A method for coupled response analysis of wind turbine bridges

Abstract

This invention relates to the field of dynamic response analysis of bridge structures and discloses a method for analyzing the coupled response of windmill bridges. The method collects wind speed, wind direction, and vehicle speed data, and constructs a dataset using coupled finite element method (FEM) and CFD numerical simulations. It then employs a parallel encoder to fuse Transformer feature extraction and LSTM time-series processing to generate a hybrid predicted response. Based on the train-bridge motion equations, it constructs physical constraints and a composite loss function, and optimizes the neural network parameters using a subtractive averaging strategy. Finally, it predicts the dynamic response through forward propagation and verifies physical consistency, forming a closed-loop model optimization process. This application integrates deep learning methods with physical equation constraints, significantly improving the accuracy and computational efficiency of windmill bridge coupled response analysis, and providing a more reliable dynamic evaluation method for bridge wind-resistant design.

Description

Technical Field

[0001] This invention relates to the field of dynamic response analysis of bridge structures, and more particularly to a method for coupled response analysis of wind turbine bridges. Background Technology

[0002] In the field of bridge structure dynamic response analysis, existing solutions related to coupled response analysis of wind turbine bridges typically employ separate time-series prediction models and physical equation constraint mechanisms. These solutions suffer from limitations such as insufficient long-term reliance on feature capture capabilities, inadequate modeling of non-stationary sequence dynamic characteristics, and a lack of physical constraint fusion strategies. Existing methods often rely on a single LSTM network or independent physical equation solving. In scenarios involving multiple coupled parameters such as wind speed, wind direction, vehicle speed, and aerodynamic coefficients, these methods are prone to fragmentation of time-series data and accumulation of residuals in the motion equations, making it difficult to meet the accuracy requirements for displacement, velocity, and acceleration dynamic response prediction. Regarding the cross-scale data fusion problem of wind-induced vibration and train loads, existing technologies generally neglect the synergistic effect of attention mechanisms and gating strategies. This results in a fragmented processing flow between time-series feature extraction and physical equation residual calculation, making it difficult to establish a continuous optimization link from feature extraction and sequence prediction to physical residual feedback under the constraints of the wind turbine bridge system's motion equations. This leads to a significant deviation between the predicted response and the actual dynamic behavior. Summary of the Invention

[0003] This invention provides a method for analyzing the coupled response of a wind turbine bridge, which addresses the problem of predicting the dynamic response of displacement, velocity, and acceleration under the physical constraints of the coupled response of a wind turbine bridge based on inputs of wind speed, wind direction, vehicle speed, and aerodynamic coefficients, through an improved attention mechanism and gating strategy.

[0004] To address the aforementioned technical problems, this invention provides a method for analyzing the coupled response of a wind turbine bridge, comprising:

[0005] Raw data on wind speed, wind direction, and vehicle speed are collected, and outliers are corrected and removed in real time through multi-sensor fusion technology. Numerical simulation based on the coupling of finite element method and computational fluid dynamics is then performed to generate a numerical dataset of the coupled response of the wind turbine bridge.

[0006] Time series samples are input into a parallel encoder containing multiple Transformer encoder units to extract Transformer features; time segments are divided from long-term dependency features and processed by an LSTM gating mechanism to generate non-stationary sequence prediction results; the LSTM prediction results are fused with Transformer long-term dependency features to generate a hybrid prediction response.

[0007] Based on the analytical displacement, velocity, and acceleration parameters of the hybrid predictive response, the motion equations of the train-bridge system are obtained and discretized by the finite difference method or finite element method to form physical constraints. The weighted L1 norm physical residuals are calculated by substituting them into the discrete equations. The data-driven mean square error and physical residuals are fused to construct a composite loss function.

[0008] Load the initial weight parameters of the hybrid neural network, configure the subtraction averaging strategy, extract gradient information and update parameters based on the composite loss function, and generate the training completed model through convergence judgment;

[0009] Load the trained model for forward propagation prediction, extract the displacement, velocity and acceleration of key nodes, and generate physical dimension dynamic results by inverse normalization based on normalization parameters; substitute into discrete motion equations to calculate physical consistency residuals and generate physical consistency reports.

[0010] Obtain the true values ​​of the test dataset and calculate the mean absolute error index; extract the residual distribution from the physical verification report and statistically analyze the mean, standard deviation, and kurtosis features to generate a physical consistency score; based on the error index and the score results, generate a model optimization instruction feedback training closed loop through multi-objective threshold rules.

[0011] Furthermore, the steps for extracting Transformer features by inputting time-series samples into a parallel encoder containing multiple Transformer encoder units include:

[0012] The parallel encoder contains multiple Transformer encoder units, each of which extracts features from the input sequence based on a self-attention mechanism;

[0013] Time series samples are input into a parallel encoder in the form of multidimensional tensors. After passing through a multi-head self-attention layer, the dependencies between time steps in the sequence are weighted and calculated to capture long-term dependency features.

[0014] The Transformer encoder injects temporal information of the time series into the feature representation through positional encoding, overcoming the problem of missing sequence order information;

[0015] By processing multiple Transformer encoder units in parallel, the diversity and robustness of feature extraction are achieved. The feature vectors output by each encoder unit are concatenated or weighted and fused to form a comprehensive long-term dependency feature representation.

[0016] Furthermore, the steps for processing the non-stationary sequence prediction results using the LSTM gating mechanism include:

[0017] Long-term dependency features are divided into multiple consecutive time segments, and the length of the time segments is preset according to the dynamic change characteristics of non-stationary sequences.

[0018] The time sequence is used as input and enters the long short-term memory network gating mechanism module. Through the input gate, forget gate and output gate, the time sequence information is selectively remembered and forgotten, so as to realize the dynamic modeling of non-stationary sequences.

[0019] The LSTM gating mechanism calculates gating weights based on the current input and the previous hidden state, dynamically adjusts the information flow path, and enhances the model's ability to respond to sequence mutations and trend changes.

[0020] The internal state of the gating mechanism is updated through the nonlinear activation function of the gating unit, forming a time-dependent hidden state sequence.

[0021] Furthermore, the steps for fusing LSTM prediction results with Transformer long-term dependency features include:

[0022] Multimodal fusion is performed between the LSTM prediction results and the long-term dependency features output by the Transformer encoder.

[0023] The fusion process employs a weighted fusion strategy, which dynamically adjusts the weights of each feature component using an attention mechanism to enhance the expressive power of the fused features.

[0024] The feature fusion module first performs dimension matching and alignment on the two input feature tensors, and then generates a fused feature vector through dot product and weighted summation operations;

[0025] The fused features are mapped through a fully connected layer and an activation function to enhance nonlinear expressive power and output a hybrid prediction response.

