents the degree of difference between the two.

[0100] Based on the data reconstruction loss, the backpropagation algorithm is used to calculate the gradients of each parameter in the prediction model. Optimizers such as Adam and Stochastic Gradient Descent (SGD) are then used to adjust the parameters of the prediction model along the gradient descent direction to reduce the data reconstruction loss. Through multiple iterative training iterations, the evolution direction information output by the prediction model continuously approximates the conditional vector field.

[0101] As described above, by obtaining the evolution direction information output by the prediction model, determining the data reconstruction loss based on the difference between the evolution direction information and the conditional vector field, and adjusting the parameters of the prediction model based on the data reconstruction loss, the model can be effectively guided to learn the evolution law from noise to physical field. This makes the evolution direction output by the prediction model continuously approach the standard evolution direction analytically derived from the optimal transport theory, ensuring the prediction accuracy of the model at the data fitting level.

[0102] In one embodiment, the prediction model can be trained using a combination of data-driven and physical-driven methods. The data-driven part approximates the optimal transmission path by constraining the evolution direction information output by the model through conditional flow matching loss, as described in the aforementioned embodiment of data reconstruction loss.

[0103] The physics-driven component embeds partial differential equations of bridge structural mechanics as constraints into the training process, ensuring that the generated bridge physical field conforms to the laws of structural mechanics. These partial differential equations describe the relationships between the displacement, strain, and stress fields of a bridge structure under stress. They can include: geometric equations describing the relationship between displacement and strain fields; material constitutive equations describing the relationship between strain and stress fields; and solid mechanics equilibrium equations describing the force equilibrium conditions that the stress field within the structure must satisfy.

[0104] First, an ordinary differential equation solver is used to integrally extrapolate the evolution direction information output by the prediction model over time, and the time points are... The evolution direction information output in time is transformed into bridge physical fields, such as displacement fields, to support mechanical verification. .

[0105] After obtaining the displacement field, the spatial derivative of the displacement field can be obtained, and the strain tensor can be calculated according to the geometric equations under the small deformation assumption. For example, the Cauchy geometric equations for the small strain tensor based on the Einstein Summation Convention can be introduced, and the strain tensor can be calculated according to the following formula 12: Formula 12 in, For the displacement field One portion, Represents the displacement components relative to spatial coordinates The partial derivatives of this equation establish the geometric relationship between the displacement field and the strain field, and it is a fundamental equation in continuum mechanics. In the three-dimensional case, and We take 1, 2, and 3 respectively, which correspond to the three coordinate directions in space.

[0106] Next, the stress tensor can be determined based on the calculated strain tensor and the constitutive relation of the bridge material. For example, for isotropic linear elastic materials, the stress tensor can be determined by incorporating the Lamé constant. and shear modulus The stress tensor is calculated according to the isotropic linear elastic generalized Hooke's law, using the following formula 13: Formula 13 in, Let Kronecker function be used when When the value is 1, The value is 0 at that time; The trace of the strain tensor, i.e., the sum of the three normal strains, is determined according to Einstein's summation convention. This equation establishes the constitutive relationship between the strain field and the stress field, and can reflect the physical properties of the material.

[0107] After obtaining the stress tensor, the physical constraint loss can be determined based on the residuals between the bridge physical field and the partial differential equations of bridge structural mechanics by calculating the residuals of the solid mechanics equilibrium equations and the boundary condition residuals. The physical constraint loss reflects the degree to which the predicted bridge physical field violates the laws of structural mechanics. By minimizing the physical constraint loss, the generated bridge physical field can be made to gradually approach a feasible solution that satisfies the laws of mechanics.

[0108] For example, physical constraint losses include at least one of the following: internal residual loss and boundary residual loss. Internal residual loss is determined based on the residuals of solid mechanics equilibrium equations such as the Navier-Cauchy equilibrium equation within the bridge structure, and can reflect whether the predicted displacement field satisfies the force equilibrium requirements throughout the structure. For example, the calculated stress tensor can be substituted into the Navier-Cauchy static equilibrium equation to construct the internal residual loss.

[0109] Boundary residual loss is determined based on the difference between the bridge physical field at the bridge structure boundary and the preset boundary conditions. It can reflect whether the predicted bridge physical field meets the specified stress conditions and displacement constraints at the boundary.

[0110] Boundary residual losses may include stress residual losses and / or displacement residual losses. Stress residual losses are determined based on the difference between the predicted stress tensor applied at the structural boundary and the preset surface force conditions, reflecting whether the predicted physical field meets the specified stress conditions at the force boundary. Displacement residual losses are determined based on the difference between the predicted displacement field value at the structural boundary and the preset displacement constraints, reflecting whether the predicted physical field meets the specified deformation compatibility conditions at the displacement boundary.

[0111] By setting internal residual loss and boundary residual loss as components of physical constraint loss, the force equilibrium conditions inside the structure and the force and displacement conditions at the structural boundary can be constrained respectively, thus achieving dual mechanical verification of the bridge's physical field at both the global domain and the boundary.

