Bridge dynamic weighing method and system based on physical information neural network

Abstract

A bridge dynamic weighing system based on a physical information neural network is characterized in that a physical information embedded Kolmogorov-Arnold network (KAN) is adopted to extract a bridge influence line from bridge actual measurement response of a calibration vehicle, and dynamic weighing of a to-be-measured vehicle is realized based on the extracted influence line. The specific implementation process is as follows: A, arranging a plurality of sensors to obtain bridge structure response, and extracting basic information such as vehicle axle number, axle distance and speed according to side span measuring point signal data; b, constructing a KAN for representing influence lines at a plurality of measuring points of the bridge; c, constructing a KAN neural network loss function for network training, and adding a physical constraint term, a boundary condition term, a regularization term and a smooth constraint term in the loss function to enhance the robustness of the network under the influence of noise interference and a vehicle dynamic effect; d, adjusting network hyper-parameters and accurately extracting a bridge influence line according to bridge characteristics and actual measurement data in calibration vehicle testing; and E, utilizing the trained KAN and real-time bridge response to realize dynamic identification of the axle load of the to-be-detected vehicle.

Description

Technical Field

[0001] This invention relates to a bridge dynamic weighing method and system based on a physical information neural network. It uses a Kolmogorov-Arnold network (KAN) with embedded physical information to extract the bridge influence line from the measured bridge response of a calibrated vehicle, and realizes dynamic weighing of the vehicle under test based on the extracted influence line. It has good engineering applicability and robustness, and can provide technical support for bridge traffic load monitoring, structural performance evaluation and bridge operation and maintenance. It belongs to the field of civil structure health monitoring. Background Technology

[0002] Bridge structures are continuously subjected to multiple factors during long-term service, including traffic loads, environmental effects, and material degradation. Among these, vehicle load is one of the key external forces affecting bridge safety and durability. Accurate identification of axle loads and total weight of vehicles passing over bridges is crucial for bridge safety assessment, operation and maintenance management, and the control of overloaded vehicles. Dynamic bridge weighing technology, by analyzing the bridge structural response caused by vehicle traffic, indirectly identifies vehicle axle loads and has become an important research direction in the field of bridge operation monitoring.

[0003] Existing bridge dynamic weighing systems typically rely on the relationship between bridge structural response and influence lines. They extract the influence lines and combine them with measured response data to invert vehicle axle loads. The influence lines, as a crucial function describing the structural response variation under unit load at different locations on the bridge, directly determine the accuracy and stability of the dynamic weighing results. In practical engineering applications, the influence line extraction process is often subject to significant errors due to interference factors such as measurement noise and vehicle dynamic effects, thus limiting the engineering applicability of dynamic weighing methods.

[0004] In recent years, machine learning algorithms have received widespread attention in bridge dynamic weighing and influence line identification. These methods learn the nonlinear mapping relationships in bridge structural response data to achieve automatic influence line modeling and vehicle axle load identification, reducing the reliance on precise modeling of structural parameters to some extent. However, existing machine learning-based bridge dynamic weighing methods mainly rely on statistical fitting or predefined function forms, lacking effective constraints on the continuity of influence lines, boundary characteristics, and physical relationships of structural responses. This results in insufficient generalization ability and robustness of the models when facing different vehicle operating conditions or noise interference.

[0005] Furthermore, bridge structural response data typically exhibits high sampling density and unstable noise levels. Relying solely on a data-driven model for influence line extraction can easily misidentify measurement noise or vehicle dynamic effects as changes in influence line characteristics, thus affecting the accuracy of vehicle axle load inversion. Therefore, there is an urgent need for a vehicle identification method that integrates the physical relationships of bridge response, influence line boundary conditions, and smoothing characteristics within a machine learning framework. This would form a bridge dynamic weighing system based on physical information neural networks, thereby improving the accuracy and robustness of vehicle axle load identification. Summary of the Invention

[0006] To address the aforementioned shortcomings of existing technologies, this invention proposes a bridge dynamic weighing method and system based on a physical information neural network, which enables accurate extraction of bridge influence lines and robust identification of vehicle axle loads.

