Load identification method and system based on physical information residual time sequence convolution network

Abstract

The application discloses a load identification method and system based on a physical information residual time sequence convolution network, an offline training identification network model, and online identification: bridge measured responses are acquired and a system transfer matrix is constructed, and an initial estimation of a moving load is obtained by using orthogonal matching pursuit sparse inversion; multi-scale feature construction is performed on the initial estimation to generate an input feature matrix; the trained network is input, a residual prediction component is output by a backbone network, a scaling coefficient and a bias term are output by a context perception calibration head, and finally, a real-time vehicle load is output. The application fuses sparse inverse problem modeling and deep time sequence feature learning to construct a unified framework of physical information and data-driven cooperation; the residual time sequence convolution network extracts multi-scale time sequence features and captures long-term and short-term evolution rules of the load; a logarithmic regularization self-supervised progressive sparse reconstruction strategy is adopted to iteratively compensate the residual and improve the reconstruction accuracy. The result is stable and reliable. The application is suitable for the field of artificial intelligence identification technology.

Description

Technical Field

[0001] This invention relates to the field of artificial intelligence recognition technology, specifically to a load recognition method and system based on a temporal convolutional network with physical information residuals. Background Technology

[0002] Dynamic excitation caused by moving vehicle loads, especially heavy and overloaded vehicles, is one of the main sources of live load during the service life of highway bridges, and a significant contributing factor to structural fatigue accumulation, stiffness degradation, and durability deterioration. Existing research shows that vehicle dynamic effects significantly amplify the response of bridge structures, causing an average damage to the bridge deck approximately 2 to 4 times greater than that under the same static axle load. Therefore, accurate identification and real-time monitoring of vehicle loads are crucial for ensuring the safety, durability, and normal service performance of bridge structures. Traditional direct vehicle load measurement methods, such as dynamic weighing systems and vehicle-mounted sensing technology, while capable of directly acquiring vehicle load information, generally suffer from high equipment installation and maintenance costs, stringent requirements for road conditions, and susceptibility to traffic environment interference in practical engineering applications.

[0003] Moving vehicle loads (especially heavy and overloaded vehicles) are the primary source of live load during the service life of highway bridges. Their dynamic effects significantly amplify structural responses (damage levels are approximately 2 to 4 times that of static axle loads), making them a key indicator for bridge safety monitoring. Currently, existing moving load identification technologies can be broadly categorized into three types, each with inherent bottlenecks: Traditional direct measurement methods, represented by dynamic weighing systems and vehicle-mounted sensing technologies. While these methods can directly acquire load information, they face challenges in engineering applications such as high equipment installation and maintenance costs, stringent requirements for road surface conditions, and susceptibility to traffic environment interference. Model-driven inverse analysis methods (traditional physical methods): These are indirect identification methods based on bridge dynamic response, essentially solving ill-conditioned inverse problems. Existing technologies often employ methods such as truncated singular value decomposition (TSVD), Tikhonov regularization, and sparse regularization. However, the identification performance of these methods highly depends on the appropriate selection of regularization parameters, and commonly used parameter selection strategies (such as the L-curve method and generalized cross-validation (GCV)) require iterative optimization, resulting in low computational efficiency and difficulty in meeting the real-time requirements of long-term online monitoring. Data-driven deep learning methods: These methods directly learn the nonlinear mapping between response and load through neural networks. While online recognition is fast, they heavily rely on a large number of high-quality labeled samples for training. However, obtaining data with real load labels in real bridge engineering is extremely costly and difficult, severely limiting their engineering generalization ability. Physical Information Neural Networks (PINN): Existing PINN methods can introduce physical constraints to alleviate data dependence, but most rely only on the governing equations to construct residual constraints, failing to fully utilize the inherent sparse prior characteristics of moving loads. This results in limitations in recognition accuracy and robustness under complex noisy environments.

[0004] Therefore, how to improve the recognition accuracy, robustness and generalization ability of mobile loads is a technical problem that urgently needs to be studied in the industry. Summary of the Invention

[0005] This invention provides a load identification method and system based on physical information residual temporal convolutional networks to solve one or more technical problems existing in the prior art, and at least provides a beneficial option or creates conditions.

[0006] This invention provides a load identification method based on physical information residual temporal convolutional networks, comprising: performing online identification using an identification network model trained in the offline stage;

[0007] The online identification method specifically includes: acquiring the measured response data of the target bridge at the current moment and constructing the system transfer matrix at the current moment;

[0008] The orthogonal matching pursuit algorithm is used to perform sparse inversion on the measured response data at the current time to obtain the initial estimated sequence of the moving load at the current time;

[0009] The same multi-scale feature construction is performed on the initial estimated sequence to generate the input feature matrix at the current time.

[0010] The input feature matrix at the current moment is input into the pre-trained recognition network model for a single forward calculation. The backbone network outputs the residual prediction component at the current moment, and the context-aware calibration head outputs the scaling factor and bias term at the current moment. The final recognition result of the moving load at the current moment is calculated. This final recognition result is equal to the scaling factor multiplied by the sum of the initial estimated sequence and the residual prediction component plus the bias term, and is output as the real-time recognition result of the current vehicle load.

[0011] Furthermore, the training method of the recognition network model in the offline stage specifically includes: acquiring sample measured response data of the sample bridge structure under the action of moving vehicle load, and constructing the system transfer matrix; using the orthogonal matching pursuit algorithm to perform sparse inversion solution on the sample measured response data to obtain the initial estimation sequence of the moving load;

[0012] Multi-scale feature construction is performed on the initial estimated sequence to generate an input feature matrix. The input feature matrix includes the initial estimated sequence itself, the first-order time difference of the initial estimated sequence, the second-order time difference of the initial estimated sequence, the statistical features of the initial estimated sequence, and the time code of the initial estimated sequence.

[0013] The input feature matrix is ​​input into a residual temporal convolutional network for temporal feature extraction. The residual temporal convolutional network includes multiple cascaded temporal convolutional modules and a context-aware calibration head. The backbone network outputs residual prediction components, and the context-aware calibration head outputs scaling factors and bias terms to obtain the prediction result of the moving load. The prediction result is equal to the scaling factor multiplied by the sum of the initial estimated sequence and the residual prediction components plus the bias term.

[0014] A progressive sparse reconstruction strategy is adopted, which dynamically updates the target load by iteratively calculating the structural response residual and compensating the residual load component based on the log-regularized objective function.

[0015] In each training cycle, the updated target load is used as the supervision signal, and the parameters of the residual temporal convolutional network are optimized and trained using the L2 norm loss function until the preset termination criterion is met. The training is then stopped and the trained recognition network model is saved.

[0016] Furthermore, in both the offline training phase and the online recognition process, the orthogonal matching pursuit algorithm is used to solve the sparse inversion problem and extract the sparse dominant dynamic components of the moving load from the measured response.

[0017] The optimization problem for sparse inversion using the orthogonal matching pursuit algorithm is expressed as follows: finding the variable values ​​when the objective function is minimized. The objective function is the measured response minus the square of the L2 norm of the system transfer matrix multiplied by the load dictionary multiplied by the sparse coefficient vector. The constraint is that the zero norm of the sparse coefficient vector is less than or equal to the preset target sparsity. The moving load is mapped to the sparse domain using a dictionary-based sparse representation method, i.e., the moving load is equal to the load dictionary multiplied by the sparse coefficient vector. The initial estimated sequence of the moving load is obtained by iteratively selecting the dictionary atom with the highest correlation to the current residual signal through the orthogonal matching pursuit algorithm.

[0018] Furthermore, the backbone network of the residual temporal convolutional network consists of multiple cascaded temporal convolutional network modules. Each temporal convolutional network module includes a one-dimensional dilated convolutional layer, a nonlinear activation function, Dropout regularization, and residual skip connections. Each level of the temporal convolutional network module is configured with an exponentially increasing dilation rate to simultaneously capture short-term local dynamic features and long-term temporal correlations in the input sequence. The backbone network outputs residual prediction components.

[0019] Furthermore, the context-aware calibration head aggregates the statistical features extracted during the multi-scale feature construction stage to form a global context vector. The global context vector is modeled by a multilayer perceptron containing fully connected layers, nonlinear activation functions, and Dropout regularization, and outputs the scaling coefficients and bias terms.