[0112] For example, the physical constraint loss can be calculated according to the following formula 14: Formula 14 in, These are the network parameters for the prediction model; The entire space of the bridge structure; For internal residual loss, The residuals of the Navier-Cauchy equilibrium equations are... These are the volume force components, characterizing the degree to which the equilibrium equations are satisfied across the entire structure. For stress residual loss, As the force boundary, To predict the surface force components of the stress tensor at the boundary, To define the surface force components, The first normal vector outside the boundary Each component represents the degree to which the force boundary conditions are satisfied. This is the weighting coefficient for the stress residual loss; For displacement residual loss, For displacement boundary, To predict displacement components, To define displacement components and characterize the degree to which displacement boundary conditions are satisfied, This represents the weighting coefficient for the displacement residual term.

[0113] When adjusting the parameters of the prediction model based on the data reconstruction loss, the parameters can be adjusted according to both the data reconstruction loss and the physical constraint loss. For example, the total loss, including the data reconstruction loss and the physical constraint loss, can be calculated using the following formula 15: Formula 15 in, The data reconstruction loss is used to constrain the difference between the evolution direction information output by the prediction model and the conditional vector field. The physical constraint loss is used for constraint prediction, and the bridge physical field satisfies the partial differential equations of bridge structural mechanics. This indicates the current training round.

[0114] These are dynamically adjustable weighting coefficients used to balance the relative influence of data reconstruction loss and physical constraint loss during joint training. The weighting coefficients can be adaptively adjusted according to the training progress. For example, in the early stages of training, a higher weight can be given to the data reconstruction loss to ensure model convergence, while in the later stages of training, the weight of the physical constraint loss can be gradually increased to enhance the model's physical accuracy. Alternatively, preset fixed weighting coefficients can be used; this embodiment of the application does not limit this approach.

[0115] As described above, the bridge physical field is obtained by integrating the evolution direction information output by the prediction model. The physical constraint loss is determined based on the residual between the bridge physical field and the partial differential equation of bridge structural mechanics. The model parameters are then adjusted by combining the data reconstruction loss and the physical constraint loss to achieve joint training of data-driven and physical-driven approaches. This enables the model to generate a physical field that satisfies mechanical equilibrium and boundary conditions, avoiding non-physical artifacts that are easily generated in engineering applications by purely data-driven models and improving the reliability of the derived bridge physical field.

[0116] Please see Figure 2 , Figure 2 A schematic diagram of the architecture of a model training system is shown. For example, the model training system may include a multi-head spatiotemporal graph attention network 21, a temporal convolutional network 22, and a prediction model 23.

[0117] During the model training phase, the structural topology information of the bridge and the sensor data collected by sensors are first acquired. The structural topology information can be constructed as a finite element topology graph, which includes all discrete finite element nodes of the bridge and the adjacent edge relationships determined based on the structural physical stiffness. The sensor data includes various types of multimodal sensor signals such as displacement observation data, acceleration data, temperature data, and strain data.

[0118] Structural topology information and sensor data are input into a multi-head spatiotemporal graph attention network 2 and a temporal convolutional network 22 for feature extraction. For example, structural topology information and sensor data are jointly input into the multi-head spatiotemporal graph attention network 21. Based on the node neighborhood relationships determined by the structural topology information, the multi-head spatiotemporal graph attention network 21 calculates the attention weights between each node and its neighboring nodes through multiple attention heads. The features of the node and its neighboring nodes are weighted and aggregated to obtain the spatial features corresponding to each attention head. Then, the spatial features corresponding to each attention head are concatenated to output the spatial features of each node after fusing neighborhood interaction information.

[0119] Sensing data is input into a temporal convolutional network 22, which performs convolution processing along the time dimension to extract temporal features. The temporal convolutional network 22 can be a gated temporal convolutional network, including dilated convolutional layers and gating units. The dilated convolutional layers expand the receptive field along the time dimension to capture long-term evolutionary patterns, while the gating units dynamically filter the temporal features to suppress irrelevant interference.

[0120] The spatial features output by the multi-head spatiotemporal graph attention network 21 and the temporal features output by the temporal convolutional network 22 are fused, and a global average pooling readout function is used to compress and map the fused features of all nodes to obtain a feature vector that represents the control information of the bridge structure.

[0121] When constructing the target evolution path and conditional vector field, the random prior distribution and the target physical field distribution are first obtained. A first sample is sampled from the random prior distribution, and a second sample is sampled from the target physical field distribution. With the goal of minimizing transmission cost, the matching relationship between the first and second samples is determined based on optimal transmission theory. According to the matching relationship, the first and second samples are weighted and combined to determine the intermediate states of the target evolution path. The conditional vector field corresponding to the target evolution path is obtained by differentiating the intermediate states of the target evolution path with respect to time.

[0122] The feature vector, the current time point, and the intermediate states of the target evolution path are input into the prediction model 23, which outputs the evolution direction information at the current time point. Using the conditional vector field as a supervision signal, the data reconstruction loss is determined based on the difference between the evolution direction information output by the prediction model 23 and the conditional vector field.