[0007] The first aspect of this invention relates to a dynamic weighing method for bridges based on a physical information neural network, comprising the following steps: A. Sensors are deployed at multiple locations in the mid-span and side spans of the bridge to collect dynamic response data of the bridge structure during vehicle passage. Based on the response signals from the side span measuring points, basic parameter information such as the number of axles, wheelbase, and driving speed of the calibrated vehicle is identified and extracted, providing basic information for subsequent influence line extraction and vehicle axle load identification. B. Construct a Kolmogorov-Arnold Network (KAN) to achieve multidimensional nonlinear mapping through the combination of one-dimensional learnable functions. It can efficiently represent complex nonlinear function relationships with fewer network parameters. Taking the bridge location as input and the static response of multiple measuring points of the bridge corresponding to the applied unit force at that location as output, the constructed KAN network is used to represent and model the influence line at multiple measuring points of the bridge. C. Construct a loss function for KAN training, and introduce physical constraint terms, influence line boundary condition terms, regularization terms and smoothing constraint terms into the loss function to suppress the interference of noise and vehicle dynamic effects on influence line extraction, thereby enhancing the stability and robustness of the network training process. D. Combining the structural characteristics of the bridge and the measured response data from the calibration vehicle test, the network hyperparameters such as the number of iterations, learning rate, number of grids, and number of splines are optimized and adjusted to accurately extract the influence lines of multiple measurement points of the bridge; E. Using the trained KAN, the bridge structure response data collected in real time is input during the passage of the vehicle under test, and the axle load of the vehicle is inverted based on the extracted bridge influence line to realize the dynamic weighing of the unknown axle load of the vehicle.

[0008] Furthermore, step A specifically includes: A1. Structural response sensors are arranged at multiple predetermined locations in the mid-span and side spans of the bridge. Dynamic sensors such as strain and displacement sensors can be used to collect dynamic response data of the bridge structure during vehicle traffic. A2. When a vehicle enters or leaves the bridge, each axle of the vehicle will cause abrupt changes in the bridge structure response signal. The abrupt changes are more obvious in the side spans. The speed, number of axles and wheelbase can be determined by identifying the abrupt change points. A3. Perform consistency verification on the number of axles, wheelbase, and driving speed of the identified calibration vehicles, eliminate abnormal identification results, and ensure the reliability of the obtained calibration vehicle parameter information, so as to provide reliable information for subsequent bridge influence line extraction and vehicle axle load identification.

[0009] Furthermore, step B specifically includes: B1. Establish a position coordinate system along the longitudinal direction of the bridge, using the longitudinal position of the bridge as the input variable of the KAN network, and using the static response at multiple measuring points when a unit force is applied to the bridge at the stated position as the network output variable. Use this network to characterize the bridge's influence line. B2. A learnable one-dimensional function can be defined as follows:

[0010] in, Represents a one-dimensional function. This represents the learnable control coefficient. The number of B-spline basis functions. Indicates the first Each segment The B-order spline basis functions can be obtained recursively.

[0011] B3. Construct a single-layer KAN, which has Dimension Input and Dimensional output The input-output relationship of this network layer can be represented as:

[0012] in This represents the one-dimensional function matrix of this layer; B4. Will Multiple single-layer KANs are combined to form Multilayer KANs utilize learnable one-dimensional function combinations to achieve multidimensional nonlinear mapping, enabling efficient representation of influence lines at multiple measurement points on bridges with fewer network parameters. The network can be represented as:

[0013] in, Indicates the longitudinal coordinates of the bridge. This indicates the network output.

[0014] Furthermore, step C specifically includes: C1. Based on the relationship between the bridge response and the influence line, a physical relationship constraint term between the bridge structural response and the influence line is introduced into the loss function. The Physics-Informed KAN (PIKAN) network, guided by physical information, satisfies the relationship between bridge response and influence line during training.