[0026] Furthermore, the steps for obtaining the motion equations of the train-bridge system and discretizing the differential equations using the finite difference method or the finite element method include:

[0027] The equations of motion are based on the principles of continuum mechanics and structural dynamics, and use differential equations to describe the dynamic characteristics of the system.

[0028] For differential equations, numerical discretization methods, including the finite difference method or the finite element method, are used to transform the dynamic equations in the continuous time domain into a system of algebraic equations at discrete time points.

[0029] During the discretization process, the system divides the motion variables into time sequences according to a preset time step;

[0030] Discretization processing supports an adaptive time step adjustment mechanism, which dynamically adjusts the time step to improve computational accuracy in response to nonlinear behavior and sudden dynamic events in the system.

[0031] Furthermore, the steps for substituting into the discrete equations to calculate the weighted L1 norm physical residual term include:

[0032] The feature analysis module separates three key dynamic response parameters: displacement, velocity, and acceleration.

[0033] The parsing module, based on the dynamic response data structure specification, uses multi-channel data splitting technology to map the multidimensional tensor data in the mixed prediction response to the corresponding dynamic physical quantity dimensions.

[0034] Based on the extracted displacement, velocity, and acceleration parameters, and in conjunction with physical constraints, the residual calculation of the motion equations is performed.

[0035] The residual calculation module calculates the difference between the predicted response and the physical constraints, i.e., the residual term, based on the algebraic expression of the discretized motion equations.

[0036] The residual calculation supports multi-scale residual analysis, calculating residuals for dynamic responses at different frequencies and time scales, and capturing local and global deviations in the dynamic characteristics of the system.

[0037] Furthermore, the steps to construct a composite loss function by integrating data-driven mean squared error and physical residuals include:

[0038] A composite loss function is constructed by combining data-driven error metrics, mean squared error, and mean absolute error.

[0039] The loss function structure uses a multi-objective weighted fusion strategy to unify the processing of data error and physical residual.

[0040] Weight coefficients are calculated for the physical residual term and the data error respectively. The weight allocation is based on the dynamic adjustment rules during the training phase, and the relative contributions of each loss component are balanced by combining the model convergence speed and the error change trend.

[0041] The weighted fusion process employs a normalized weighting mechanism.

[0042] Furthermore, the steps of loading the initial weight parameters of the hybrid neural network and configuring the subtractive averaging strategy include:

[0043] The weight parameters cover the weights of the multi-head self-attention layer, position encoding weights, and multi-layer feedforward network weights of the Transformer encoder, as well as the input gate, forget gate, output gate, and cell state weights in the long short-term memory network gating mechanism.

[0044] The weight parameters are initialized using a random initialization method based on uniform or normal distribution, combined with He initialization or Xavier initialization strategies;

[0045] Based on the structural characteristics of the composite loss function, a subtraction averaging optimization strategy is configured. This strategy dynamically adjusts the overall network parameters by gradually subtracting and averaging the differences in the weights of multiple sub-networks, thereby suppressing gradient oscillations and overfitting.

[0046] The subtractive averaging strategy first divides the network weights into several subsets, each subset corresponding to a specific module or layer in the network. For each subset weight, the difference between the current gradient and the historical gradient is calculated, and a weighted subtractive averaging operation is performed to form an adjustment vector.

[0047] Furthermore, the steps for gradient information extraction and parameter updating based on the composite loss function include:

[0048] The gradient of the composite loss function with respect to the network weight parameters is calculated using an automatic differentiation mechanism;

[0049] The gradient calculation process involves multi-objective joint gradient backpropagation, which includes mean squared error, mean absolute error, and physical residual terms.

[0050] According to the subtraction averaging optimization strategy, the corresponding gradient information is extracted for each sub-network weight subset, gradient difference calculation is performed, and the current gradient is subtracted from the historical gradient to form the gradient adjustment vector.

[0051] The gradient adjustment vector is normalized to prevent gradient explosion or gradient vanishing problems, and weighted accumulation is performed in combination with momentum factor to improve the smoothness and convergence speed of gradient updates.

[0052] Based on the adjusted gradient, the system calls the learning rate scheduler to adjust the current learning rate according to the preset learning rate dynamic adjustment rules, supporting step decay, cosine annealing and adaptive adjustment mechanisms.

[0053] Furthermore, by integrating data-driven mean squared error and physical residuals, the expression for the composite loss function includes:

[0054] An improved discretized model is established based on the dynamic equations of the train-bridge system, and the time-domain discrete equations are defined as follows:

[0055]

[0056] in, The quality matrix is ​​discretized. The damping matrix is ​​discretized. The discretized stiffness matrix; For the first The displacement vector at the time step; For the first The velocity vector at the time step; For the first The acceleration vector at the time step; For the first The force vector at the time step depends on the wind speed. and vehicle speed ; This is the wind speed vector; For vehicle speed parameters; For time step index;

[0057] Substitute the displacement-velocity parameters from the hybrid predicted response into the discrete equation to calculate the weighted L1 norm physical residual term, and define the physical residual term:

[0058]

[0059] in, For the first The physical residual of the time step; For the improved weighted L1 norm;

[0060] By integrating data-driven mean squared error and physical residuals, a composite loss function is constructed:

[0061]

[0062] in, This represents the composite loss function value. The mean squared error is driven by data. These are dynamic weighting coefficients; This is the sum of the physical residuals for all time steps.

[0063] The key innovations of this invention include:

[0064] (1) By combining parallel encoder with Transformer feature extraction technology, the ability to capture long-term dependent features is enhanced, and efficient feature vector extraction is achieved in the input stage of time series samples.

[0065] (2) The LSTM gating mechanism is used to process the time segments in the long-term dependent features to generate non-stationary sequence prediction results, thereby improving the dynamic characteristic modeling capability of time segments.

[0066] (3) In the preliminary prediction stage, the hybrid architecture prediction response is generated by feature fusion processing, realizing the synchronous optimization of dynamic response prediction and physical constraints under multi-source parameter input.

[0067] The following are its main beneficial effects:

[0068] (1) The application of the long-term dependency feature in the Transformer feature extraction stage ensures the continuity of time series feature extraction, effectively avoids the problem of insufficient long-term dependency feature capture capability in the background technology, and is suitable for complex windmill bridge coupling scenarios.

[0069] (2) The non-stationary sequence prediction results generated by the LSTM gating mechanism effectively improve the sufficiency of the dynamic characteristics modeling of time segments, and ensure the accuracy of the prediction results in non-stationary sequence scenarios. It is applicable to multi-parameter coupled scenarios of wind speed, wind direction, vehicle speed and aerodynamic coefficient.