[0123] Physical constraints can also be introduced during training. An ordinary differential equation solver is used to integrally extrapolate the evolution direction information output by the prediction model 23 over time to obtain the displacement field. The spatial derivative of the displacement field is calculated, and the strain tensor is calculated based on the geometric equations under the small deformation assumption. Then, based on the constitutive relations of the bridge material, such as the generalized Hooke's law for isotropic linear elastic materials, the stress tensor is calculated from the strain tensor. The stress tensor is substituted into solid mechanics equilibrium equations such as the Navier-Cauchy equilibrium equation to calculate its residuals within the bridge structure, thus obtaining the internal residual loss.

[0124] The difference between the predicted bridge physical field at the structural boundary and the preset boundary conditions can also be calculated to obtain the boundary residual loss. The physical constraint loss is determined by combining the internal residual loss and the boundary residual loss. Based on the combination of data reconstruction loss and physical constraint loss, the prediction model 23 is iteratively trained.

[0125] Please see Figure 3 , Figure 3 A flowchart of another model training method is shown. This method describes the training process of a prediction model; for detailed implementation, please refer to the foregoing embodiments. The method may include the following steps: Step S301: Obtain the structural topology information and sensor data of the bridge.

[0126] Step S302: Generate feature vectors based on sensor data and structural topology information.

[0127] In this step, features of neighboring nodes can be aggregated among the bridge's nodes based on structural topology information to obtain spatial features. Then, convolution processing is performed on the sensor data along the time dimension to extract temporal features. Finally, the spatial and temporal features are fused to obtain a feature vector representing the bridge's structural control information.

[0128] Step S303: Obtain the random prior distribution and the target physical field distribution.

[0129] Step S304: Construct the target evolution path based on the optimal transmission theory.

[0130] In this step, a first sample is sampled from a random prior distribution, and a second sample is sampled from the target physical field distribution. With the goal of minimizing transmission cost, an optimal coupling scheme is determined based on optimal transmission theory, thus obtaining the matching relationship between the first and second samples.

[0131] Based on the matching relationship, the first and second samples are weighted and combined to determine the intermediate states of the target evolution path. The intermediate states corresponding to all time points are concatenated to form the target evolution path from the first sample to the second sample.

[0132] Step S305: Determine the conditional vector field corresponding to the target evolution path.

[0133] In this step, the intermediate states of the target evolution path are differentiated with respect to time, and the conditional vector field is determined based on the difference between the second sample and the first sample.

[0134] Step S306: Determine whether the probability flow displacement interpolation is smooth.

[0135] In this step, the smoothness of the probability flow displacement interpolation corresponding to the target evolution path is verified, that is, whether there are unreasonable abrupt changes, distortions, or divergences in the path. If the probability flow displacement interpolation is smooth, step S308 is executed; if the probability flow displacement interpolation is not smooth, step S307 is executed.

[0136] Step S307: Adjust the coupling strategy and metric parameters of the optimal transmission theory.

[0137] In this step, when step S306 determines that the probabilistic flow displacement interpolation is not smooth, the coupling strategy and metric parameters of the optimal transport theory are adjusted. For example, the coupling scheme, regularization parameters, or sampling strategy of the optimal transport theory can be adjusted to redetermine the matching relationship between the first sample and the second sample. Then, the process returns to step S304 to reconstruct the target evolution path until the probabilistic flow displacement interpolation meets the smoothness requirements.

[0138] Step S308: Train the prediction model.

[0139] In this step, the feature vector generated in step S302 is used as the conditional input, and the conditional vector field determined in step S305 is used as the supervision signal. The intermediate state of the target evolution path and the current time point are input into the prediction model. The prediction model forward extrapolates and outputs the evolution direction information to train the prediction model.

[0140] Step S309: Determine the data reconstruction loss.

[0141] In this step, the evolution direction information output by the prediction model is compared with the conditional vector field, which serves as the supervision signal. The difference between the two is calculated, and the data reconstruction loss is determined based on the difference.

[0142] Step S310: Determine whether the data reconstruction loss is lower than the preset threshold.

[0143] In this step, it is determined whether the data reconstruction loss calculated in step S309 is lower than a preset threshold. If the data reconstruction loss is lower than the preset threshold, step S312 is executed; if the data reconstruction loss is not lower than the preset threshold, step S311 is executed.

[0144] Step S311: Adjust the parameters of the prediction model.

[0145] In this step, when step S310 determines that the data reconstruction loss is not lower than a preset threshold, the parameters of the prediction model are adjusted according to the data reconstruction loss. For example, the gradient of each parameter in the prediction model is calculated using the backpropagation algorithm, and the network parameters are updated along the gradient descent direction using the optimizer to reduce the data reconstruction loss. After the parameters are adjusted, the process returns to step S309, the data reconstruction loss is recalculated, and iterative training continues until the data reconstruction loss is lower than the preset threshold.

[0146] Step S312: Integrate the evolution direction information to obtain the bridge physical field.

[0147] In this step, an ordinary differential equation solver can be used to perform integral derivation on the evolution direction information output by the prediction model in the time dimension, and transform the evolution direction information into bridge physical fields such as displacement field, strain field and stress field.

[0148] Step S313: Determine the physical constraint loss.