[0020] 6. The load identification method based on physical information residual temporal convolutional networks according to claim 2, characterized in that the progressive sparse reconstruction strategy specifically includes:

[0021] In the i-th training cycle, the structural response residual is calculated based on the moving load reconstructed in the previous training cycle. This residual is equal to the measured response minus the system transfer matrix multiplied by the moving load in the previous training cycle.

[0022] The residual load component is reconstructed by solving the residual sparsity coefficient through a log-regularized objective function. This residual load component is equal to the load dictionary multiplied by the residual sparsity coefficient. The residual sparsity coefficient is obtained by minimizing the log-regularized objective function. The log-regularized objective function is to calculate for each element the sum of the load dictionary multiplied by the system transfer matrix multiplied by the residual sparsity coefficient minus the absolute value of the structural response residual divided by the logarithm of the adaptive scaling parameter, and then sum over all elements.

[0023] The target load is updated to the initial estimated sequence plus the sum of the residual load components from each training cycle;

[0024] The adaptive scaling parameter is a parameter that controls the transition characteristics of the logarithmic function; the logarithmic regularization objective function is solved by combining the gradient descent algorithm and the Adam optimization algorithm.

[0025] Furthermore, the preset termination criterion includes: the relative change between two adjacent iterations of predicted load is less than 10. -6 .

[0026] Furthermore, the preset termination criterion also includes: the relative change between the structural response reconstructed from the identified load and the measured response is less than 10%. -6 .

[0027] Furthermore, the preset termination criterion also includes: the training cycle reaches the maximum number of iterations, 200.

[0028] On the other hand, a load identification system based on physical information residual temporal convolutional network is provided, including: an online identification module, which is used to perform online identification using the identification network model trained in the offline stage in the above technical solution.

[0029] This invention has at least the following beneficial effects: The method of this invention utilizes a pre-trained recognition network model from the offline stage for online recognition, and provides a complete step-by-step process for online recognition. A unified physical information moving load recognition framework integrating sparse inverse problem modeling and deep temporal feature learning is constructed, achieving the synergistic fusion of physical models and data-driven learning. A residual temporal convolutional network is designed to effectively learn the long-term and short-term dynamic evolution laws of moving loads through multi-scale temporal feature extraction. A self-supervised progressive sparse reconstruction strategy based on logarithmic regularization is proposed, achieving high-precision reconstruction of moving loads by iteratively compensating response residuals and dynamically updating the target load. By sharing the same feature construction and network forward computation logic between the defined online recognition method and the offline training stage, the consistency of data processing between the training and inference stages is ensured, improving the reliability and stability of the recognition results. This invention also provides a corresponding system, the beneficial effects of which are similar to the method, and will not be repeated here. This invention is mainly used in the field of artificial intelligence recognition technology. Attached Figure Description

[0030] The accompanying drawings are provided to further understand the technical solutions of the present invention and constitute a part of the specification. They are used together with the embodiments of the present invention to explain the technical solutions of the present invention, and do not constitute a limitation on the technical solutions of the present invention.

[0031] Figure 1 This is a flowchart of the online identification steps of a load identification method based on physical information residual temporal convolutional networks;

[0032] Figure 2 This is a flowchart illustrating the steps of the offline training method for identifying network models.

[0033] Figure 3 It is a two-dimensional vehicle-bridge coupling model that describes the interaction mechanism between vehicles and bridge structures;

[0034] Figure 4 This is the overall architecture of the PI-ResTCN framework;

[0035] Figure 5 It is the overall architecture of the residual temporal convolution backbone;

[0036] Figure 6 It is a framework process for self-supervised physical information residual temporal convolutional networks (PI-ResTCN);

[0037] Figure 7 This refers to the road surface roughness and the corresponding bridge response under RSR 'D'.

[0038] Figure 8 It compares the identification results of different vehicle types;

[0039] Figure 9 It is a comparison of time-domain recognition results under different sparsity levels;

[0040] Figure 10 It is a comparison of frequency domain recognition results under different sparsity levels;

[0041] Figure 11 This is a box plot of RPE at different noise levels;

[0042] Figure 12 This is a box plot of RPE under different road surface roughness conditions;

[0043] Figure 13 It is the experimental setup for MLI in the laboratory;

[0044] Figure 14 It is a comparison between the measured response and the updated finite element method generated response;

[0045] Figure 15 It is the time history of the identified moving payload;

[0046] Figure 16 It is the spectrum of the identified moving load. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0048] It should be noted that although functional modules are divided in the system diagram and the logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the system or the order in the flowchart. The terms "first," "second," etc., in the specification, claims, and the aforementioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0049] Before describing the embodiments of this technology, the system formed between the vehicle and the bridge will be explained. When a vehicle crosses the bridge, the bridge's vibration response is influenced by a combination of factors, including the characteristics of the vehicle's suspension system, the bridge's own dynamic characteristics, and road surface unevenness. Therefore, establishing an accurate Vehicle-Bridge Interaction (VBI) model is crucial for characterizing the bridge response and the vehicle's moving loads.

[0050] Road surface roughness (RSR) introduces additional stochastic excitation into the vehicle-bridge coupled system, thereby altering the dynamic response characteristics of both the vehicle and the bridge, and further affecting the accuracy of Moving Load Identification (MLI). This paper describes road surface roughness based on the Power Spectral Density (PSD) model recommended by the ISO 8608 standard, whose spatial power spectral density function is expressed as: (1);

[0051] in, For the spatial frequency of the road surface; Reference spatial frequency; The road surface roughness coefficient is the reference spatial frequency.

[0052] To generate random road surface irregularities in the spatial domain, this paper employs the Harmonic Superposition Method, which synthesizes the road surface irregularity signal by superimposing a series of harmonic components with random initial phases. The expression for this method is as follows: (2);

[0053] Where N is the total number of discrete frequency components; Frequency interval; To conform to the interval [0, Uniformly distributed random phase angles.

[0054] refer to Figure 3 , Figure 3 This is a two-dimensional vehicle-bridge coupling model describing the interaction mechanism between the vehicle and the bridge structure. In this model, the bridge structure is simulated using an Euler–Bernoulli beam, whose main parameters include the bridge span L, mass per unit length ρ, bending stiffness EI, and damping coefficient C. The vehicle subsystem adopts a four-degree-of-freedom half-vehicle model, consisting of the vehicle body, front and rear suspension systems, and front and rear wheels.

[0055] Assume the degrees of freedom of the vehicle subsystem and the bridge subsystem are respectively and The number of wheel bridge contact points is The motion equations of the vehicle subsystem can then be expressed as:

[0056] (3);

[0057]

[0058] in, , and These represent the mass matrix, damping matrix, and stiffness matrix of the vehicle subsystem, respectively. Their corresponding submatrices describe the suspension coupling effect and geometric relationship between the vehicle body and tires. Specific definitions of the relevant parameters are provided in Appendix A. L This is a geometric distribution matrix used to map the local interaction forces at the wheel axle contact point into generalized forces acting on the vehicle's center of mass; and These represent the vertical displacement and pitch angle of the vehicle body, respectively. and These represent the vertical displacements of the front and rear wheels, respectively.

[0059] The interaction force at the i-th wheel bridge contact point It can be represented as:

[0060] (4);

[0061] in, This indicates the vertical displacement of the bridge at the wheel-bridge contact point; This refers to the road surface unevenness at the corresponding location; Let be the static wheel load corresponding to the i-th wheel.

[0062] Based on d'Alembert's principle, by coupling the vehicle subsystem and the bridge subsystem through wheel-bridge contact conditions, the dynamic equations of the vehicle-bridge coupled system (VBI) can be established:

[0063] (5);

[0064] in, , and These are the mass matrix, damping matrix, and stiffness matrix of the bridge subsystem, respectively. Let C be the generalized displacement vector of the bridge. The coupling matrix is ​​C. bb C bv C bv K bb K bv and K bv Both parameters change continuously with the vehicle's position, used to describe the dynamic coupling between the vehicle and the bridge. The corresponding coupling matrix and excitation vector can be expressed as:

[0065] (6);

[0066] in, The position mapping matrix changes over time and is used to distribute the wheel-bridge contact force to the corresponding nodes of the bridge, thereby establishing a dynamic coupling relationship between the vehicle and the bridge.

[0067] refer to Figure 1 and Figure 2 , Figure 1 This is a flowchart illustrating the steps of an online load identification method based on physical information residual temporal convolutional networks. Figure 2 This is a flowchart illustrating the steps involved in the offline training method for identifying network models.