[0070] (3) The generation of the hybrid architecture prediction response makes the dynamic response prediction and physical constraints more closely integrated, reducing the problem of residual accumulation of motion equations, and is suitable for the continuous optimization link from feature extraction to physical residual feedback in wind turbine bridge system. Attached Figure Description

[0071] Figure 1 This is a flowchart illustrating a method for analyzing the coupled response of a wind turbine bridge, as provided in an embodiment of this application. Detailed Implementation

[0072] Example 1: Refer to Figure 1 This is a flowchart illustrating a wind turbine bridge coupling response analysis method provided in an embodiment of the present invention. The flowchart may include at least steps S100-S600:

[0073] S100: Collect raw data on wind speed, wind direction and vehicle speed, correct and remove outliers in real time through multi-sensor fusion technology, and perform numerical simulation based on the coupling of finite element method and computational fluid dynamics to generate a numerical dataset of the coupled response of the wind turbine bridge.

[0074] S200. Input the time series samples into a parallel encoder containing multiple Transformer encoder units to extract Transformer features; divide the time series segments from the long-term dependency features and process them through the LSTM gating mechanism to generate non-stationary sequence prediction results; fuse the LSTM prediction results with the Transformer long-term dependency features to generate a hybrid prediction response.

[0075] S300: Based on the analytical displacement, velocity, and acceleration parameters of the hybrid predictive response, obtain the motion equations of the train-bridge system and discretize the differential equations using the finite difference method or finite element method to form physical constraints; substitute them into the discrete equations to calculate the weighted L1 norm physical residuals; and fuse the data-driven mean square error and physical residuals to construct a composite loss function.

[0076] S400: Load the initial weight parameters of the hybrid neural network, configure the subtraction averaging strategy, extract gradient information and update parameters based on the composite loss function, and generate the training completed model through convergence judgment.

[0077] S500: Load the trained model and perform forward propagation prediction; extract the displacement, velocity and acceleration of key nodes; generate physical dimension dynamic results by inverse normalization based on normalized parameters; substitute into discrete motion equations to calculate physical consistency residuals and generate physical consistency reports.

[0078] S600: Obtain the true value of the test dataset and calculate the mean absolute error index; extract the residual distribution from the physical verification report and statistically analyze the mean, standard deviation, and kurtosis features to generate a physical consistency score; based on the error index and the score results, generate a model optimization instruction feedback training closed loop through multi-objective threshold rules.

[0079] Step S100 includes at least steps S110-S130:

[0080] S110. Obtain raw data of wind speed, wind direction and vehicle speed, perform numerical simulation processing, and obtain numerical dataset of wind turbine bridge coupling response.

[0081] Specifically, the acquisition step first collects raw physical quantity data such as wind speed, wind direction, and train speed from a preset wind environment monitoring system and train operation database, ensuring that the data acquisition time and spatial resolution meet the requirements of wind turbine-bridge coupled dynamic response analysis. During the data acquisition process, multi-sensor fusion technology is used to correct wind speed and wind direction in real time, eliminating outliers and noise interference. The train speed data is simultaneously acquired from the speed feedback signal of the train operation control system to ensure the temporal consistency and integrity of the data. Further, the raw data is input into a numerical simulation platform through a preprocessing module. Using a simulation model based on the coupling of the Finite Element Method (FEM) and Computational Fluid Dynamics (CFD), the dynamic response of the wind turbine and bridge system under wind load is simulated, generating a coupled response numerical dataset containing multi-dimensional indicators such as displacement, velocity, acceleration, and aerodynamic coefficients. This process includes boundary condition configuration, mesh generation, time step selection, and nonlinear dynamic solution, ensuring that the numerical simulation results reflect the complex coupling effects of actual working conditions. During the simulation, the system automatically records simulation parameters and abnormal events. If numerical oscillations or convergence failures occur, the system adaptively adjusts the time step and number of iterations for recalculation to ensure the accuracy and stability of the dataset. Finally, the wind turbine bridge coupled response numerical dataset generated by the numerical simulation is used as the output field "raw numerical dataset" for subsequent step S120's "numerical dataset," completing the complete data preparation from physical quantity acquisition to numerical response simulation.

[0082] S120. Extract input features from the numerical dataset, perform standardization processing, and generate normalized input features;

[0083] Specifically, the "raw numerical dataset" output by S110 is used as input. First, a feature selection module filters key variables such as wind speed, wind direction, vehicle speed, and aerodynamic coefficients, eliminating irrelevant or redundant data to ensure the representativeness and effectiveness of the input features. During feature extraction, an automatic filtering algorithm based on statistical analysis and correlation determination is used, combined with domain expert experience rules, to form an input feature set. Further, the input features are standardized, specifically by calculating the mean and standard deviation for each feature dimension and normalizing using the zero-mean-unit-variance (Z-score) method to eliminate the influence of different physical quantities and their ranges. This standardization is performed at the batch data level, supporting both online and offline modes to ensure real-time updates and historical consistency of the normalization parameters. For missing or outlier values, the system uses interpolation or nearest-neighbor substitution strategies to complete them, ensuring the integrity and continuity of the input features. The normalized input features are stored in multidimensional tensor form, conforming to the input requirements of the subsequent hybrid neural network architecture, and the normalization parameters are recorded for subsequent denormalization. Finally, the normalized input features generated by the process are used as the output field "Normalized Input Features" for S210 to call, realizing a smooth transition of data from numerical simulation results to neural network input.

[0084] S130. Perform sequence partitioning on the normalized input features to generate a time series sample structure;

[0085] Specifically, the step takes the "normalized input features" output by S120 as input and, based on preset time window and sliding step parameters, divides the continuous normalized feature data into multiple overlapping or non-overlapping time series samples. The length of the time window is determined according to the dynamic characteristics of the windmill bridge coupling response and training requirements, ensuring that each time series sample contains sufficient temporal information to capture long-term dependencies and non-stationary features. During the division process, the system automatically aligns the time series boundaries to avoid time misalignment caused by missing or abnormal data, and uses a timestamp synchronization mechanism to ensure the temporal continuity of the sequence. Furthermore, the divided time series samples are format-converted to generate a multidimensional tensor structure that conforms to the input specifications of the Transformer encoder and LSTM network, specifically including a unified definition of batch size, time step, and feature dimensions. The processing supports multi-threaded parallel computation, improving the efficiency of sequence division, and automatically records the sequence division parameters and sample indices, facilitating data tracking and reproduction during training. Finally, the time series sample is used as the output field "time series sample" for the subsequent step S210 "input sequence" to complete the conversion of data from normalized feature vector to time series sample, laying the foundation for time series feature extraction of hybrid neural network.

[0086] Step S200 includes at least steps S210-S230:

[0087] S210. Input the time series samples into the parallel encoder and perform Transformer feature extraction to obtain the long-term dependency feature vector.