[0149] In this step, the spatial derivative of the displacement field can be obtained, the strain tensor can be calculated based on the geometric equations, and the stress tensor can be calculated from the strain tensor according to the constitutive relation of the bridge material. The stress tensor is then substituted into the solid mechanics equilibrium equations to calculate its internal residual loss within the bridge structure. The difference between the bridge's physical field at the structural boundaries and the preset boundary conditions is also calculated to obtain the boundary residual loss. Finally, the physical constraint loss is determined by combining the internal residual loss and the boundary residual loss.

[0150] Step S314: Determine whether the physical constraint loss has converged.

[0151] In this step, it is determined whether the physical constraint loss determined in step S313 has converged. If the physical constraint loss has converged, for example, if it is lower than a preset threshold or the change in multiple consecutive training rounds is less than a preset tolerance, it indicates that the prediction model has simultaneously met the requirements of data reconstruction accuracy and physical law constraints, and step S316 is executed; if the physical constraint loss has not converged, step S315 is executed.

[0152] Step S315: Adjust the loss weight parameters.

[0153] In this step, when step S314 determines that the physical constraint loss has not converged, the weight coefficients between the data reconstruction loss and the physical constraint loss, as well as the weight coefficients of the internal residual loss and boundary residual loss within the physical constraint loss, can be dynamically adjusted based on the current training progress and the magnitude differences of the various losses. After parameter adjustment, return to step S313 to recalculate the physical constraint loss until it converges.

[0154] Step S316: Generate the trained prediction model.

[0155] In this step, when step S314 determines that the physical constraint loss has converged, it indicates that the prediction model has simultaneously met the requirements of data reconstruction accuracy and physical law constraints, and the trained prediction model is generated for bridge state prediction.

[0156] Please see Figure 4 , Figure 4 This is a flowchart illustrating a method for determining the physical field of a bridge according to an exemplary embodiment of this application. This method can be executed by electronic devices such as monitoring terminals and local industrial control computers, or by servers such as cloud servers and cluster servers, or by a combination of electronic devices and servers. This application does not impose any limitations on this method.

[0157] like Figure 4 As shown, the method may include the following steps: Step S401: Obtain the structural topology information of the bridge and the sensing data collected by the sensors on the bridge.

[0158] In this step, we acquire the pre-constructed structural topology information of the bridge, as well as sensor data collected by sensors deployed on the bridge. The structural topology information may include all discrete mesh nodes in the finite element topology diagram, the stiffness adjacency relationships between nodes, and boundary constraints. The sensor data consists of multimodal signals acquired at the current time point, which may include displacement observation data, acceleration data, temperature data, strain data, etc.

[0159] Step S402: Generate feature vectors based on sensor data and structural topology information.

[0160] In this step, based on the acquired sensor data and structural topology information, a feature vector is generated to characterize the bridge's structural control information. The specific generation method of this feature vector can be found in the description of feature extraction in the aforementioned model training method embodiment, and will not be repeated here. This feature vector represents the bridge's overall stiffness distribution, boundary constraints, and external loads at the current time point, and can serve as constraints in subsequent simulations.

[0161] Step S403: Using the feature vector as a conditional constraint, input the random noise vector into the prediction model trained by the method described in any embodiment.

[0162] In this step, a random noise vector is sampled from the random prior distribution. Using the generated feature vector as a conditional constraint, the random noise vector is input into the prediction model trained using the method described in any of the preceding embodiments. The random prior distribution can be a standard Gaussian distribution in a high-dimensional space. The feature vector, as a conditional constraint, is embedded in the input layer of the prediction model to guide the evolution direction of the prediction model's output to match the current structural control information of the bridge.

[0163] Step S404: Integrate the evolution direction information output by the prediction model to obtain the bridge physical field.

[0164] In this step, an ordinary differential equation solver is used to integrally extrapolate the evolution direction information output by the prediction model over time to obtain the bridge's physical field. For example, constructing from... arrive The initial value problem of ordinary differential equations, with random noise vector as the initial state. Using the feature vector as a conditional constraint, the current state is changed in each iteration. Current time point The feature vector and the feature vector are input into the prediction model, and the prediction model outputs the evolution direction information at the current time point.

[0165] The current state is from arrive The intermediate state at any time point on the probability density path is represented by the current state, which has the same dimension as the bridge's physical field and is used to characterize the current position in the evolution process. The evolution direction information indicates the direction and rate of change of the state variables in order to evolve towards the target state along the optimal transmission path in the current state. The ordinary differential equation solver updates the current state according to the evolution direction information output by the prediction model, using an adaptive step size.

[0166] For example, for the first The level function is evaluated, and the solver calculates the values ​​of the evolution direction information in the current state. ,in, For the trained prediction model, These are the eigenvectors. The solver calculates based on each... The weighted combination of these factors is used to update the current state according to the following formula 16, which quickly approximates the final integral state with a minimal number of network feature evaluations: Formula 16 in, This is the updated state; This is the current state; The current integration step size is adaptively adjusted by the solver based on the error estimate. For the first Evolutionary direction information obtained from the evaluation of the level function; These are the corresponding weighting coefficients. The solver can employ a high-order explicit Runge-Kutta method, such as the Dormand-Prince 45 method, to obtain a high-precision weighted combination of evolution direction information through multiple function evaluations within a single integration step, as illustrated in the above formula (6 levels of evaluation). This enables accurate updates to the current state and automatic adjustment of the step size through local truncation error estimation.