[0068] To address the problems existing in the prior art, this application discloses a load identification method based on a physical information residual temporal convolutional network. The load identification method based on the physical information residual temporal convolutional network is executed by an intelligent device. When the intelligent device executes the method, the steps include: performing online identification using an identification network model trained offline.

[0069] The online identification method specifically includes: S100, acquiring the measured response data of the target bridge at the current moment, and constructing the system transfer matrix at the current moment;

[0070] S200. The orthogonal matching pursuit algorithm is used to perform sparse inversion on the measured response data at the current time to obtain the initial estimated sequence of the moving load at the current time.

[0071] S300. Perform the same multi-scale feature construction on the initial estimated sequence to generate the input feature matrix at the current time.

[0072] S400. Input the current input feature matrix into the pre-trained recognition network model for a single forward calculation. The backbone network outputs the residual prediction component at the current time, and the context-aware calibration head outputs the scaling factor and bias term at the current time. Calculate the final recognition result of the moving load at the current time. The final recognition result is equal to the scaling factor multiplied by the sum of the initial estimated sequence and the residual prediction component plus the bias term, and is output as the real-time recognition result of the current vehicle load.

[0073] The following is a specific practical example to further illustrate this technical solution. For instance, in the actual deployment of a bridge structural health monitoring system, a three-span continuous steel box girder bridge has pre-completed the offline training phase of the network model training, and the trained recognition network model parameters have been permanently stored in the on-site industrial control computer.

[0074] When a heavy-duty truck crosses the bridge at a speed of 60 kilometers per hour, strain sensors and acceleration sensors deployed at key sections of the bridge deck collect structural response signals in real time at a sampling frequency of 200 Hz, and transmit the signals to the industrial control computer through a data acquisition card.

[0075] The industrial control computer first receives the measured response data collected at the current moment. This data contains 3200 sampling points from 8 measuring channels within a 2-second time window. Based on the bridge finite element model, it constructs the system transfer matrix at the current moment. This matrix has a dimension of 3200 rows multiplied by 150 columns, where 150 represents the time history degrees of freedom of the moving load to be identified.

[0076] Subsequently, the system calls the orthogonal matching pursuit algorithm to perform sparse inversion solution on the measured response data. The algorithm sets the target sparsity to 30. After 30 iterations, it obtains the initial estimation sequence of the moving load at the current time. This sequence contains load amplitude estimates at 150 discrete time points.

[0077] The system further constructs multi-scale features from the initial estimated sequence, calculates its first-order and second-order time differences, extracts the mean (0.87) and standard deviation (0.23) of the sequence as statistical features, and introduces temporal position encoding. The five feature components are stacked to form an input feature matrix of dimension 150 x 5. The industrial control computer inputs this feature matrix into a pre-loaded, trained recognition network model in the graphics processor's memory. The model performs a single forward propagation calculation. The residual temporal convolutional backbone network extracts temporal features through six layers of dilated convolutional modules and outputs residual prediction components. The context-aware calibration head outputs a scaling factor of 1.02 and a bias term of -0.08 based on the aggregated global context vector. Finally, the system calculates the final recognition result of the moving load at the current moment, which is the dynamic load time history of the heavy-duty truck acting on each axis of the bridge at the current moment. The system stores this result in a local database and uploads it to the cloud monitoring platform, completing one real-time recognition cycle.

[0078] This embodiment utilizes a pre-trained recognition network model from the offline phase for online recognition and provides a complete step-by-step flowchart for online recognition. A unified physical information moving load recognition framework integrating sparse inverse problem modeling and deep temporal feature learning is constructed, achieving a synergistic fusion of physical models and data-driven learning. A residual temporal convolutional network is designed to effectively learn the long-term and short-term dynamic evolution laws of moving loads through multi-scale temporal feature extraction. A self-supervised progressive sparse reconstruction strategy based on log-regularization is proposed, achieving high-precision reconstruction of moving loads by iteratively compensating response residuals and dynamically updating the target load. By sharing the same feature construction and network forward computation logic between the online recognition method and the offline training phase, consistency in data processing between the training and inference phases is ensured, improving the reliability and stability of the recognition results.

[0079] Specifically, the training method for the offline stage of the identification network model includes: S401, obtaining the measured response data of the sample bridge structure under the action of moving vehicle load, and constructing the system transfer matrix;

[0080] S402. The orthogonal matching pursuit algorithm is used to perform sparse inversion on the measured response data of the sample to obtain the initial estimated sequence of the moving load;

[0081] S403. Perform multi-scale feature construction on the initial estimated sequence to generate an input feature matrix. The input feature matrix includes the initial estimated sequence itself, the first-order time difference of the initial estimated sequence, the second-order time difference of the initial estimated sequence, the statistical features of the initial estimated sequence, and the time code of the initial estimated sequence.

[0082] S404. Input the input feature matrix into the residual temporal convolutional network for temporal feature extraction. The residual temporal convolutional network includes multiple cascaded temporal convolutional modules and a context-aware calibration head. The backbone network outputs residual prediction components, and the context-aware calibration head outputs scaling factors and bias terms to obtain the prediction result of the moving load. The prediction result is equal to the scaling factor multiplied by the sum of the initial estimated sequence and the residual prediction components plus the bias term.

[0083] S405. A progressive sparse reconstruction strategy is adopted, which calculates the structural response residuals iteratively and compensates the residual load components based on the log-regularized objective function, and dynamically updates the target load.

[0084] In each training cycle, the updated target load is used as a supervision signal, and the parameters of the residual temporal convolutional network are optimized and trained using the L2 norm loss function until the preset termination criterion is met, at which point the training stops and the trained recognition network model is saved.

[0085] In this embodiment, sparse initialization of physical information is performed using the orthogonal matching pursuit algorithm. This provides the network with an initial load estimate that conforms to structural dynamics before training begins, effectively reducing the network parameter search space and accelerating training convergence. Multi-scale feature construction combines first-order difference, second-order difference, statistical features, and temporal encoding with the initial load sequence to form an input feature matrix. This enables the network to simultaneously perceive load amplitude information, variation trends, global statistical characteristics, and temporal location information, significantly improving the network's ability to learn the dynamic evolution of loads. The residual temporal convolutional network, combined with a backbone network and a context-aware calibration head, employs a dual-module design. This allows for the extraction of multi-scale temporal dependencies and the adaptive calibration of prediction results using global statistical information, improving the accuracy and robustness of load identification. The progressive sparse reconstruction strategy compensates for response residuals periodically and dynamically updates the target load, achieving progressive optimization of the target load without requiring real labels, effectively solving the problem of scarce labeled data in engineering applications. The L2 norm loss function, combined with a preset termination criterion, avoids unnecessary iterative calculations while ensuring training accuracy, thus improving training efficiency.

[0086] In some further specific embodiments, the orthogonal matching pursuit algorithm is used for sparse inversion solution in both the offline training stage and the online recognition process to extract the sparse dominant dynamic components of the moving load from the measured response;

[0087] The optimization problem for sparse inversion using the orthogonal matching pursuit algorithm is expressed as: finding the variable values ​​when the objective function is minimized. The objective function is the measured response minus the square of the L2 norm of the system transfer matrix multiplied by the load dictionary multiplied by the sparse coefficient vector. The constraint is that the zero norm of the sparse coefficient vector is less than or equal to the preset target sparsity. A dictionary-based sparse representation method is used to map the moving load to the sparse domain, i.e., the moving load is equal to the load dictionary multiplied by the sparse coefficient vector.

[0088] The specific mathematical expression is: ;

[0089] in, It is a sparse coefficient vector. To preset the target sparsity, a dictionary-based sparse representation method is used to map the moving load to the sparse domain, i.e. ,in A predefined load dictionary.

[0090] The initial estimated sequence of the moving load is obtained by iteratively selecting dictionary atoms that are most correlated with the current residual signal using the orthogonal matching pursuit algorithm.