[0015] in, Indicates the sensor index number. Indicates the first The bridge structural response collected by a single sensor Represents the vehicle axle load matrix. Indicates the first The influence line identified by each sensor, Indicates the first The measured response of each sensor. This represents the L2 norm; since the static response of the bridge is zero when vehicles are on either side, boundary constraints need to be added. Ensure that the influence line is at a vertical position of 0 and At this point, the value approaches 0; a regularization term is introduced. To suppress overfitting and improve the generalization ability of influence line recognition results, constraints are imposed on the learnable parameters in KAN; an influence line smoothing constraint term is introduced. This ensures that the influence line maintains continuous and smooth characteristics outside the inflection point, thereby reducing the impact of measurement noise and vehicle dynamic effects on the influence line extraction results, and further enhancing the stability and robustness of the network training process. C2. Utilize the relationship between the loss function and the number of iterations to determine the values ​​of KAN training hyperparameters such as the number of iterations and grid values; C3. Based on the type of structural response collected by the bridge and sensors, determine the order of the linear function that KAN can learn.

[0016] Furthermore, step D specifically includes: D1. Using a calibration vehicle with known axle load or partially known axle load information, cross the bridge to obtain the bridge's dynamic structural response in order to extract the bridge's influence line; D2. Extracting the bridge influence line using the structural response to vehicle excitation with known axle load can be transformed into a network parameter optimization problem, which can be expressed as:

[0017] in, , and These represent the weighting coefficients for different terms, each set to 1. and ; D3. Due to the limitations of the size and accuracy of the weighbridge in practical applications, it is difficult to obtain all the axle load information of the calibrated vehicle. Only some information such as the sum of some axle loads is known. The unknown axle load can be set as an unknown number, and the optimization problem represented by equation (5) can be changed into a joint optimization problem of PIKAN network parameters and axle load parameters. Specifically, it can be expressed as:

[0018] D4. The optimization problems represented by equations (5) and (6) above can be solved using the Limited-memory BroydenFletcher Goldfarb Shanno (L-BFGS) algorithm.

[0019] Furthermore, step E specifically includes: E1. During the passage of the vehicle under test across the bridge, the dynamic response data of the bridge structure is collected in real time at multiple measuring points in the middle and side spans of the bridge, and the vehicle axle count, wheelbase and driving speed information are identified. E2. Using the influence line results of the bridge multi-measurement points output by the neural network, the parameter optimization problem shown in the improved equation (6) can be expressed as follows:

[0020] By solving this optimization problem, the axle load of the vehicle under test can be identified.

[0021] A second aspect of the present invention relates to a bridge dynamic weighing system based on a physical information neural network, comprising a memory and one or more processors, wherein the memory stores executable code, and the one or more processors execute the executable code to implement the bridge dynamic weighing method based on a physical information neural network of the present invention.

[0022] The innovations of this invention are as follows: First, it proposes a bridge dynamic weighing system based on Physical Information-Driven KAN (Kinetic Animation Array). By embedding the physical relationship between the bridge structural response, influence lines, and vehicle axle loads into the neural network learning process, it achieves joint identification of influence lines and vehicle axle loads, enabling stable vehicle axle load identification even when the axle load information of the calibration vehicle is unknown. Second, it uses KAN to model the bridge influence lines, utilizing a combination of one-dimensional learnable functions to achieve multi-dimensional nonlinear mapping. This efficiently characterizes the spatial distribution characteristics of influence lines with fewer network parameters, improving the accuracy and robustness of influence line extraction under the influence of measurement noise and vehicle dynamic effects. Third, it integrates bridge structural response data from multiple measurement points for vehicle axle load identification and introduces influence line boundary constraints and smoothing constraints during network training to effectively suppress the interference of measurement noise and vehicle dynamic effects on the dynamic weighing results, thereby achieving high-precision dynamic weighing of vehicle axle loads.

[0023] The working principle of this invention is as follows: a physical information-driven KAN characterization of the bridge influence line is constructed. During the network training process, physical relationship constraints, boundary condition regularization constraints, and smoothing constraints between the bridge response and the influence line are introduced to guide the network to accurately extract the bridge influence line. Combined with calibration vehicle tests, the influence line and vehicle axle load are jointly optimized. When the vehicle under test passes, the vehicle axle load is inverted based on the extracted influence line and real-time bridge response data, thereby achieving robust dynamic weighing of the vehicle axle load.