[0167] Repeat the above iterative process until the integration time is reached. Reach the preset destination Because the target evolution path is constructed based on optimal transport theory during the training phase, the evolution direction information output by the prediction model changes gradually. Therefore, the ordinary differential equation solver can use a large step size for integral derivation, requiring only a very small number of integration steps to complete the entire evolution from a random noise vector to the bridge's physical field, and the final integral state. This refers to the reconstructed physical field of the bridge.

[0168] The bridge physics field determination method in this embodiment acquires the structural topology information of the bridge and the sensing data collected by sensors on the bridge; based on the sensing data and structural topology information, a feature vector is generated; using the feature vector as a constraint, a random noise vector is input into the trained prediction model; the evolution direction information output by the prediction model is integrally deduced to obtain the bridge physics field. Since the prediction model has learned the evolution law from noise to the global bridge physics field under the constraint of structural control information during the training stage, the bridge physics field is obtained by integrally deducing the evolution direction information output by the model. Within a very small integration step, the rapid reconstruction from sparse local observation data to the global bridge physics field is achieved.

[0169] To further explain the process of determining the physical field of a bridge Figure 5 A flowchart of another method for determining the physical field of a bridge is shown. This method may include the following steps: Step S501: Obtain the structural topology information and sensor data of the bridge; Step S502: Generate feature vectors based on sensor data and structural topology information.

[0170] Step S503: Sample a random noise vector from the random prior distribution.

[0171] In this step, a random noise vector is sampled from the random prior distribution as the initial state for the integral derivation of the ordinary differential equation solver.

[0172] Step S504: Construct the initial value problem for the ordinary differential equation.

[0173] In this step, the random noise vector sampled in step S503 is used as the initial state, and the eigenvector generated in step S502 is used as the conditional constraint to construct an initial value problem for the ordinary differential equation. Under the conditional constraint of the eigenvector, the state variable starts from the random noise vector and gradually approaches the target physical field according to the evolution direction indicated by the prediction model.

[0174] Step S505: Input the current state, current time point, and feature vector into the trained prediction model.

[0175] In this step, the current state, the current time point, and the feature vector are input into the prediction model trained using the method described in any of the preceding embodiments, and the prediction model outputs the evolution direction information at the current time point.

[0176] Step S506: Perform integral deduction on the evolution direction information output by the prediction model.

[0177] In this step, the ordinary differential equation solver updates the current state based on the evolution direction information output by the prediction model. The evolution direction information is the velocity field or gradient field at the current time point, representing the instantaneous rate of change of the state variables at the current position. By multiplying the evolution direction information by the integration step size, the change in the state variables within the current step size can be calculated, thereby updating the current state.

[0178] Step S507: Determine whether the current time point has reached the preset endpoint.

[0179] In this step, the integration time is determined. Has the preset endpoint been reached? .

[0180] If the integration time reaches the preset endpoint, it indicates that the integration derivation has been completed, and step S509 is executed; if the integration time does not reach the preset endpoint, step S508 is executed to continue the iteration.

[0181] Step S508: Perform large step size adaptive integral stepping.

[0182] In this step, when step S507 determines that the integration time has not met the target, the ordinary differential equation solver adaptively determines the next integration step size based on the current error estimate and updates the current state. And advance the points time to After the step size is determined, return to step S504 and continue executing the integral derivation process until the integration time reaches the preset endpoint.

[0183] Step S509: Generate the displacement field based on the final state of integration.

[0184] In this step, after the integration time reaches the preset endpoint, the final state of integration is the reconstructed displacement field.

[0185] Step S510: Map the global stress field according to the geometric tensor and Hooke's law.

[0186] In this step, based on the displacement field obtained in step S509, the strain tensor can be calculated based on the geometric equation under the assumption of small deformation. Then, based on the constitutive relation of the bridge material, such as the generalized Hooke's law for isotropic linear elastic materials, the stress tensor is calculated from the strain tensor, and the global stress field is obtained by mapping.

[0187] Step S511: Determine whether the global stress field satisfies the mechanical boundary conditions.

[0188] In this step, it is determined whether the global stress field mapped in step S510 satisfies the mechanical boundary conditions to verify whether the mechanical boundary conditions and the physical state are consistent. For example, it checks whether the stress field inside the structure satisfies the equilibrium equations of solid mechanics, and whether the surface force conditions and displacement constraints at the structural boundaries are consistent with the preset boundary conditions. If the global stress field satisfies the mechanical boundary conditions, it indicates that the reconstructed bridge physical field conforms to the laws of structural mechanics, and step S513 is executed. If the global stress field does not satisfy the mechanical boundary conditions, it indicates that there is a mechanical violation in the bridge physical field at the boundaries or inside, and step S512 is executed.

[0189] Step S512: Perform local corrections by applying physical mechanism constraints.