[0091] In this specific embodiment, the optimization problem of solving the orthogonal matching pursuit sparse inversion problem is defined by specific mathematical expressions and constraints. By explicitly specifying that the sparse constraint is less than or equal to T, the moving load identification problem is transformed into a sparse coefficient solving problem. This fully utilizes the sparse prior characteristics of the moving load in the dictionary domain, fundamentally improving the solution stability of the ill-conditioned inverse problem. A dictionary-based sparse representation method is used to map the moving load to the sparse domain, overcoming the problem that the moving load in the original time domain usually lacks sparsity, enabling the orthogonal matching pursuit algorithm to effectively identify the main sparse components of the load. The orthogonal matching pursuit algorithm iteratively selects dictionary atoms with the highest correlation to the current residual signal, ensuring the algorithm's convergence speed. Simultaneously, it can gradually refine the sparse coefficient estimation during the iteration process, achieving a good balance between noise resistance and computational efficiency. Fourth, this technical feature is applicable to both offline training and online identification stages, ensuring the consistency of the physical information initialization method during training and inference, and avoiding additional errors introduced by different initialization methods.

[0092] In some further specific embodiments, the backbone network of the residual temporal convolutional network consists of multiple cascaded temporal convolutional network modules. Each temporal convolutional network module includes a one-dimensional dilated convolutional layer, a nonlinear activation function, Dropout regularization, and residual skip connections. Each level of the temporal convolutional network module is configured with an exponentially increasing dilation rate to simultaneously capture short-term local dynamic features and long-term temporal correlations in the input sequence. The backbone network outputs residual prediction components.

[0093] By combining one-dimensional dilated convolutional layers with an exponentially increasing dilation rate, the network exponentially expands its effective receptive field without increasing the number of parameters. This allows it to simultaneously capture short-term local dynamic features in the input sequence, such as the impact response of a vehicle passing through a single axle, and long-term temporal correlations, such as load patterns during continuous multi-axle passage. This provides a powerful representation of the multi-scale temporal characteristics of moving loads. Residual skip connections in each temporal convolutional network module provide a direct propagation path for gradients, effectively mitigating the vanishing gradient problem in deep network training and enabling the network to be trained smoothly to 8 layers or even deeper. The introduction of the GELU nonlinear activation function enables the network to fit complex nonlinear mappings, while Dropout regularization randomly discards neuron outputs with a certain probability, effectively suppressing overfitting and improving the model's generalization performance. The temporal preservation design of the backbone network ensures consistent input and output sequence lengths, facilitating seamless integration with the context-aware calibration head and simplifying the network architecture design.

[0094] In some further specific embodiments, the context-aware calibration head aggregates the statistical features extracted in the multi-scale feature construction stage to form a global context vector. The global context vector is modeled by a multilayer perceptron containing fully connected layers, non-linear activation functions, and Dropout regularization, and outputs the scaling coefficients and bias terms.

[0095] By effectively reusing the statistical features extracted during the multi-scale feature construction stage to the calibration head, information sharing between feature extraction and result calibration is achieved, improving the efficiency of network parameter utilization. The global context vector compresses and represents the amplitude level and dispersion of the entire load sequence. Based on this global information, the multilayer perceptron adaptively generates affine transformation parameters, ensuring that the final prediction result remains consistent with the initial estimate and residual prediction in a global statistical sense, avoiding the cumulative amplification of local prediction biases. The affine calibration mechanism of scaling factor 'a' and bias term 'b' is simple in structure and computationally efficient, requiring only a few additional parameters to achieve global adjustment of the prediction result without significantly increasing the computational burden on the network. The lightweight multilayer perceptron design of the calibration head includes Dropout regularization, effectively preventing overfitting to the calibration parameters themselves during the training phase and ensuring the generalization ability of the calibration coefficients on new data.

[0096] In some further specific embodiments, the progressive sparse reconstruction strategy specifically includes: in the i-th training cycle, calculating the structural response residual based on the moving load reconstructed in the previous training cycle, the residual being equal to the measured response minus the system transfer matrix multiplied by the moving load in the previous training cycle.

[0097] The residual load component is reconstructed by solving the residual sparsity coefficient through a log-regularized objective function. This residual load component is equal to the load dictionary multiplied by the residual sparsity coefficient. The residual sparsity coefficient is obtained by minimizing the log-regularized objective function. The log-regularized objective function is to calculate for each element the sum of the load dictionary multiplied by the system transfer matrix multiplied by the residual sparsity coefficient minus the absolute value of the structural response residual divided by the logarithm of the adaptive scaling parameter, and then sum over all elements.

[0098] The target load is updated to the initial estimated sequence plus the sum of the residual load components from each training cycle;

[0099] The adaptive scaling parameter is a parameter that controls the transition characteristics of the logarithmic function; the logarithmic regularization objective function is solved by combining the gradient descent algorithm and the Adam optimization algorithm.

[0100] The residual load components are reconstructed using a log-regularized objective function. This objective function effectively suppresses the impact of abnormal residual fluctuations on the optimization process without introducing additional regularization parameters, and is inherently robust to measurement noise and modeling errors. The adaptive scaling parameter is dynamically set according to the current residual distribution characteristics, ensuring that the transition interval of the logarithmic function adaptively matches the current residual magnitude, thus improving the accuracy and stability of residual reconstruction. The gradient descent algorithm combined with the Adam optimizer solves the logarithmic objective function, guaranteeing efficient convergence in the residual sparse coefficient solution process, and the adaptive learning rate characteristic of the Adam optimizer reduces the workload of manual parameter tuning.

[0101] In some further specific embodiments, the preset termination criterion includes the following three termination conditions: the relative change between two adjacent iterations of predicted load is less than 10. -6 The relative change between the structural response reconstructed from the identified loads and the measured response is less than 10%. -6 The training cycle reaches the maximum number of iterations, 200. The offline training phase stops when any one of the termination conditions is met.

[0102] The technical solution will now be described in more detail.

[0103] By establishing a linear mapping relationship between the bridge structural response and the moving vehicle load, the Moving Load Identification (MLI) problem can be formulated as an inverse dynamics problem. Under the assumption that the structure satisfies linear elasticity, the measured response of the bridge can be expressed as: (7);

[0104] in, Transfer matrix for the system; and These represent the structural response measurement vector and the moving load vector, respectively; This indicates measurement noise.

[0105] Because the inverse problem described by equation (7) is typically ill-conditioned, existing model-driven and data-driven methods often struggle to balance physical consistency, recognition accuracy, and computational efficiency. Therefore, this paper proposes a self-supervised Physical Information Residual Temporal Convolutional Network (PI-ResTCN) framework that integrates a progressive sparse reconstruction strategy. Figure 4 As shown, Figure 4 This is the overall architecture of the PI-ResTCN framework. The framework consists of three interconnected phases.

[0106] First, the Orthogonal Matching Pursuit (OMP) algorithm is used for sparse initialization of physical information. The initial estimate of the moving load is obtained based on the measured response of the bridge, and the initial load is projected onto a multi-scale feature space to construct the network input features.

[0107] Secondly, a Residual Temporal Convolutional Network (ResTCN) is designed to establish a nonlinear temporal mapping relationship between the initial load characteristics and the target load, thereby fully exploring the multi-scale temporal dependency characteristics of the moving load.

[0108] Finally, to address the problem of obtaining accurate moving load labels in practical engineering, a progressive sparse reconstruction strategy is proposed. The target load is iteratively updated through self-supervised learning, and the network training process is gradually optimized without the need for real label supervision, thereby achieving high-precision identification of moving loads.

[0109] Existing deep learning-based Moving Load Identification (MLI) methods typically use the measured structural response as the network input. However, this input method inevitably contains a large amount of redundant information, which not only easily obscures the dominant features of the moving load but also increases the difficulty of network training. To extract physically meaningful load-related features, this paper introduces the Orthogonal Matching Pursuit (OMP) algorithm as a sparse inversion method for physical information, extracting the sparse dominant dynamic components of the moving load from the measured response. The corresponding sparse inversion problem can be expressed as:

[0110] (8);

[0111] Among them, due to moving loads Since it typically lacks sparsity in the original time domain, a dictionary-based sparse representation method is used to map it to the sparse domain, i.e. .in, For a predefined load dictionary, For the corresponding sparse coefficient vector, The target sparsity is set as a preset value.

[0112] The OMP algorithm iteratively selects dictionary atoms that are most correlated with the current residual signal, effectively suppressing noise interference while extracting the most representative structural dynamic features. After sparse inversion solving, an initial estimation sequence of the moving load can be obtained. .