[0088] The time-series samples are taken as input and first fed into a parallel encoder structure. Specifically, the parallel encoder contains multiple Transformer encoder units, each of which extracts features from the input sequence based on a self-attention mechanism (SAM). The time-series samples are input into the parallel encoder in the form of multi-dimensional tensors. A multi-head attention layer (MHAL) is used to weight the dependencies between time steps in the sequence, capturing long-term dependency features. Furthermore, the Transformer encoder injects temporal information into the feature representation through positional encoding, overcoming the problem of missing sequence order information. By processing multiple Transformer encoder units in parallel, the diversity and robustness of feature extraction are achieved. The feature vectors output by each encoder unit are concatenated or weighted and fused to form a comprehensive long-term dependency feature representation. During processing, the system automatically monitors the attention weight distribution, identifies potential anomalous feature responses, and marks anomalous samples for subsequent analysis. The long-term dependency features are output in tensor form as the "long-term dependency features" field, which is used by the "input features" in the subsequent step S220 to complete the conversion from time series samples to deep time series features, laying the foundation for subsequent non-stationary sequence prediction.

[0089] S220. Extract time segments from long-term dependency features, process them using LSTM gating mechanism, and generate non-stationary sequence prediction results.

[0090] Based on the long-term dependency features output by S210, further temporal segment extraction and gating mechanisms are applied. Specifically, the long-term dependency features are divided into multiple consecutive temporal segments. The length of each temporal segment is preset according to the dynamic characteristics of the non-stationary sequence to ensure that the time-varying nature of local temporal features can be captured. These temporal segments are used as input to a Long Short-Term Memory (LSTM) gating mechanism module. This module selectively memorizes and forgets temporal information through input gates, forget gates, and output gates, achieving dynamic modeling of non-stationary sequences. Specifically, the LSTM gating mechanism calculates gating weights based on the current input and the previous hidden state, dynamically adjusting the information flow path to enhance the model's responsiveness to sequence mutations and trend changes. The internal state of the gating mechanism is updated through the nonlinear activation function of the gating unit, forming a temporally dependent hidden state sequence. Furthermore, the LSTM module combines batch normalization (BN) and dropout layers to mitigate overfitting and improve model generalization ability. The processing supports multi-layer stacked structures, enhancing the ability to capture complex nonlinear temporal patterns. The prediction results of the non-stationary sequences are output in tensor form as the "LSTM prediction result" field, which is then used in the "preliminary prediction" step S230 to achieve the transformation from long-term dependent features to dynamic temporal prediction.

[0091] S230. Perform feature fusion processing on the preliminary prediction to generate a hybrid architecture prediction response;

[0092] The preliminary prediction results output by S220 are subjected to feature fusion processing. Specifically, the LSTM prediction results are fused with the long-term dependency features output by the Transformer encoder in a multimodal manner. The fusion process employs a weighted fusion strategy, dynamically adjusting the weights of each feature component using an attention mechanism to enhance the expressive power of the fused features. Specifically, the feature fusion module first performs dimensionality matching and alignment on the two input feature tensors, then generates a fused feature vector through dot product and weighted summation operations. Further, the fused features are mapped through a fully connected layer and activation function to enhance nonlinear expressive power, outputting a hybrid prediction response. During the fusion process, the system automatically calculates the covariance matrix of the fused features and monitors changes in the correlation between features to ensure the stability and consistency of the fusion results. The hybrid architecture prediction response is output as the "hybrid prediction response" field for subsequent step S310's "initial prediction," completing the transformation from preliminary single prediction to multi-feature fusion prediction and improving prediction accuracy and robustness.

[0093] Step S300 includes at least steps S310-S330:

[0094] S310. Obtain the motion equations of the train-bridge system, perform differential equation discretization, and obtain the physical constraints.

[0095] Specifically, using the "hybrid predicted response" output by S230 as a basis, and combining it with a pre-defined train-bridge system dynamics model, the motion equations of the train-bridge system are first clarified from the perspective of system dynamics theory. These motion equations include the relationship between dynamic response variables such as displacement, velocity, and acceleration and external excitation forces. The motion equations are based on the principles of continuum mechanics and structural dynamics, and use differential equations to describe the dynamic characteristics of the system. Further, for these differential equations, numerical discretization methods, including the Finite Difference Method (FDM) or the Finite Element Method, are used to transform the continuous-time domain dynamic equations into a system of algebraic equations at discrete time points. Specifically, during the discretization process, the system divides the motion variables into time sequences according to a preset time step, ensuring that the time step matches the dynamic characteristics of the windmill bridge coupling response, avoiding numerical oscillations and error accumulation. The discretization process supports an adaptive time step adjustment mechanism, dynamically adjusting the time step to improve computational accuracy for nonlinear system behavior and sudden dynamic events. Furthermore, the discretized equations of motion include structural parameters such as the mass matrix, damping matrix, and stiffness matrix. These parameters are initialized using a structural design database and experimental data, and updated according to environmental changes during operation. The discretization results of the equations of motion undergo boundary condition verification and stability analysis, eliminating numerically unstable or outlier solutions. Relevant anomaly information and processing logs are recorded in the system anomaly management module. Finally, the physical constraints generated by the discretization process are output as the "Physical Constraints" field for use in the subsequent step S320's "Constraint Parameters," completing the conversion from a continuous dynamics model to discrete physical constraints and ensuring the effective embedding of physical information.

[0096] S320. Extract displacement, velocity and acceleration parameters from the mixed predicted response, perform motion equation residual calculation, and generate physical residual terms;

[0097] Specifically, the steps take the "hybrid predicted response" output by S230 as input. First, the feature parsing module separates three key dynamic response parameters: displacement, velocity, and acceleration. This parsing module, based on the dynamic response data structure specification, employs multi-channel data splitting technology to map the multidimensional tensor data in the hybrid predicted response to the corresponding dynamic physical quantity dimensions. Further, for the extracted displacement, velocity, and acceleration parameters, combined with the "physical constraints" output by S310, residual calculation of the motion equations is performed. Specifically, the residual calculation module calculates the difference between the predicted response and the physical constraints, i.e., the residual term, based on the algebraic expression of the discretized motion equations. This calculation process includes substituting the predicted dynamic response into the left and right sides of the motion equations and obtaining the residual value through numerical comparison. The residual calculation supports multi-scale residual analysis, calculating residuals for dynamic responses at different frequencies and time scales to capture local and global deviations in the system's dynamic characteristics. Further, the system performs anomaly detection on the residual terms, identifying numerically abnormal or physically unreasonable residual values. Relevant anomaly information is stored in the residual anomaly log for subsequent model optimization reference. The residual terms are normalized to eliminate the influence of differences in physical dimensions on the residual weights, and a weighted strategy is used to adjust the contribution of different residuals to the overall error. Finally, the physical residual terms generated by the residual calculation are output as the "Physical Residual Term" field for subsequent steps in S330 to call the "Residual Data", realizing the quantitative conversion from mixed prediction response to physical consistency error.