[0190] In this step, when step S511 determines that the global stress field does not meet the mechanical boundary conditions, the bridge physical field can be locally corrected. For example, a small mechanical compensation can be applied to the region where the residual exceeds the limit, such as locally fine-tuning the displacement field based on the sign and magnitude of the equilibrium equation residuals, to reduce the degree of violation of the boundary conditions and equilibrium equations. After correction, return to step S509, regenerate the displacement field, and verify it again until the mechanical boundary conditions are met.

[0191] Step S513: Determine the assessment results of the bridge structure safety status.

[0192] In this step, after determining that the global stress field satisfies the mechanical boundary conditions, the generated displacement and stress fields are compared with preset safety thresholds such as the preset maximum deflection limit and the preset maximum stress limit to determine the assessment result of the bridge structure's safety status. The assessment result can be used to determine whether the bridge is in a safe state under the current load conditions.

[0193] Step S514: Determine whether the evaluation result is higher than the preset reliability threshold.

[0194] In this step, it is determined whether the confidence level of the security status assessment result determined in step S513 is higher than a preset confidence threshold. Due to the randomness of the generation process, the initial state is a randomly sampled random noise vector, and each reconstruction result may fluctuate. If the confidence level of the assessment result is higher than the preset confidence threshold, it indicates that the reconstruction result is stable and reliable, and step S516 is executed. If the confidence level is not higher than the preset confidence threshold, it indicates that the reliability of this reconstruction result is insufficient, and step S515 is executed.

[0195] Step S515: Secondary downsampling and reconstruction confirmation.

[0196] In this step, if step S514 determines that the confidence level of the evaluation result is insufficient, a new random noise vector is sampled from the random prior distribution, and the integral derivation process is executed again to verify the consistency of the multiple reconstruction results. Through multiple sampling and reconstruction confirmations, the random bias introduced by randomness in a single reconstruction can be eliminated, thereby improving the reliability of the evaluation results.

[0197] Step S516: Output the bridge physics field.

[0198] In this step, after determining that the confidence level of the assessment result meets the requirements, the bridge physical field can be output for use in scenarios such as updating the state of the bridge digital twin, generating structural safety assessment reports, and supporting operation and maintenance decisions.

[0199] Understandably, the aforementioned model training and bridge physics determination method possesses cross-bridge transfer and generalization capabilities. Essentially, this method is based on a conditional reconstruction framework driven by structural topology information. The prediction model does not directly learn a fixed mapping relationship for a specific bridge, but rather learns the evolutionary law from a random prior distribution to the target physics distribution under the joint constraints of structural topology information and sensor data. When applied to different bridges, the input of structural topology information changes accordingly, thereby driving the model to output a physics reconstruction result adapted to the target bridge structure.

[0200] For bridges with similar structural types and topological relationships, the trained prediction model can be used for inference without retraining. For bridges with different structural forms or topological relationships, the sensor data and structural topological information of the bridge can be used to perform transfer learning or parameter fine-tuning based on the trained prediction model, so as to adapt the model to the mechanical characteristics of the new bridge with a small training cost.

[0201] Figure 6 This is a schematic diagram illustrating the structure of an electronic device according to an exemplary embodiment of this application. The electronic device may be, for example, a mobile phone, computer, digital broadcasting terminal, messaging device, game console, tablet device, personal digital assistant, server, smart home appliance, in-vehicle system, etc. (Reference) Figure 6 At the hardware level, the electronic device includes a processor 601, an internal bus 602, a network interface 603, memory 604, and non-volatile memory 605, and may also include other hardware required for business operations. The processor 601 reads the corresponding computer program from the non-volatile memory 605 into the memory 604 and then runs it, forming a model training device or a bridge physics field determination device at the logical level. Of course, in addition to software implementation, this application does 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 individual logic units, but can also be hardware or logic devices.

[0202] Figure 7 This is a block diagram illustrating a model training apparatus according to an exemplary embodiment of this application. (Refer to...) Figure 7 The device may include: The first acquisition module 701 acquires the structural topology information of the bridge and the sensing data collected by the sensors on the bridge. The first generation module 702 is used to generate a feature vector representing the structural control information of the bridge based on the sensing data and the structural topology information. The determination module 703 is used to construct a target evolution path from a random prior distribution to a target physical field distribution, and to determine the conditional vector field corresponding to the target evolution path; wherein, the target evolution path is a path that evolves from the random prior distribution to the target physical field distribution in the time dimension, and the conditional vector field is used to characterize the guiding information of the evolution from the random prior distribution to the target physical field distribution; The training module 704 is used to train the prediction model using the feature vector as a conditional input and the conditional vector field as a supervision signal.

[0203] Optionally, the first generation module 702, when generating a feature vector characterizing the structural control information of the bridge based on the sensing data and the structural topology information, includes: For each node in the structural topology information, the features of the node and its neighboring nodes are aggregated to obtain the spatial features of the node; Extract the temporal features of the sensor data; The spatial features and the temporal features are fused to obtain the feature vector.