[0113] Building upon this foundation, to further characterize the temporal evolution, local dynamic changes, and global statistical information of moving loads, this paper constructs a multi-scale feature representation, whose input feature matrix is ​​defined as: (9);

[0114] in, and These represent the first-order and second-order time difference operators of the initial load sequence, used to describe the rate of load change and its trend. This represents the statistical characteristics extracted from the initial load sequence, including the mean and standard deviation. The time code representing the initial load sequence is used to enhance the network's ability to express temporal location information.

[0115] To effectively capture the long-term temporal dependencies and transient dynamics inherent in the input features, this paper employs a Residual Temporal Convolutional Network (ResTCN) as the temporal feature extraction module. This network consists of two parts: a residual temporal convolutional backbone network and a context-aware calibration head.

[0116] (1) Residual temporal convolutional backbone network;

[0117] The residual temporal convolutional backbone network serves as the core dynamic feature extractor of the proposed framework. For example... Figure 5 As shown, Figure 5 This is the overall architecture of the residual temporal convolutional backbone. The backbone network consists of multiple cascaded temporal convolutional network blocks (TCN blocks). Each TCN block includes a one-dimensional dilated convolution, a non-linear activation function, Dropout regularization, and residual skip connections. To expand the network's effective receptive field while maintaining temporal resolution, each TCN block is configured with an exponentially increasing dilation factor. This design enables the network to simultaneously model both short-term local fluctuations and long-term temporal correlations in the input sequence, thereby achieving a full representation of multi-scale dynamic information.

[0118] After multi-layer TCN module extraction, a high-level temporal feature representation can be obtained. Subsequently, the backbone network outputs a residual load correction term, denoted as... .

[0119] (2) Context-aware calibration head;

[0120] To further utilize global statistical information for adaptive calibration of residual prediction results, this paper introduces a context-aware calibration head. Specifically, the statistical descriptors extracted during the multi-scale feature construction stage are first aggregated to form a compact global context vector. This context vector is then modeled using a lightweight multilayer perceptron (MLP) consisting of a fully connected layer (FC), a nonlinear activation function, and dropout regularization. The calibration head ultimately outputs two affine transformation parameters: a scaling factor (a) and a bias term (b). The final moving load prediction result is expressed as:

[0121] (10);

[0122] (3) Network training and hyperparameter setting;

[0123] ResTCN is trained using the AdamW optimizer, which effectively decouples weight decay from gradient-based parameter updates, thereby improving the model's generalization ability and training stability. Furthermore, this paper introduces a cosine annealing warm restarts learning rate scheduling strategy to achieve a smoother optimization process, accelerate model convergence, and enhance the robustness of the training process against local optima. The key optimization hyperparameters of the proposed ResTCN are shown in Table 1. Table 1 shows the ResTCN hyperparameter settings.

[0124]

[0125] Table 1.

[0126] Although initialization based on Orthogonal Matching Pursuit (OMP) can obtain the main components of the moving load, weaker dynamic components are often difficult to recover effectively due to sparsity constraints and noise suppression effects. To reconstruct these missing dynamic details, this paper proposes a Progressive Sparse Reconstruction (PSR) strategy for self-supervised learning. This strategy achieves progressive and refined reconstruction of the target load by gradually compensating and iteratively optimizing the residual components, thereby continuously improving the reconstruction quality of the target load.

[0127] However, response residuals are highly sensitive to measurement noise. To enhance the model's robustness to outliers and random perturbations, this paper introduces a logarithmic function as a smooth and robust optimization criterion. Existing research has shown that this logarithmic objective function can effectively suppress the impact of abnormal residual fluctuations on the optimization process without introducing additional regularization parameters.

[0128] In the i-th training epoch, the target load update process includes the following three steps.

[0129] Step 1: Residual Response Calculation; Based on the initial moving load identified by the OMP algorithm, calculate the structural response residuals: (11); among which, This represents the moving load reconstructed in the previous training cycle.

[0130] Step 2: Sparse residual compensation;

[0131] The residual load components are reconstructed by solving the following logarithmic optimization objective function: (12); among which, Represents the residual sparsity coefficient The number of elements, To control the adaptive scaling parameter of the logarithmic function's transition characteristics, equation (12) is solved using a combination of gradient descent and Adam optimization algorithms.

[0132] Step 3: Target load update; After completing sparse residual compensation, the target load is updated as follows: (13); where N represents the number of training cycles of ResTCN.

[0133] After obtaining the updated target payload in each training cycle, the network parameters are optimized using the L2 norm loss function: (14);

[0134] To avoid unnecessary iterations and improve computational efficiency, this paper sets the following termination criteria: (1) The relative change between the predicted loads of two adjacent iterations is less than 10. -6 (2) The relative change between the structural response obtained from the identified load reconstruction and the measured response is less than 10%. -6 (3) The training cycle reaches the maximum number of iterations of 200.

[0135] The training process stops when any one of the termination conditions is met. See also... Figure 6 , Figure 6 It is a framework process for self-supervised physical information residual temporal convolutional networks (PI-ResTCN).

[0136] To verify the effectiveness and robustness of the method presented in this technical solution, this paper establishes the following... Figure 3 The vehicle-bridge interaction (VBI) model is shown. The bridge is simulated using a simply supported Euler-Bernoulli beam model, with the following main parameters: span L = 36 m, flexural stiffness EI = 2.3 × 10⁻⁶ m. 10 N·m 2 Mass per unit length ρ = 5 × 10 3 kg / m, and a uniform modal damping ratio ξ = 0.02 is used for all vibration modes.

[0137] To simulate different axle arrangement configurations and load characteristics, this paper constructs three representative vehicle models, denoted as Type 1, Type 2, and Type 3, with detailed mechanical parameters listed in Table 2. Table 2 shows the parameters of the different vehicle models. Type 3 differs from Type 1 only in geometric parameters and is used to further investigate the impact of axle load distribution on the performance of moving load identification. Figure 7 The pavement roughness profile under the international road surface roughness (RSR) level D condition and the vertical response of the bridge generated by the vehicle-bridge coupling system are presented.

[0138]

[0139] Table 2.

[0140] Table 3 summarizes four response combinations constructed based on the structural responses measured at the 1 / 4, 1 / 2, and 3 / 4 spans of the bridge, used to study the impact of different sensor information combinations on the accuracy of Moving Load Identification (MLI). The sampling frequency for all numerical simulations was uniformly set to 50 Hz.

[0141] Sensor cases Number of input responses Response combinations 1 3 1 / 4m & 1 / 2m & 3 / 4m 2 3 1 / 4m & 1 / 2m & 1 / 2a 3 4 1 / 4m & 1 / 2m & 3 / 4m & 1 / 2a 4 4 1 / 4m&1 / 2m&1 / 2a&3 / 4a

[0142] Table 3.

[0143] Table 3 shows the response combination settings. In Table 3, "m" and "a" represent the bridge bending moment and acceleration response, respectively; 1 / 4, 1 / 2, and 3 / 4 correspond to the measurement positions of bridge spans L / 4, L / 2, and 3L / 4, respectively.

[0144] The results of vehicle load identification are discussed below.

[0145] During training, vehicle speed *v* and vehicle mass *mv* are used as randomly varying parameters to enhance the generalization ability of the proposed method under complex vehicle operating conditions. Specifically, vehicle speed is randomly sampled within the interval [10, 30] m / s, and vehicle mass is randomly selected within the interval [10000, 20000] kg. Based on the three vehicle parameters given in Table 2, and combined with the generated vehicle speed and mass, the bridge bending moment and acceleration response corresponding to different measuring point locations can be obtained.

[0146] Subsequently, the OMP (Orthogonal Matching Pursuit) algorithm is used to initially identify moving loads from noisy response measurements, and the identification results are further converted into multi-scale features, which are used as input features for ResTCN. It should be noted that when using the OMP algorithm for initial load identification, it is not necessary to pre-define the true sparsity of the vehicle loads.

[0147] For three different vehicle types, 200 sets of simulation samples were generated for each type, totaling 600 sets of samples for training the self-supervised network. The dataset was divided into training and test sets in a 4:1 ratio. Unless otherwise stated, all numerical simulations were conducted under the RSR "D" condition.

[0148] In the initial load identification process, a dictionary constructed from cosine basis functions is used to represent sparse dynamic components, and its mathematical expression is as follows:

[0149] (15);

[0150] Among them, t i This represents the i-th discrete sampling time within the time interval [0, T], and n represents the number of columns in the dictionary matrix, which determines the frequency resolution of the dictionary.