[0024] The advantages of this invention are: it can perform fusion analysis on bridge response data from multiple measurement points without relying on precise bridge structural parameter modeling; it can suppress the interference of noise and vehicle dynamic effects on influence line extraction and axle load identification through physical information constraints; and it can improve the accuracy and robustness of bridge dynamic weighing. It has advantages such as strong adaptability, stable identification process, and good engineering applicability. Attached Figure Description

[0025] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a schematic diagram of a bridge dynamic weighing system implementing the method of the present invention; Figure 3 This is a schematic diagram illustrating the basic information of the calibration and testing vehicle of this invention; Figure 4 This is a comparison diagram of the bridge identification influence line and the actual influence line of the present invention; Figure 5 This is a schematic diagram of the iterative optimization process of the axle weight of each axle of the vehicle under test in this invention; Figure 6 This is a comparison chart of the axle load identification results of the vehicle under test according to the present invention; Figure 7 This is a system structure diagram of the present invention. Detailed Implementation

[0026] The present invention will now be described in further detail with reference to the accompanying drawings.

[0027] Example 1

[0028] like Figure 1 As shown, this embodiment relates to a dynamic weighing method for bridges based on a physical information neural network, specifically including the following steps: A. Sensors are deployed at multiple locations in the mid-span and side spans of the bridge to collect dynamic response data of the bridge structure during vehicle traffic. Based on the response signals from the side span measuring points, basic parameter information such as the number of axles, wheelbase, and driving speed of the calibrated vehicles is identified and extracted, providing foundational information for subsequent influence line extraction and vehicle axle load identification; specifically including: A1. Structural response sensors are deployed at multiple predetermined locations in the mid-span and side spans of the bridge to collect bridge response data for subsequent analysis. The bridge dynamic weighing system is as follows: Figure 2 As shown, this example uses a strain sensor to collect dynamic response data generated by the bridge structure during vehicle passage. The data acquisition frequency in this example is 100Hz. A2. When a vehicle enters or leaves the bridge, each axle of the vehicle will cause abrupt changes in the bridge structure's response signal. Known information about calibrating vehicle A and test vehicle B is as follows: Figure 3 As shown, by driving across the bridge at different speeds, abrupt changes can be identified using data from the side span measuring points to determine the vehicle speed, number of axles, and wheelbase. A3. Perform consistency verification on the number of axles, wheelbase, and driving speed of the identified calibration vehicles, eliminate abnormal identification results, and ensure the reliability of the obtained calibration vehicle parameter information, so as to provide reliable information for subsequent bridge influence line extraction and vehicle axle load identification.

[0029] B. Construct a Kolmogorov-Arnold Network (KAN) to achieve multidimensional nonlinear mapping through a combination of one-dimensional learnable functions. This allows for efficient characterization of complex nonlinear functional relationships with fewer network parameters. Using the bridge location as input and the static responses at multiple bridge measuring points corresponding to a unit force applied at that location as output, the constructed KAN network is used to represent and model the influence lines at multiple bridge measuring points. Specifically, this includes: B1. Establish a position coordinate system along the longitudinal direction of the bridge. The longitudinal position coordinates of the bridge are used as the input variables of KAN. The static structural response of each measuring point when a unit force is applied at the position is used as the network output variable. KAN is used to perform a function representation of the bridge influence line. B2. The KAN describes the mapping relationship between the longitudinal position of the bridge and the structural response through a one-dimensional learnable function. The one-dimensional learnable function is composed of multiple spline basis functions, and its control parameters are adaptively updated during network training, thereby realizing a flexible representation of the influence line morphology. B3. A single-layer KAN is used to establish the mapping relationship between the longitudinal position of the bridge and the structural response at multiple measurement points. It consists of multiple sets of one-dimensional learnable functions to realize the nonlinear transformation from input variables to output variables. B4. Multilayer KAN is formed by connecting multiple single-layer KANs in sequence. Multidimensional nonlinear mapping is achieved through the layer-by-layer combination of one-dimensional learnable functions, and accurate representation of the influence line of multiple measurement points of bridge is achieved with fewer network parameters.