[0098] S330. Perform weighted fusion processing on the physical residual terms to generate a composite loss function structure;

[0099] Specifically, the steps take the "physical residual term" output by S320 as input and combine it with data-driven error metrics, such as mean squared error and mean absolute error, to construct a composite loss function. This loss function structure uses a multi-objective weighted fusion strategy to unify the processing of data error and physical residual. Specifically, firstly, weight coefficients are calculated for the physical residual term and data error respectively. The weight allocation is based on dynamic adjustment rules during the training phase, combining model convergence speed and error change trends to balance the relative contributions of each loss component. Furthermore, the weighted fusion process employs a normalized weight mechanism to ensure that different error terms are weighted and summed under the same dimensions, avoiding a single error term dominating the training process. The composite loss function structure supports gradient backpropagation; the loss gradient is passed to the model parameter update module through a chain rule, promoting the coordinated optimization of physical constraints and data fitting. During processing, the system automatically records the historical change curves of each loss component and weight adjustment logs, facilitating monitoring and optimization during the training process. The composite loss function structure has been numerically stable to avoid gradient explosion or vanishing problems, ensuring the stable progress of the optimization process. Finally, the composite loss function generated by the weighted fusion is output as the "composite loss function" field for subsequent step S400's "loss function" call, completing the effective integration of physical constraints and data errors, and providing a unified objective function for subtractive averaging optimization training.

[0100] In another embodiment, in step S310, an improved discretized model is established based on the dynamic equations of the train-bridge system, and the time-domain discrete equations are defined:

[0101]

[0102] in, The quality matrix is ​​discretized. The damping matrix is ​​discretized. The discretized stiffness matrix; For the first The displacement vector at the time step; For the first The velocity vector at the time step; For the first The acceleration vector at the time step (the second derivative of the displacement). For the first The force vector at the time step depends on the wind speed. and vehicle speed ; This is the wind speed vector; For vehicle speed parameters; For time step index, step size Second.

[0103] Furthermore, in step S320, the displacement-velocity parameters in the hybrid predicted response are substituted into the discrete equation to calculate the weighted L1 norm physical residual term, and the physical residual term is defined as follows:

[0104]

[0105] in, For the first The physical residual of the time step; For the improved weighted L1 norm, the weight coefficients are derived from the importance scores of each degree of freedom.

[0106] Furthermore, in step S330, a composite loss function is constructed. Specifically, the data-driven mean squared error and the physical residual are fused to construct the composite loss function:

[0107]

[0108] in, This represents the composite loss function value. For data-driven mean square error, calculate the difference between the predicted value and the numerical simulation baseline value; This is a dynamic weighting coefficient with an initial value of 0.7, which is automatically adjusted based on the residual convergence speed during the training phase. This is the sum of the physical residuals for all time steps.

[0109] Technical Achievements: By establishing improved discretized dynamic equations and calculating physical residual terms, the dual constraints of data-driven prediction and physical conservation laws are achieved. The construction of the composite loss function enables the model to simultaneously optimize prediction accuracy and physical plausibility during training, forming a verifiable closed-loop optimization mechanism.

[0110] Step S400 includes at least steps S410-S430:

[0111] S410. Load the initial weight parameters of the hybrid neural network, configure the subtraction averaging strategy, and obtain the initial state of the optimizer.

[0112] Specifically, using the "composite loss function" output by S330 as the optimization objective, the initial weight parameters of the hybrid neural network are first loaded from the preset network structure configuration file. These weight parameters encompass the weights of the multi-head self-attention layer, positional encoding weights, and multi-layer feedforward network weights of the Transformer encoder, as well as the input gate, forget gate, output gate, and unit state weights in the Long Short-Term Memory (LSTM) gating mechanism. The weight parameters are initialized using a random initialization method based on a uniform or normal distribution, combined with He initialization or Xavier initialization strategies, to ensure that the initial state of the parameters has a suitable variance distribution, meeting the stability requirements of deep network training. Furthermore, based on the structural characteristics of the composite loss function, the system configures a subtractive averaging (SA) optimization strategy. This strategy dynamically adjusts the overall network parameters by progressively subtracting and averaging the differences in weights across multiple sub-networks, suppressing gradient oscillations and overfitting. Specifically, the subtractive averaging strategy first divides the network weights into several subsets, each corresponding to a specific module or layer in the network. For each subset weight, the difference between the current gradient and the historical gradient is calculated, and a weighted subtractive averaging operation is performed to form an adjustment vector. This adjustment vector is used to update the global weight parameters, achieving the fusion and optimization of multi-path gradient information. The optimizer's initial state includes the weight parameter matrix, gradient cache, momentum term, and initial values ​​of the learning rate scheduler, all stored in the optimizer state management module. During the initialization phase, the system performs a completeness check on the weight parameters to ensure no missing or outlier values. Abnormal situations are alerted through the log recording module and trigger a re-initialization process. Furthermore, the subtractive averaging strategy configuration supports the preset and dynamic adjustment of hyperparameters, including initial learning rate values, momentum factors, weight decay coefficients, and subset partitioning rules. All configuration parameters are stored in the optimizer parameter library for real-time access and modification during training. After the initialization process is completed, the generated optimizer initial state record is recorded as "initial optimization parameters," which is used for subsequent steps in S420 to call "initial parameters," achieving effective transfer and configuration from the composite loss function to the optimizer state.

[0113] S420. Extract gradient information from the composite loss function, perform parameter update calculations, and generate adjusted network weights.

[0114] Specifically, the "initial optimization parameters" output by S410 and the "composite loss function" output by S330 are used as inputs. First, the gradient of the composite loss function with respect to the network weight parameters is calculated using an Automatic Differentiation (AD) mechanism. This gradient calculation process encompasses multi-objective joint gradient backpropagation, including Mean Squared Error (MSE), Mean Absolute Error (MAE), and physical residuals, ensuring that both data-driven errors and physical constraint errors are included in the gradient update scope. Further, based on a subtractive averaging optimization strategy, the system extracts corresponding gradient information for each subset of sub-network weights and performs gradient difference calculation, i.e., subtracting historical gradients from the current gradient to form a gradient adjustment vector. This gradient adjustment vector is normalized to prevent gradient explosion or vanishing problems, and then weighted and accumulated using a momentum factor to improve the smoothness and convergence speed of gradient updates. Based on the adjusted gradient, the system calls the learning rate scheduler to adjust the current learning rate according to preset dynamic learning rate adjustment rules, supporting step decay, cosine annealing, and adaptive adjustment mechanisms to adapt to error changes during training. The parameter update calculation employs a gradient descent-based optimization algorithm, specifically including stochastic gradient descent with momentum or a variant of Adaptive Moment Estimation (Adam), combined with a subtractive averaging strategy to update weights. During the update process, the system performs weight constraint checks to prevent weight values ​​from exceeding preset ranges. Abnormal weights are handled through truncation or reset operations, and abnormal events are recorded for subsequent analysis. The updated network weight parameter matrix is ​​written into the optimizer state management module, forming an "adjusted weights" field, which is then called by the "parameters to be updated" in subsequent step S430, achieving a closed-loop update from gradient information to weight parameters.