[0151] To simulate the structural response under real measurement conditions, Gaussian white noise is introduced into the bridge response signal. The corresponding noisy response can be expressed as: (16);

[0152] Among them, Y n Y and Y represent the noisy and noiseless bridge responses, respectively; The noise level is set; P is the total number of elements in the response vector Y; rand represents a Gaussian white noise vector that follows a standard normal distribution.

[0153] Furthermore, the relative percentage error (RPE) is used as a quantitative evaluation index to assess the accuracy of the proposed moving load identification method, and its definition is as follows: (17); among which, and These represent the actual vehicle load and the identified vehicle load, respectively.

[0154] For different sensor operating conditions, the sparsity was set to 20 and the noise level to 5% during model training. Subsequently, the trained model was compared with the OMP method in terms of moving load recognition performance, and the corresponding recognition results are summarized in Table 4. Table 4 compares the recognition results obtained by different methods at a 5% noise level.

[0155]

[0156] Table 4.

[0157] As shown in Table 4, under all test conditions, the proposed PI-ResTCN method demonstrates superior accuracy and robustness compared to the OMP method in both front and rear axle load identification. For Type 1 and Type 3 vehicles, the RPE of the PI-ResTCN method consistently remains within a narrow range of 1.59%–3.39%; while the RPE of the OMP method in front axle load identification typically exceeds 5%, and in some conditions, the rear axle RPE even exceeds 10%. Although the OMP method shows some improvement in Type 2 vehicles, with an RPE of approximately 3%–6%, its overall identification accuracy is still lower than that of the proposed PI-ResTCN method. Especially under sensor condition 4, PI-ResTCN can further reduce the RPE of both front and rear axle loads to approximately 1%.

[0158] Furthermore, when bending moment and acceleration responses are used in combination, both methods achieve relatively better identification results. This indicates that multi-source response measurements can provide more complete frequency domain information related to vehicle loads. Among them, the bending moment response is more sensitive to low-frequency load components, while the acceleration response is better at capturing high-frequency dynamic effects. The combination of the two helps to improve the observability and identifiability of the moving load identification (MLI) problem.

[0159] To more intuitively compare the recognition results of the two methods, Figure 8 Load identification time history curves for different vehicle types under sensor condition 2 are presented. It can be seen that the proposed PI-ResTCN method can accurately reconstruct the load time history of various vehicles, showing a high degree of consistency with the actual load. For both front and rear axle moving loads, this method can effectively capture the changing trend and dynamic fluctuation characteristics of the load amplitude. In contrast, although the OMP method can recover the overall trend of load evolution to some extent, it still has significant deviations in peak amplitude, local oscillations, and fine-scale dynamic characteristics. This deficiency mainly stems from the fact that, when the actual sparsity is unknown, the OMP method relies on preset sparsity parameters to select atoms from the load dictionary to reconstruct the signal. However, vehicle-bridge coupled loads simultaneously contain low-frequency and complex high-frequency components caused by road surface unevenness, resulting in complex time-frequency characteristics. The preset atom set often fails to fully represent the complete characteristics of the actual load, leading to amplitude distortion and frequency deviation in the identification results.

[0160] The PI-ResTCN method does not rely on a single fixed sparse representation, but introduces a stepwise sparse reconstruction mechanism based on the initial OMP estimate. By continuously mining the unexplained load information in the residual response, it iteratively compensates and corrects the missing load components, thereby effectively reducing the bias caused by the preset sparse parameters and significantly improving the ability to identify complex dynamic loads.

[0161] Overall, the proposed PI-ResTCN method not only possesses excellent feature extraction capabilities and good generalization performance across vehicle types, but also continuously utilizes effective components in the residual information through a stepwise sparse reconstruction strategy, thereby achieving more accurate and reliable mobile load identification results.

[0162] To evaluate the robustness of the proposed method to the preset sparsity parameters, five sparsity levels were further considered: 10, 20, 30, 40, and 50. The proposed method was compared with the OMP method under different sparsity settings, and the corresponding recognition results are summarized in Table 5. Table 5 compares the recognition results of the proposed method and OMP at different sparsity levels.

[0163]

[0164] Table 5.

[0165] As shown in Table 5, the proposed method exhibits significant robustness to variations in the preset sparsity. When the sparsity increases from 10 to 50, the RPE of the front axle load remains consistently within the range of 2.88%–3.55%, while the RPE of the rear axle load fluctuates only slightly between 2.03%–2.44%. However, the OMP method shows a clear dependence on the preset sparsity, with its front and rear axle RPEs varying between 6.21%–7.53% and 7.55%–9.78%, respectively, indicating a significant decrease in recognition accuracy compared to the proposed PI-ResTCN method.

[0166] Figure 9 and Figure 10 The comparison results of the moving load time histories and their corresponding power spectral density (PSD) identified by the two methods are presented for sparsity of 10, 30, and 50. It can be clearly observed that even with significant changes in the preset sparsity parameters, the PI-ResTCN method can still accurately reconstruct the load time histories and their spectral characteristics, further demonstrating that the trained PI-ResTCN model has strong robustness to changes in sparsity parameters.

[0167] In contrast, OMP-based identification results are highly sensitive to sparsity parameters. When the sparsity is set to 10, the rear axle load identification is significantly underestimated due to the limited number of available atoms, and many high-frequency dynamic components cannot be effectively recovered, such as... Figure 10 As shown in (a), with increasing sparsity, the number of atoms available for signal representation increases, and the recognition results gradually improve in terms of frequency component and amplitude accuracy. However, even at higher sparsity settings, there are still significant differences between the recognition results and the actual load.

[0168] Therefore, compared with the OMP method, the PI-ResTCN method significantly reduces the dependence on prior sparsity parameters and has better applicability in real-world engineering applications, since the true sparsity is usually difficult to determine accurately in real-world scenarios.

[0169] Existing deep learning-based load identification methods are typically limited by fixed input and output dimensions. When vehicle speed changes, signal length, time-frequency distribution, and dynamic characteristics all alter, often requiring model reconstruction or retraining. In contrast, the proposed PI-ResTCN method is not limited by input feature dimensions, can directly process data acquired under different vehicle speed conditions, and exhibits stronger generalization ability. Table 6 presents the load identification results of this method at different vehicle speeds.

[0170]

[0171] Table 6.

[0172] It can be observed that the proposed method exhibits high recognition accuracy for all three vehicle types within a speed range of 10–30 m / s. The RPE of both front and rear axle loads remains at a low level, with all results controlled within 5%, indicating that the method has a strong adaptability to changes in vehicle speed.

[0173] It is worth noting that the recognition accuracy decreases slightly at vehicle speeds of 10 m / s and 30 m / s compared to the 15–25 m / s range. For example, for Type 1 vehicles, at 20 m / s, the RPE (Relative Performance Equivalent) for front and rear axle loads is 3.21% and 2.27%, respectively; while at 10 m / s, these figures increase to 4.31% and 3.52%, and at 30 m / s, they are 3.88% and 2.89%, respectively. This phenomenon can be attributed to the boundary effect of the speed distribution in the training data. Specifically, the training data covers a speed range of 10–30 m / s, with 10 m / s and 30 m / s at the extremes of the distribution. In the generalization process of machine learning, boundary samples typically have low data density, resulting in a relatively weak feature representation ability of the model in this region, which in turn leads to a certain degree of error amplification.

[0174] Although the boundary effect affects the generalization consistency of the model across the entire velocity domain to some extent, the model's adaptability to endpoint conditions can be further improved by increasing the sample density in the velocity distribution boundary interval.

[0175] To further analyze the stability and robustness of the trained model under random measurement noise, the test response was regenerated based on vehicle type A and sensor condition 2, and noise levels of 5%, 10% and 15% were introduced into the response, respectively. Figure 11Box plots of the moving load identification results (RPE) under three noise levels are presented. For each noise scenario, 10 independent random noise implementations were generated and superimposed on the response measurement to evaluate the statistical reliability of the proposed method.

[0176] It can be observed that with increasing noise levels, the relative accuracy (RPE) of both front and rear axle loads generally increases, while the error distribution range gradually widens. This trend indicates that measurement noise inevitably reduces the accuracy of moving load identification (MLI). Under 5% noise conditions, the RPE distribution is concentrated and the median is low, indicating high identification accuracy and strong statistical stability. When the noise level increases to 10% and 15%, the increase in interquartile range and whisker length indicates increased uncertainty in the identification results. However, the corresponding median RPE remains at a low level, showing only a slight increase.