[0030] C. Construct a loss function for KAN training, introducing physical constraint terms, influence line boundary condition terms, regularization terms, and smoothing constraint terms into the loss function to suppress the interference of noise and vehicle dynamic effects on influence line extraction, thereby enhancing the stability and robustness of the network training process; specifically including: C1. A physical consistency constraint term between the bridge structural response and the influence line is introduced into the training loss function of KAN, ensuring that the influence line output by the network remains consistent with the measured response when reconstructing the bridge structural response. This constructs a Physics-Informed KAN (PIKAN) to achieve physical constraint learning of the influence line. Considering the physical characteristic that the bridge does not produce a static response when the vehicle is outside the bridge, boundary condition constraints for the influence line are introduced during network training, making the extracted influence line approach zero at both ends of the bridge, ensuring that the influence line representation results meet the actual bridge boundary conditions. To suppress overfitting during network training, regularization constraints are introduced into the learnable parameters in KAN, limiting the range of parameter values ​​and improving the generalization ability of the influence line recognition results under different vehicle conditions and environmental conditions. Addressing the spatial continuity and smoothness characteristics of the bridge influence line, a smoothing constraint mechanism is introduced during network training, ensuring that the extracted influence line remains continuous and smooth in non-abrupt regions. This effectively reduces the impact of measurement noise and vehicle dynamic effects on the influence line extraction results, enhancing the stability and robustness of network training. C2. Based on the convergence characteristics of the loss function during network training, adaptive selection of training hyperparameters such as the number of network iterations and grid partitioning is performed to ensure the accuracy and training efficiency of the influence line extraction results. When the number of network grids increases, the loss function gradually converges, and the number of iterations corresponding to the convergence value of the loss function is selected; when the number of network partitions increases, the convergence value of the loss function no longer decreases, and the number of network grids at this point is selected; according to the sensor layout and influence line extraction requirements, the network input and output sizes are 1 and 5 respectively, with the intermediate hidden layer dimension set to 16. C3. Based on the bridge structure type and the structural response form collected by the sensors, reasonably determine the complexity setting of the one-dimensional learnable function in KAN to balance the influence line representation ability and computational efficiency. For the stress influence line of a simply supported beam bridge with uniform cross-section, the order can be 1; for the displacement influence line of a simply supported beam bridge with uniform cross-section, the order can be 3; for other unknown cases, the order can be 3, and then adjusted according to the convergence of the loss function.

[0031] D. Combining the structural characteristics of the bridge and the measured response data from the calibration vehicle test, the network hyperparameters such as the number of iterations, learning rate, number of grids, and number of splines are optimized and adjusted to accurately extract the influence lines of multiple measurement points on the bridge; specifically including: D1. Select a calibration vehicle with known or partially known axle load information to pass through the bridge, and collect structural dynamic response data of multiple measuring points on the bridge during the passage of the calibration vehicle, which will serve as the calibration data source for influence line extraction and model training; D2. Using the bridge structural response data obtained under calibrated vehicle excitation, the bridge influence line extraction problem is transformed into a physical information-guided neural network parameter optimization problem. By minimizing the error between the network's predicted response and the measured response, accurate identification of the bridge's influence lines at multiple measurement points is achieved. The bridge influence line identification results are as follows: Figure 4 As shown; D3. In practical engineering projects, due to the limitations of weighbridge size and accuracy, it is difficult to obtain all axle load information of calibrated vehicles. Unknown axle load parameters can be used as variables to be optimized and incorporated into a unified optimization framework along with neural network parameters to achieve joint inversion of bridge influence lines and vehicle axle loads. D4. The L-BFGS algorithm is used to solve the above joint optimization problem. By iteratively updating the network parameters and axle weight parameters, the model convergence process is accelerated, and the computational efficiency and stability of influence line extraction and axle weight identification are improved.