[0115] S430. Perform convergence judgment on the adjusted weights to generate the trained model.

[0116] Specifically, the steps take the "adjusted weights" output by S420 as input, and combine the error indicators and weight change trends during training to execute a convergence determination algorithm. The convergence determination first calculates the composite loss function value for the current training epoch, compares it with historical loss values, and uses a sliding window averaging method to smooth the loss curve and identify the convergence trend of the loss function. Further, the system calculates the change magnitude of the weight parameters, including the L2 norm and the maximum absolute difference, to monitor the stability of weight updates and avoid training getting stuck in local optima or oscillations. The convergence determination uses a multi-condition composite criterion, including a loss function change rate threshold, a weight change rate threshold, and a preset maximum training epoch; meeting any one of these conditions triggers a training termination signal. If training fails to converge, the system adjusts the learning rate parameters based on feedback from the learning rate scheduler and continues executing the parameter update loop. During the convergence determination process, the system automatically records training logs, including the loss value curve, historical weight changes, and gradient information, facilitating visualization and tracking of the training process. After the convergence condition is met, the system calls the model saving module to solidify the currently adjusted weight parameters into a trained model. The model format conforms to the loading specifications of the subsequent prediction module and includes network structure configuration, weight parameters, and normalized parameter metadata. The trained model is marked with a "trained model completed" field for use in the subsequent "prediction model" step S510, achieving a smooth transition from the training phase to the inference phase. After training is complete, the system triggers the model verification and backup process to ensure the integrity and security of model version management, and sends a training end signal to the training monitoring module, preparing to enter the dynamic response prediction execution phase.

[0117] Step 500 includes at least steps S510-S530:

[0118] S510. Load the trained model, perform forward propagation calculations, and obtain the predicted values ​​of displacement velocity and acceleration.

[0119] The input source for step S510 is the "trained model" output from S430. Specifically, the trained model is loaded as a "prediction model" and input to the prediction execution module. The loading process first calls the trained model file through the model management system. This file contains the complete structural definition of the hybrid neural network, the weight parameter matrix, and normalized parameter metadata. According to the model format specifications, the system parses the model configuration file, reconstructs the multi-head self-attention layer, positional encoding, and multi-layer feedforward network structure of the Transformer encoder, and simultaneously restores the input gate, forget gate, output gate, and unit state weights in the Long Short-Term Memory (LSTM) gating mechanism. Specifically, the model loading module performs a completeness check on the weight parameters, including weight dimension matching, numerical range detection, and data format consistency. Abnormal weights or missing parameters automatically trigger an error handling process, record an error log, and return a loading failure signal. After loading is complete, the trained model is mapped to the neural network inference engine, initializing the runtime environment, including memory allocation, computation graph construction, and tensor scheduling mechanisms. Furthermore, the inference engine configures the data preprocessing pipeline according to the normalized input feature format requirements to ensure strict alignment between the input data and the model input interface. The forward propagation computation process is controlled by the inference engine. First, the normalized input features are passed to the Transformer encoder module, where sequence features are extracted using a multi-head self-attention mechanism. Then, temporal dynamics are processed through an LSTM gating mechanism, and finally, the predicted value is mapped and output by a fully connected layer. During the forward propagation process, the system dynamically monitors the usage of computational resources and the activation values ​​of intermediate layers, automatically identifying abnormal activations or gradient explosion phenomena, and triggering model self-checking and correction mechanisms. The inference process supports both batch input and single-sample prediction modes to adapt to different application scenarios. After forward propagation computation, the system outputs multi-dimensional dynamic response prediction values ​​including displacement, velocity, and acceleration. The results are stored in tensor form and output as the "Dynamic Response Prediction Value" field for subsequent step S520's "Original Prediction," realizing the conversion and transfer from the trained model to dynamic response prediction.

[0120] S520. Extract key node data from the predicted dynamic response values, perform inverse normalization processing, and generate physical dimension prediction results.

[0121] The input to step S520 is the "dynamic response prediction value" output by S510. Specifically, key node data is extracted from the dynamic response prediction value, and inverse normalization processing is performed to generate physical dimension prediction results. The key node data extraction module first selects representative displacement, velocity, and acceleration data points from the multidimensional prediction tensor according to a preset node selection strategy. The nodes include key sections of the bridge structure, stress points of wind turbine blades, and key positions of train operation, ensuring that the prediction results cover the main dynamic response areas of the system. The node selection is dynamically adjusted according to the structural dynamic characteristics and engineering application requirements, supporting both static configuration and dynamic adaptive modes. Further, the inverse normalization processing is performed according to the normalization parameters recorded in step S120, specifically including applying the corresponding mean and standard deviation inverse transformation to each prediction variable to restore the normalized values ​​to the original physical quantity level. The process supports batch data inverse normalization, automatically handles missing values ​​and abnormal prediction results, and completes them through interpolation or nearest-neighbor substitution strategies to ensure the integrity of the physical dimension prediction results. The denormalization module standardizes the output format, generating a data structure that conforms to engineering application standards, including timestamps, node identifiers, and corresponding dynamic response values. The physical dimension prediction results undergo range checking and consistency verification by the data validation module; abnormal data is automatically marked and recorded for subsequent analysis. Finally, the generated physical dimension prediction results are output as a "Physical Dimension Result" field, which is then used in the "Physical Verification Report" of subsequent step S530. This achieves the conversion from normalized prediction values ​​to engineering physical quantity level results, completing the preparation for the engineering applicability of the prediction results.