[0177] Furthermore, no significant outliers were observed in the identification results obtained from different random noise levels across all noise levels. This result further validates that the proposed method can effectively preserve key load-related feature information while suppressing the influence of high-frequency random noise.

[0178] Figure 12 RPE box plots of moving load identification results under different RSR (Road Roughness Rating) conditions are presented. According to ISO standards, the road profile is divided into five levels, A–E, and 10 independent random seeds are considered for each roughness level.

[0179] It can be observed that as the RSR level gradually deteriorates from Class A to Class E, the RPE of both front and rear axle loads generally shows an upward trend. This degradation in recognition accuracy is mainly due to the enhanced road surface excitation, which introduces stronger random fluctuations and high-frequency dynamic disturbances into the vehicle-bridge interaction response, thereby increasing the difficulty of moving load identification (MLI).

[0180] For relatively smooth Class A and Class B pavements, both the front and rear axle load identification errors exhibit narrow interquartile ranges and low medians, indicating that the proposed method can stably and accurately identify moving load information. As pavement roughness increases, the error distribution gradually becomes more discrete, reflecting the enhanced influence of dynamic disturbances caused by pavement excitation. However, even under high roughness conditions, the error distribution remains within a reasonable range of concentration, demonstrating that the proposed method maintains good stability and robustness under high roughness conditions.

[0181] To facilitate laboratory experiments on this technical solution, the experimental model design is described below.

[0182] A vehicle-bridge coupled experimental system was constructed in the laboratory, such as... Figure 13As shown in (a), the system mainly consists of a model vehicle, a truss bridge model, a speed measurement system, and a dynamic data acquisition system, which can stably acquire the dynamic response of the bridge under vehicle load.

[0183] The experimental truss bridge has a total length of 3.0 m, a width of 0.4 m, and a total height of 0.16 m. Figure 13 As shown in (b), the bridge truss consists of upper and lower chords, fabricated from 25 mm × 25 mm square hollow steel tubes with a wall thickness of 2 mm. The secondary beams have the same cross-sectional dimensions and are directly welded to the chords. The bridge deck is a 355 mm wide, 2 mm thick steel plate, fixed to the secondary beams by continuous welding. The web members are made of Q235 angle steel (20 mm × 20 mm × 2 mm) and connected to the chords by bolts.

[0184] In addition, an auxiliary beam is installed on one side of the truss bridge, and seven photoelectric sensors are evenly arranged along it with a spacing of 0.5 m. By recording the time when a vehicle passes each sensor in sequence, the photoelectric sensing system can acquire the spatiotemporal information of the vehicle, which serves as a key input for Moving Load Identification (MLI).

[0185] The experimental support and model vehicle are respectively as follows Figure 13 (c) and Figure 13 As shown in (d), strain and acceleration sensors were placed at L / 4, L / 2, and 3L / 4 positions on the upper chord to comprehensively acquire the dynamic response characteristics of the bridge. All measurement signals were acquired using the LMS dynamic data acquisition system at a sampling frequency of 1024Hz.

[0186] In addition, based on the geometric parameters and material properties of the laboratory truss bridge, a vehicle-bridge coupled finite element model (FEM) was established in MATLAB. To ensure the consistency between the numerical model and the experimental structure, the parameters of both the bridge and vehicle models were calibrated and updated. The bridge model was updated by correcting key parameters such as equivalent mass density, bending stiffness and bearing stiffness. The model correction method and parameter selection strategy are referenced in

[46] . The vehicle model was designed based on the dynamic similarity theory of vehicle-bridge coupled system (VBI) to ensure the consistency between the scaled model and the prototype system in terms of mass, stiffness and dynamic response characteristics. The detailed parameters of the vehicle-bridge system are summarized in Table 7. Table 7 shows the parameters of the experimental vehicle-bridge model.

[0187]

[0188] Table 7.

[0189] To enrich the training samples and improve the generalization ability of the proposed PI-ResTCN model, this technical solution adopts a hybrid dataset construction strategy that integrates numerical simulation and experimental measurement.

[0190] In terms of numerical data generation, vehicle mass and speed were used as the main variables. Vehicle mass varied from 5 kg to 15 kg, and vehicle speed varied from 1.0 m / s to 1.5 m / s. Considering the relatively smooth surface of the experimental bridge, ISO Class A road surface unevenness was used in the numerical simulation to minimize the impact of random road surface excitation on the bridge's dynamic response.

[0191] The experimental data were derived from five representative operating conditions, involving different axle load distributions and vehicle speeds, detailed in Table 8. Table 8 shows the experimental scenarios and corresponding test conditions. To further expand the experimental dataset and improve sample diversity, random noise perturbation was introduced into the measured signals to generate additional samples with random characteristics.

[0192]

[0193] Table 8.

[0194] By combining numerical simulation and experimental measurements, a total of 150 sets of samples were generated. The dataset was then divided into training and test sets in a 4:1 ratio.

[0195] To verify the accuracy of the updated finite element model (FEM), the experimentally measured strain and acceleration response of the bridge were compared with the corresponding numerical simulation results under experimental condition 1. Figure 14 As shown, the simulation results and the measured results exhibit good consistency in terms of time history evolution, peak amplitude, and dominant vibration characteristics. This indicates that the established vehicle-bridge coupled finite element model can accurately reproduce the dynamic behavior of the bridge under moving vehicle loads, thus providing a reliable foundation for dataset generation and subsequent moving load identification (MLI).

[0196] The following section describes the experimental verification of moving load identification.

[0197] In the experimental study, the network structure, training strategy, and convergence criteria remained consistent with those in the numerical simulation. The preset sparsity parameter was set to 20, and the response combination "1 / 4m&1 / 2m&1 / 2a&3 / 4a" was used.

[0198] It should be noted that, due to experimental limitations, instantaneous wheel-axle interaction loads could not be directly measured. Therefore, the static axle load obtained from vehicle weighing tests was used as a reference value for performance evaluation. The axle load percentage error was defined as: (18).

[0199] in, This indicates the axle load measured in the experiment. This indicates the identified axle load. Gross Vehicle Weight (GVW) is defined as the sum of the axle loads on the front and rear axles of a two-axle vehicle.

[0200] The axle load identification results under different experimental conditions are summarized in Table 9. Table 9 shows the identification results under six different experimental conditions.

[0201] Since the proposed PI-ResTCN method can reconstruct the time-varying vehicle load history, it first transforms the identified load signal to the frequency domain using a Fast Fourier Transform (FFT). Then, it extracts the amplitude of the zero-frequency component, which represents the static component in the load time history, and determines the corresponding axle load accordingly.

[0202]

[0203] Table 9. Where TPWw is the percentage error between the identified total vehicle weight and the actual total vehicle weight.

[0204] As shown in Table 9, the proposed method can accurately identify the front and rear axle loads under different vehicle speeds and axle load distributions. The PEw corresponding to both types of axle loads is stably controlled within ±5%, indicating that the proposed method has good robustness and reliability under different operating conditions. For the identification of the total vehicle weight (GVW), the absolute value of TPEw obtained by the proposed method is between 0.19% and 2.54%, indicating that it has excellent consistency and overall accuracy. The improvement in GVW identification performance is mainly attributed to the significant reduction in the number of unknown variables when the front and rear axle loads are treated as a whole, thereby reducing the dimensionality of the inverse problem, making the solution space more stable, and improving the identification accuracy.

[0205] Taking experimental condition 1 as an example, Figure 15 The identified front and rear axle load time histories are presented. Figure 16 The corresponding FFT spectrum results are shown. For example... Figure 15 As shown, the identified front and rear axle loads exhibit dynamic fluctuations around their respective actual axle loads. This phenomenon is consistent with the actual vehicle load mechanism and highly matches the physical behavior of the vehicle-axle coupling system (VBI). The identification results not only successfully captured the static axle load component but also accurately reflected the dynamic changes caused by the vehicle-axle coupling effect.

[0206] Figure 16The FFT results show that the zero-frequency component amplitudes corresponding to the load time histories of the front and rear axles are 56.5946 N and 54.4571 N, respectively, which can effectively characterize the axle load information of the vehicle. These results demonstrate that the proposed method can effectively extract vehicle load information from the structural response and achieves stable and reliable load identification performance under experimental conditions.