[0032] E. Using the trained KAN, real-time bridge structural response data is input during the passage of the vehicle under test. Based on the extracted bridge influence lines, the vehicle axle load is inverted to achieve dynamic weighing of the unknown vehicle axle load; specifically including: E1. During the passage of vehicle B across the bridge, the dynamic response data of the bridge structure is collected in real time at multiple measuring points in the middle and side spans of the bridge, and the basic driving parameters such as the number of axles, wheelbase and driving speed of the vehicle are identified simultaneously. E2. Based on the influence line results of the bridge at multiple measurement points output by the trained physical information neural network, and combined with the real-time collected bridge structural response data, the axle load of each axle of the vehicle under test is calculated. The iterative process for each axle load is as follows: Figure 5 As shown, the identified axle load results are compared with the true values, for example... Figure 6 As shown.

[0033] Example 2

[0034] Reference Figure 7 This embodiment relates to a bridge dynamic weighing system based on a physical information neural network, including a memory and one or more processors. The memory stores executable code, and when the one or more processors execute the executable code, they are used to implement the bridge dynamic weighing method based on a physical information neural network of Embodiment 1.

[0035] The embodiments described in this specification are merely examples of implementations of the inventive concept. The scope of protection of this invention should not be considered as limited to the specific forms stated in the embodiments. The scope of protection of this invention also extends to equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.

Claims

1. A dynamic weighing method for bridges based on physical information neural networks, comprising the following steps: A. Sensors are deployed at multiple locations in the mid-span and side spans of the bridge to collect dynamic response data of the bridge structure during vehicle passage. Based on the response signals from the side span measuring points, basic parameter information such as the number of axles, wheelbase, and driving speed of the calibrated vehicle is identified and extracted, providing basic information for subsequent influence line extraction and vehicle axle load identification. B. Construct a Kolmogorov-Arnold Network (KAN) to achieve multidimensional nonlinear mapping through the combination of one-dimensional learnable functions. It can efficiently represent complex nonlinear function relationships with fewer network parameters. Taking the bridge location as input and the static response of multiple measuring points of the bridge corresponding to the applied unit force at that location as output, the constructed KAN network is used to represent and model the influence line at multiple measuring points of the bridge. C. Construct a loss function for KAN training, and introduce physical constraint terms, influence line boundary condition terms, regularization terms and smoothing constraint terms into the loss function to suppress the interference of noise and vehicle dynamic effects on influence line extraction, thereby enhancing the stability and robustness of the network training process. D. Combining the structural characteristics of the bridge and the measured response data from the calibration vehicle test, the network hyperparameters such as the number of iterations, learning rate, number of grids, and number of splines are optimized and adjusted to accurately extract the influence lines of multiple measurement points of the bridge; E. Using the trained KAN, the bridge structure response data collected in real time is input during the passage of the vehicle under test, and the axle load of the vehicle is inverted based on the extracted bridge influence line to realize the dynamic weighing of the unknown axle load of the vehicle.

2. The bridge dynamic weighing method based on a physical information neural network as described in claim 1, characterized in that, Step A specifically includes: A1. Structural response sensors are arranged at multiple predetermined locations in the mid-span and side spans of the bridge. Dynamic sensors such as strain and displacement sensors can be used to collect dynamic response data of the bridge structure during vehicle traffic. A2. When a vehicle enters or leaves the bridge, each axle of the vehicle will cause abrupt changes in the bridge structure response signal. The abrupt changes are more obvious in the side spans. The speed, number of axles and wheelbase can be determined by identifying the abrupt change points. A3. Perform consistency verification on the number of axles, wheelbase, and driving speed of the identified calibration vehicles, eliminate abnormal identification results, and ensure the reliability of the obtained calibration vehicle parameter information, so as to provide reliable information for subsequent bridge influence line extraction and vehicle axle load identification.