[0204] Optionally, the first generation module 702, when aggregating the features of the node and its neighboring nodes to obtain the spatial features of the node, includes: The attention weights between the node and its neighboring nodes are determined using multiple attention heads. Based on the attention weights, the features of the node and the neighboring nodes are weighted and aggregated to obtain the spatial features corresponding to each attention head; The spatial features corresponding to the multiple attention heads are spliced ​​together to obtain the spliced ​​spatial features.

[0205] Optionally, the first generation module 702, when extracting the temporal features of the sensing data, includes: The sensor data is convolved along the time dimension to extract the temporal features of the sensor data.

[0206] Optionally, the determining module 703, when constructing the target evolution path from the random prior distribution to the target physical field distribution, includes: Obtain a first sample from the random prior distribution and a second sample from the target physical field distribution; Determine the matching relationship between the first sample and the second sample; Based on the matching relationship, the first sample and the second sample are weighted and combined to determine the intermediate state of the target evolution path; wherein, the weight of the first sample is negatively correlated with the time point of the target evolution path in the time dimension, and the weight of the second sample is positively correlated with the time point.

[0207] Optionally, the determining module 703, when determining the conditional vector field corresponding to the target evolution path, includes: The conditional vector field is obtained by taking the time derivative of the intermediate states of the target evolution path.

[0208] Optionally, the determining module 703, when determining the conditional vector field corresponding to the target evolution path, includes: Obtain multiple condition vector fields corresponding to multiple matching relationships; The multiple conditional vector fields are weighted and averaged to obtain the weighted averaged conditional vector field.

[0209] Optionally, the training module 704, when training the prediction model using the feature vector as conditional input and the conditional vector field as supervision signal, includes: Obtain the evolution direction information output by the prediction model; The data reconstruction loss is determined based on the difference between the evolution direction information and the conditional vector field; The parameters of the prediction model are adjusted based on the data to reconstruct the loss.

[0210] Optionally, after obtaining the evolution direction information output by the prediction model, the apparatus further includes: The training and deduction module is used to perform integral deduction on the evolution direction information to obtain the bridge physical field; The residual determination module is used to determine the physical constraint loss based on the residual between the bridge physical field and the partial differential equation of bridge structural mechanics. The training module 704, when used to adjust the parameters of the prediction model based on the data reconstruction loss, includes: The parameters of the prediction model are adjusted based on the data reconstruction loss and the physical constraint loss.

[0211] Optionally, the physical constraint loss includes at least one of the following: Internal residual loss, which is determined based on the residuals within the bridge structure according to the equilibrium equations of solid mechanics; Boundary residual loss, which is determined based on the difference between the bridge physical field at the bridge structural boundary and the preset boundary conditions.

[0212] Figure 8 This is a block diagram illustrating a bridge physics field determination device according to an exemplary embodiment of this application. (Refer to...) Figure 8 The device may include: The second acquisition module 801 is used to acquire the structural topology information of the bridge and the sensing data collected by the sensors on the bridge. The second generation module 802 is used to generate a feature vector based on the sensing data and the structural topology information; The input module 803 is used to input a random noise vector into a prediction model trained using the method described in any embodiment, with the feature vector as a conditional constraint. The integration module 804 is used to integrate and extrapolate the evolution direction information output by the prediction model to obtain the bridge physical field.

[0213] The specific implementation process of the functions and roles of each unit in the above device can be found in the implementation process of the corresponding steps in the above method, and will not be repeated here.

[0214] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The modules described as separate components may or may not be physically separate, and the components shown as modules may or may not be physical modules, that is, they may be located in one place or distributed across multiple network modules. Some or all of the modules can be selected to achieve the purpose of this application according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0215] In an exemplary embodiment, a non-transitory computer-readable storage medium including instructions, such as a memory including instructions, is also provided, which can be executed by a processor of a model training device or a bridge physics determination device to implement the method as described in any of the above embodiments.

[0216] The non-transitory computer-readable storage medium may be ROM, random access memory (RAM), CD-ROM, magnetic tape, floppy disk and optical data storage device, etc., and this application does not limit it.

[0217] In an exemplary embodiment, a computer program product including a computer program / instruction is also provided, which can be executed by a processor of a model training device or a bridge physics determination device to implement the method described in any of the above embodiments.

[0218] The foregoing has described specific embodiments of this application. 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 results. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0219] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the invention filed herein. This application is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and alterations can be made without departing from its scope. The scope of this application is limited only by the appended claims.

[0220] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A model training method, characterized in that, The method includes: Obtain the structural topology information of the bridge, as well as the sensing data collected by the sensors on the bridge; Based on the sensor data and the structural topology information, a feature vector is generated to characterize the structural control information of the bridge. Construct a target evolution path from a random prior distribution to a target physical field distribution, and determine the conditional vector field corresponding to the target evolution path; wherein, the target evolution path is the path of evolution from the random prior distribution to the target physical field distribution in the time dimension, and the conditional vector field is used to characterize the guiding information of the evolution from the random prior distribution to the target physical field distribution; The prediction model is trained using the feature vector as a conditional input and the conditional vector field as a supervision signal.