[0122] S530. Perform motion equation verification on the physical dimension results and generate a physical consistency report;

[0123] The input to step S530 is the "physical dimension result" output by S520. Specifically, based on the physical dimension result, motion equation verification processing is performed to generate a physical consistency report. First, the verification module calls the "physical constraints" generated in step S310, including the discretized train-bridge system motion equations and related structural parameters, as the theoretical basis for physical verification. The verification process substitutes the displacement, velocity, and acceleration data from the physical dimension prediction results into the motion equations, calculates the numerical differences between the left and right sides of the motion equations, and forms physical consistency residuals. This residual calculation supports multi-timescale, multi-node parallel processing, covering the physical consistency determination of global and local dynamic responses. Further, the system performs statistical analysis on the residual data, calculates the mean, variance, and maximum value of the residuals, and identifies potential areas or time periods of physical inconsistency. The residual analysis results, combined with the structural dynamics knowledge base, automatically generate anomaly diagnostic information, indicating possible model deviations or sources of prediction errors. The verification module simultaneously performs time-series trend analysis of the residuals, monitors the dynamic changes in physical consistency over time, and supports the triggering of anomaly warning mechanisms. The physical consistency report includes residual statistics, anomaly diagnostic results, and time-series analysis charts. The report format conforms to engineering evaluation standards and supports subsequent manual or automated review. During report generation, the system automatically records all input / output data and calculation logs during the verification process, ensuring the traceability and reproducibility of the verification results. Finally, the physical consistency report is output as the "Physical Verification Report" field, which is used in the subsequent step S630's "Verification Data" to confirm the physical rationality and quality control of the prediction results.

[0124] Step S600 includes at least steps S610-S630:

[0125] S610. Obtain the true values ​​of the test dataset, calculate the prediction error, and obtain the mean absolute error index.

[0126] Specifically, the "physical dimension result" output from step S520 is used as input, combined with the pre-prepared true values ​​of the test dataset. These true values ​​originate from experimental measurement data and high-precision numerical simulation results, including actual observed values ​​of displacement, velocity, and acceleration of key bridge nodes. The true values ​​of the test dataset are uniformly scheduled through the data management system to ensure strict alignment between timestamps and prediction results, achieving spatiotemporal consistency of the data. Further, the error calculation module performs error index calculation node-by-node and time-step-by-time for the physical dimension result and the true values ​​of the test dataset, using the Mean Absolute Error (MAE) as the primary evaluation index. Specifically, the calculation process iterates through the absolute values ​​of the differences between the predicted and true values ​​of all test samples and performs a weighted average of these values ​​in terms of time and space dimensions. The weights are dynamically adjusted based on node importance and time-time sensitivity. The error calculation supports batch parallel processing, employs multi-threading technology to improve computational efficiency, and automatically removes missing values ​​and outliers during the calculation process to avoid interference from abnormal data on the error index. The system automatically records the local error distribution for each node and time period, generating an error statistics report including the error mean, variance, maximum value, and distribution map for subsequent analysis. The error index data undergoes format conversion to form a multidimensional tensor structure conforming to the input specifications of the model evaluation module, containing a time-series error vector and a spatial node error matrix. Finally, the mean absolute error index generated from the error calculation is output as the "error index data" field, which is then used in the "evaluation parameters" of subsequent step S620, realizing the conversion and transfer from physical quantity prediction results to error evaluation indicators.

[0127] S620. Extract the residual distribution from the physical verification report, perform statistical feature analysis, and generate a physical consistency score.

[0128] Specifically, the "Physical Verification Report" output from step S530 is used as input. First, the physical consistency residual data in the report is retrieved. This residual data contains residual values ​​of the motion equations corresponding to multiple time points and spatial locations, reflecting the deviation between the predicted response and physical constraints. The residual distribution data is preprocessed through a data parsing module, including outlier removal, missing data imputation, and smoothing filtering, ensuring the continuity and stability of the residual data. Further, a statistical analysis module performs multidimensional statistical feature extraction on the preprocessed residual data, calculating indicators such as the mean, standard deviation, kurtosis, skewness, and maximum value of the residuals to reveal the central tendency and distribution pattern of the residuals. The statistical feature analysis, combined with time series analysis methods, calculates the autocorrelation function and power spectral density of the residuals, evaluating the temporal correlation and frequency domain characteristics of the residuals. Based on the above statistical features, the system constructs a physical consistency scoring model. This scoring model uses a weighted multi-index fusion algorithm to convert the residual statistical features into a single physical consistency score. The score range is preset from 0 to 1; a larger value indicates higher consistency between the predicted response and physical constraints. The weighting coefficients are set based on historical training data and expert experience, and support online dynamic adjustment to adapt to different working conditions and model states. During the score generation process, the system automatically records intermediate results and weight distributions in the score calculation process, ensuring the transparency and interpretability of the scoring process. The physical consistency score result is output in scalar form, conforming to the input specifications of the subsequent model iteration decision module. Finally, the physical consistency score generated by the statistical feature analysis is output as the "Physical Consistency Score" field, which is called by the "Evaluation Result" in the subsequent step S630, realizing the quantitative mapping from physical verification residuals to unified physical scores.

[0129] S630. Iterative decision processing is performed on the evaluation results to generate model optimization instructions. Specifically, the "error index data" output from step S610 and the "physical consistency score" output from step S620 are used as inputs and comprehensively analyzed by the iterative decision module. The decision module first performs trend analysis on the error index data to identify the direction and magnitude of error changes, and combines the historical change trajectory of the physical consistency score to determine the stability and improvement space of the current model performance. Further, the decision logic, based on preset threshold rules and multi-objective optimization strategies, comprehensively considers the weight allocation of the error index and the physical consistency score to determine whether to trigger model optimization. Specifically, if the mean absolute error index exceeds the preset allowable range and the physical consistency score is lower than the threshold, the system determines that the model has obvious performance defects and generates targeted optimization instructions. The model optimization instructions include, but are not limited to, data augmentation parameter adjustment, network structure fine-tuning suggestions, loss function weight redistribution, and optimizer hyperparameter update schemes. The decision module dynamically generates optimization schemes by combining a rule engine with machine learning-assisted algorithms, supporting multi-round iterative optimization loops. The system automatically records the generated model optimization instructions in the model iteration log, including the instruction type, triggering conditions, and expected effects, facilitating subsequent tracking and verification. These optimization instructions are stored in structured data format, conforming to the input specifications for the "data augmentation parameters" in subsequent step S110, thus achieving closed-loop feedback in the model training process. Finally, the model optimization instructions generated by the iterative decision processing are output as the "model iteration instruction" field, which is then used by the "data augmentation parameters" in subsequent step S110, achieving a closed-loop connection from evaluation results to model training parameter adjustment.