3. The bridge dynamic weighing method based on a physical information neural network as described in claim 1, characterized in that, Step B specifically includes: B1. Establish a position coordinate system along the longitudinal direction of the bridge, take the longitudinal position of the bridge as the input variable of KAN, and take the static response of multiple measuring points when a unit force is applied to the bridge at the position as the network output variable. Use this network to characterize the bridge influence line. B2. Define a learnable one-dimensional function, expressed as: in, Represents a one-dimensional function. This represents the learnable control coefficient. The number of B-spline basis functions. Indicates the first Each segment The B-order spline basis functions are obtained through recursive calculation. B3. Construct a single-layer KAN, which has Dimension Input and Dimensional output The input-output relationship of this network layer can be represented as: in This represents the one-dimensional function matrix of this layer; B4. Will Multiple single-layer KANs are combined to form Multilayer KANs utilize learnable one-dimensional function combinations to achieve multidimensional nonlinear mapping, enabling efficient representation of influence lines at multiple measurement points on bridges with fewer network parameters. The network can be represented as: in, Indicates the longitudinal coordinates of the bridge. This indicates the network output.

4. The bridge dynamic weighing method based on a physical information neural network as described in claim 1, characterized in that, Step C specifically includes: C1. Based on the relationship between the bridge response and the influence line, a physical relationship constraint term between the bridge structural response and the influence line is introduced into the loss function. The Physics-Informed KAN (PIKAN) network, guided by physical information, satisfies the relationship between bridge response and influence line during training. in, Indicates the sensor index number. Indicates the first The bridge structural response collected by a single sensor Represents the vehicle axle load matrix. Indicates the first The influence line identified by each sensor, Indicates the first The measured response of each sensor. This represents the L2 norm; since the static response of the bridge is zero when vehicles are on either side, boundary constraints need to be added. Ensure that the influence line is at a vertical position of 0 and At this point, the value approaches 0; a regularization term is introduced. To suppress overfitting and improve the generalization ability of influence line recognition results, constraints are imposed on the learnable parameters in KAN; an influence line smoothing constraint term is introduced. This ensures that the influence line maintains continuous and smooth characteristics outside the inflection point, thereby reducing the impact of measurement noise and vehicle dynamic effects on the influence line extraction results, and further enhancing the stability and robustness of the network training process. C2. Utilize the relationship between the loss function and the number of iterations to determine the values ​​of KAN training hyperparameters such as the number of iterations and grid values; C3. Based on the type of structural response collected by the bridge and sensors, determine the order of the linear function that KAN can learn.

5. The bridge dynamic weighing method based on a physical information neural network as described in claim 1, characterized in that, Step D specifically includes: D1. Using a calibration vehicle with known axle load or partially known axle load information, cross the bridge to obtain the bridge's dynamic structural response in order to extract the bridge's influence line; D2. Extracting the bridge influence line using the structural response to vehicle excitation with known axle load can be transformed into a network parameter optimization problem, which can be expressed as: in, , and These represent the weighting coefficients for different terms, each set to 1. and ; D3. Due to the limitations of the size and accuracy of the weighbridge in practical applications, it is difficult to obtain all the axle load information of the calibrated vehicle. Only some information such as the sum of some axle loads is known. The unknown axle load can be set as an unknown number, and the optimization problem represented by equation (5) can be changed into a joint optimization problem of PIKAN network parameters and axle load parameters. Specifically, it can be expressed as: D4. The optimization problems represented by equations (5) and (6) above can be solved using the Limited-memory BroydenFletcher Goldfarb Shanno (L-BFGS) algorithm.

6. The bridge dynamic weighing method based on a physical information neural network as described in claim 1, characterized in that, Step E specifically includes: E1. During the passage of the vehicle under test across the bridge, the dynamic response data of the bridge structure is collected in real time at multiple measuring points in the middle and side spans of the bridge, and the vehicle axle count, wheelbase and driving speed information are identified. E2. Using the influence line results of the bridge multi-measurement points output by the neural network, the parameter optimization problem shown in the improved equation (6) can be expressed as: By solving this optimization problem, the axle load of the vehicle under test can be identified.

7. A bridge dynamic weighing system based on a physical information neural network, characterized in that, The device includes a memory and one or more processors, wherein the memory stores executable code, and the one or more processors execute the executable code to implement the bridge dynamic weighing method based on a physical information neural network as described in any one of claims 1-6.

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