2. The method according to claim 1, characterized in that, The step of generating a feature vector characterizing the structural control information of the bridge based on the sensing data and the structural topology information includes: For each node in the structural topology information, the features of the node and its neighboring nodes are aggregated to obtain the spatial features of the node; Extract the temporal features of the sensor data; The spatial features and the temporal features are fused to obtain the feature vector.

3. The method according to claim 2, characterized in that, The aggregation of features of the node and its neighboring nodes to obtain the spatial features of the node includes: The attention weights between the node and its neighboring nodes are determined using multiple attention heads. Based on the attention weights, the features of the node and the neighboring nodes are weighted and aggregated to obtain the spatial features corresponding to each attention head; The spatial features corresponding to the multiple attention heads are spliced ​​together to obtain the spliced ​​spatial features.

4. The method according to claim 2, characterized in that, The extraction of temporal features from the sensing data includes: The sensor data is convolved along the time dimension to extract the temporal features of the sensor data.

5. The method according to claim 1, characterized in that, The construction of the target evolution path from the random prior distribution to the target physical field distribution includes: Obtain a first sample from the random prior distribution and a second sample from the target physical field distribution; Determine the matching relationship between the first sample and the second sample; Based on the matching relationship, the first sample and the second sample are weighted and combined to determine the intermediate state of the target evolution path; The weight of the first sample is negatively correlated with the time point of the target evolution path in the time dimension, while the weight of the second sample is positively correlated with the time point.

6. The method according to claim 5, characterized in that, Determining the conditional vector field corresponding to the target evolution path includes: The conditional vector field is obtained by taking the time derivative of the intermediate states of the target evolution path.

7. The method according to claim 5, characterized in that, Determining the conditional vector field corresponding to the target evolution path includes: Obtain multiple condition vector fields corresponding to multiple matching relationships; The multiple conditional vector fields are weighted and averaged to obtain the weighted averaged conditional vector field.

8. The method according to claim 1, characterized in that, The step of training the prediction model using the feature vector as a conditional input and the conditional vector field as a supervision signal includes: Obtain the evolution direction information output by the prediction model; The data reconstruction loss is determined based on the difference between the evolution direction information and the conditional vector field; The parameters of the prediction model are adjusted based on the data to reconstruct the loss.

9. The method according to claim 8, characterized in that, After obtaining the evolution direction information output by the prediction model, the method further includes: By integrating and extrapolating the evolution direction information, the physical field of the bridge is obtained; The physical constraint loss is determined based on the residual between the bridge physical field and the partial differential equation of bridge structural mechanics. The step of adjusting the parameters of the prediction model based on the data reconstruction loss includes: The parameters of the prediction model are adjusted based on the data reconstruction loss and the physical constraint loss.

10. The method according to claim 9, characterized in that, The physical constraint loss includes at least one of the following: Internal residual loss, which is determined based on the residuals within the bridge structure according to the equilibrium equations of solid mechanics; Boundary residual loss, which is determined based on the difference between the bridge physical field at the bridge structural boundary and the preset boundary conditions.

11. A method for determining the physical field of a bridge, characterized in that, The method includes: Obtain the structural topology information of the bridge, as well as the sensing data collected by the sensors on the bridge; Based on the sensing data and the structural topology information, a feature vector is generated; Using the feature vector as a conditional constraint, a random noise vector is input into a prediction model trained using the method described in any one of claims 1 to 10; The evolution direction information output by the prediction model is integrated and extrapolated to obtain the bridge physical field.

12. A model training device, characterized in that, The device includes: The first acquisition module acquires the structural topology information of the bridge and the sensing data collected by the sensors on the bridge. The first generation module is used to generate a feature vector representing the structural control information of the bridge based on the sensing data and the structural topology information. A determination module is used to construct a target evolution path from a random prior distribution to a target physical field distribution, and to determine the conditional vector field corresponding to the target evolution path; wherein, the target evolution path is a path that evolves from the random prior distribution to the target physical field distribution in the time dimension, and the conditional vector field is used to characterize the guiding information of the evolution from the random prior distribution to the target physical field distribution; The training module is used to train the prediction model using the feature vector as a conditional input and the conditional vector field as a supervision signal.

13. A device for determining the physical field of a bridge, characterized in that, The device includes: The second acquisition module is used to acquire the structural topology information of the bridge and the sensing data collected by the sensors on the bridge. The second generation module is used to generate feature vectors based on the sensing data and the structural topology information; An input module is used to input a random noise vector into a prediction model trained using the method described in any one of claims 1 to 10, with the feature vector as a conditional constraint. The integration module is used to integrate and extrapolate the evolution direction information output by the prediction model to obtain the bridge physical field.

14. A computer program product having a computer program / instructions stored thereon, characterized in that, When the computer program / instructions are executed by the processor, they implement the model training method as described in any one of claims 1-10 or the bridge physics field determination method as described in claim 11.

15. An electronic device, characterized in that, include: processor; Memory used to store processor-executable instructions; The processor executes the executable instructions to implement the model training method as described in any one of claims 1-10 or the bridge physics field determination method as described in claim 11.

16. A computer-readable storage medium storing computer instructions thereon, characterized in that, When executed by the processor, this instruction implements the model training method as described in any one of claims 1-10 or the bridge physics field determination method as described in claim 11.

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