[0207] On the other hand, this application also provides a load identification system based on a physical information residual temporal convolutional network. The system includes an online identification module, which is used to perform online identification using an identification network model trained in the offline stage in any of the above specific embodiments.

[0208] On the other hand, a computer-readable storage medium is provided, wherein a processor-executable program is stored, which, when executed by a processor, is used to implement the load identification method based on a physical information residual temporal convolutional network as described in any of the above specific embodiments.

[0209] This application also discloses a computer program product, including a computer program or computer instructions, which are stored in a computer-readable storage medium. The processor of the computer device reads the computer program or computer instructions from the computer-readable storage medium and executes the computer program or computer instructions, causing the computer device to perform the load identification method based on physical information residual temporal convolutional networks as described in any of the preceding embodiments.

[0210] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a particular order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms “comprising” and “having,” and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatuses.

[0211] It should be understood that in this application, "at least one (item)" means one or more, and "more than" means two or more. "And / or" is used to describe the relationship between related objects, indicating that three relationships can exist. For example, "A and / or B" can represent three cases: only A exists, only B exists, and both A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0212] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, apparatuses, or units, and may be electrical, mechanical, or other forms.

[0213] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0214] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0215] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0216] Although the description of this application has been quite detailed and particularly focused on several of the described embodiments, it is not intended to limit itself to any of these details or embodiments or any particular embodiment. Rather, it should be considered as effectively covering the intended scope of this application by referring to the appended claims and taking into account the prior art, which provides for a broad possible interpretation of these claims. Furthermore, the foregoing description of this application with respect to embodiments foreseeable by the inventors is intended to provide a useful description, and non-substantial modifications to this application that have not yet been foreseen may still represent equivalent modifications.

[0217] It should be noted that in all specific embodiments of this application, when processing data related to user identity or characteristics, such as user information, user behavior data, user historical data, and user location information, user permission or consent is obtained first. Furthermore, the collection, use, and processing of this data comply with relevant laws, regulations, and standards. In addition, when embodiments of this application require access to sensitive personal information of users, separate permission or consent from the user is obtained through pop-ups or redirection to confirmation pages. Only after obtaining the user's separate permission or consent is the necessary user-related data required for the proper functioning of these embodiments acquired.

Claims

1. A load identification method based on a temporal convolutional network with physical information residuals, characterized in that, include: Online recognition is performed using a recognition network model that has been trained offline. The online identification method specifically includes: Obtain the measured response data of the target bridge at the current moment, and construct the system transfer matrix at the current moment; The orthogonal matching pursuit algorithm is used to perform sparse inversion on the measured response data at the current time to obtain the initial estimated sequence of the moving load at the current time; The same multi-scale feature construction is performed on the initial estimated sequence to generate the input feature matrix at the current time. The input feature matrix at the current moment is input into the pre-trained recognition network model for a single forward calculation. The backbone network outputs the residual prediction component at the current moment, and the context-aware calibration head outputs the scaling factor and bias term at the current moment. The final recognition result of the moving load at the current moment is calculated. This final recognition result is equal to the scaling factor multiplied by the sum of the initial estimated sequence and the residual prediction component plus the bias term, and is output as the real-time recognition result of the current vehicle load.

2. The load identification method based on physical information residual temporal convolutional networks according to claim 1, characterized in that, The training method for the recognition network model in the offline stage specifically includes: acquiring sample measured response data of the sample bridge structure under moving vehicle load, and constructing the system transfer matrix; using the orthogonal matching pursuit algorithm to perform sparse inversion solution on the sample measured response data to obtain the initial estimation sequence of the moving load; Multi-scale feature construction is performed on the initial estimated sequence to generate an input feature matrix. The input feature matrix includes the initial estimated sequence itself, the first-order time difference of the initial estimated sequence, the second-order time difference of the initial estimated sequence, the statistical features of the initial estimated sequence, and the time code of the initial estimated sequence. The input feature matrix is ​​input into a residual temporal convolutional network for temporal feature extraction. The residual temporal convolutional network includes multiple cascaded temporal convolutional modules and a context-aware calibration head. The backbone network outputs residual prediction components, and the context-aware calibration head outputs scaling factors and bias terms to obtain the prediction result of the moving load. The prediction result is equal to the scaling factor multiplied by the sum of the initial estimated sequence and the residual prediction components plus the bias term. A progressive sparse reconstruction strategy is adopted, which dynamically updates the target load by iteratively calculating the structural response residual and compensating the residual load component based on the log-regularized objective function. In each training cycle, the updated target load is used as the supervision signal, and the parameters of the residual temporal convolutional network are optimized and trained using the L2 norm loss function until the preset termination criterion is met. The training is then stopped and the trained recognition network model is saved.

3. The load identification method based on physical information residual temporal convolutional networks according to claim 2, characterized in that, In both the offline training phase and the online recognition process, the orthogonal matching pursuit algorithm is used to solve the sparse inversion problem and extract the sparse dominant dynamic components of the moving load from the measured response. The optimization problem for sparse inversion using the orthogonal matching pursuit algorithm is expressed as follows: finding the variable values ​​when the objective function is minimized. The objective function is the measured response minus the square of the L2 norm of the system transfer matrix multiplied by the load dictionary multiplied by the sparse coefficient vector. The constraint is that the zero norm of the sparse coefficient vector is less than or equal to the preset target sparsity. The moving load is mapped to the sparse domain using a dictionary-based sparse representation method, i.e., the moving load is equal to the load dictionary multiplied by the sparse coefficient vector. The initial estimated sequence of the moving load is obtained by iteratively selecting the dictionary atom with the highest correlation to the current residual signal through the orthogonal matching pursuit algorithm.

4. The load identification method based on physical information residual temporal convolutional networks according to claim 2, characterized in that, The backbone of the residual temporal convolutional network consists of multiple cascaded temporal convolutional network modules. Each temporal convolutional network module includes a one-dimensional dilated convolutional layer, a nonlinear activation function, Dropout regularization, and residual skip connections. Each level of the temporal convolutional network module is configured with an exponentially increasing dilation rate to simultaneously capture short-term local dynamic features and long-term temporal correlations in the input sequence. The backbone network outputs residual prediction components.

5. The load identification method based on physical information residual temporal convolutional networks according to claim 2, characterized in that, The context-aware calibration head aggregates the statistical features extracted during the multi-scale feature construction stage to form a global context vector. The global context vector is modeled by a multilayer perceptron containing fully connected layers, non-linear activation functions, and Dropout regularization, and outputs the scaling coefficients and bias terms.

6. The load identification method based on physical information residual temporal convolutional networks according to claim 2, characterized in that, The progressive sparse reconstruction strategy specifically includes: In the i-th training cycle, the structural response residual is calculated based on the moving load reconstructed in the previous training cycle. This residual is equal to the measured response minus the system transfer matrix multiplied by the moving load in the previous training cycle. The residual load component is reconstructed by solving the residual sparsity coefficient through a log-regularized objective function. This residual load component is equal to the load dictionary multiplied by the residual sparsity coefficient. The residual sparsity coefficient is obtained by minimizing the log-regularized objective function. The log-regularized objective function is to calculate for each element the sum of the load dictionary multiplied by the system transfer matrix multiplied by the residual sparsity coefficient minus the absolute value of the structural response residual divided by the logarithm of the adaptive scaling parameter, and then sum over all elements. The target load is updated to the initial estimated sequence plus the sum of the residual load components from each training cycle; The adaptive scaling parameter is a parameter that controls the transition characteristics of the logarithmic function; the logarithmic regularization objective function is solved by combining the gradient descent algorithm and the Adam optimization algorithm.

7. The load identification method based on physical information residual temporal convolutional networks according to claim 2, characterized in that, The preset termination criterion includes: the relative change between two adjacent iterations of predicted load is less than 10. -6 .

8. The load identification method based on physical information residual temporal convolutional networks according to claim 2, characterized in that, The preset termination criterion also includes: the relative change between the structural response obtained from the identified load reconstruction and the measured response is less than 10%. -6 .

9. The load identification method based on a physical information residual temporal convolutional network according to claim 2, characterized in that, The preset termination criteria also include: the training cycle reaches the maximum number of iterations, 200.

10. A load identification system based on a physical information residual temporal convolutional network, characterized in that, include: An online recognition module is used to perform online recognition using the recognition network model trained in the offline stage as described in claim 1.

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