Claims

1. A method for analyzing the coupled response of a wind turbine bridge, characterized in that, include: Raw data on wind speed, wind direction, and vehicle speed are collected, and outliers are corrected and removed in real time through multi-sensor fusion technology. Numerical simulation based on the coupling of finite element method and computational fluid dynamics is then performed to generate a numerical dataset of the coupled response of the wind turbine bridge. Time series samples are input into a parallel encoder containing multiple Transformer encoder units to extract Transformer features; time segments are divided from long-term dependency features and processed by an LSTM gating mechanism to generate non-stationary sequence prediction results; the LSTM prediction results are fused with Transformer long-term dependency features to generate a hybrid prediction response. Based on the analytical displacement, velocity, and acceleration parameters of the hybrid predictive response, the motion equations of the train-bridge system are obtained and discretized by the finite difference method or finite element method to form physical constraints. The weighted L1 norm physical residuals are calculated by substituting them into the discrete equations. The data-driven mean square error and physical residuals are fused to construct a composite loss function. Load the initial weight parameters of the hybrid neural network, configure the subtraction averaging strategy, extract gradient information and update parameters based on the composite loss function, and generate the training completed model through convergence judgment; Load the trained model for forward propagation prediction, extract the displacement, velocity and acceleration of key nodes, and generate physical dimension dynamic results based on the normalized parameters through inverse normalization. Substitute the discrete motion equations to calculate the physical consistency residuals and generate a physical consistency report; Obtain the true values ​​of the test dataset and calculate the mean absolute error index; extract the residual distribution from the physical verification report and statistically analyze the mean, standard deviation, and kurtosis features to generate a physical consistency score; based on the error index and the score results, generate a model optimization instruction feedback training closed loop through multi-objective threshold rules.

2. The wind turbine bridge coupling response analysis method according to claim 1, characterized in that, The steps for extracting Transformer features by inputting time-series samples into a parallel encoder containing multiple Transformer encoder units include: The parallel encoder contains multiple Transformer encoder units, each of which extracts features from the input sequence based on a self-attention mechanism; Time series samples are input into a parallel encoder in the form of multidimensional tensors. After passing through a multi-head self-attention layer, the dependencies between time steps in the sequence are weighted and calculated to capture long-term dependency features. Transformer encoders inject temporal information of time series into feature representations through positional encoding, overcoming the problem of missing sequence order information; By processing multiple Transformer encoder units in parallel, the diversity and robustness of feature extraction are achieved. The feature vectors output by each encoder unit are concatenated or weighted and fused to form a comprehensive long-term dependency feature representation.

3. The wind turbine bridge coupling response analysis method according to claim 1, characterized in that, The steps for generating non-stationary sequence prediction results using the LSTM gating mechanism include: Long-term dependency features are divided into multiple consecutive time segments, and the length of the time segments is preset according to the dynamic change characteristics of non-stationary sequences. The temporal sequence is used as input and enters the long short-term memory network gating mechanism module. Through the input gate, forget gate and output gate, the temporal information is selectively remembered and forgotten, so as to realize the dynamic modeling of non-stationary sequences. The LSTM gating mechanism calculates gating weights based on the current input and the previous hidden state, dynamically adjusts the information flow path, and enhances the model's ability to respond to sequence mutations and trend changes. The internal state of the gating mechanism is updated through the nonlinear activation function of the gating unit, forming a time-dependent hidden state sequence.

4. The wind turbine bridge coupling response analysis method according to claim 1, characterized in that, The steps to fuse LSTM prediction results with Transformer long-term dependency features include: Multimodal fusion is performed between the LSTM prediction results and the long-term dependency features output by the Transformer encoder. The fusion process employs a weighted fusion strategy, which dynamically adjusts the weights of each feature component using an attention mechanism to enhance the expressive power of the fused features. The feature fusion module first performs dimension matching and alignment on the two input feature tensors, and then generates a fused feature vector through dot product and weighted summation operations; The fused features are mapped through a fully connected layer and an activation function to enhance nonlinear expressive power and output a hybrid prediction response.

5. The wind turbine bridge coupling response analysis method according to claim 1, characterized in that, The steps to obtain the equations of motion for a train-bridge system and discretize them using the finite difference method or the finite element method include: The equations of motion are based on the principles of continuum mechanics and structural dynamics, and use differential equations to describe the dynamic characteristics of the system. For differential equations, numerical discretization methods, including the finite difference method or the finite element method, are used to transform the dynamic equations in the continuous time domain into a system of algebraic equations at discrete time points. During the discretization process, the system divides the motion variables into time sequences according to a preset time step. Discretization processing supports an adaptive time step adjustment mechanism, which dynamically adjusts the time step to improve computational accuracy in response to nonlinear behavior and sudden dynamic events in the system.

6. The wind turbine bridge coupling response analysis method according to claim 1, characterized in that, The steps for substituting into the discrete equation to calculate the weighted L1 norm physical residual term include: The feature analysis module separates three key dynamic response parameters: displacement, velocity, and acceleration. The parsing module, based on the dynamic response data structure specification, uses multi-channel data splitting technology to map the multidimensional tensor data in the mixed prediction response to the corresponding dynamic physical quantity dimensions. Based on the extracted displacement, velocity, and acceleration parameters, and in conjunction with physical constraints, the residual calculation of the motion equations is performed. The residual calculation module calculates the difference between the predicted response and the physical constraints, i.e., the residual term, based on the algebraic expression of the discretized motion equations. The residual calculation supports multi-scale residual analysis, calculating residuals for dynamic responses at different frequencies and time scales, and capturing local and global deviations in the dynamic characteristics of the system.

7. The wind turbine bridge coupling response analysis method according to claim 1, characterized in that, The steps to construct a composite loss function by integrating data-driven mean squared error and physical residuals include: A composite loss function is constructed by combining data-driven error metrics, mean squared error, and mean absolute error. The loss function structure uses a multi-objective weighted fusion strategy to unify the processing of data error and physical residual. Weight coefficients are calculated for the physical residual term and the data error respectively. The weight allocation is based on the dynamic adjustment rules during the training phase, and the relative contributions of each loss component are balanced by combining the model convergence speed and the error change trend. The weighted fusion process employs a normalized weighting mechanism.

8. The wind turbine bridge coupling response analysis method according to claim 1, characterized in that, The steps for loading the initial weight parameters of the hybrid neural network and configuring the subtractive averaging strategy include: The weight parameters cover the weights of the multi-head self-attention layer, position encoding weights, and multi-layer feedforward network weights of the Transformer encoder, as well as the input gate, forget gate, output gate, and cell state weights in the long short-term memory network gating mechanism. The weight parameters are initialized using a random initialization method based on uniform or normal distribution, combined with He initialization or Xavier initialization strategies; Based on the structural characteristics of the composite loss function, a subtraction averaging optimization strategy is configured. This strategy dynamically adjusts the overall network parameters by gradually subtracting and averaging the differences in the weights of multiple sub-networks, thereby suppressing gradient oscillations and overfitting. The subtractive averaging strategy first divides the network weights into several subsets, each subset corresponding to a specific module or layer in the network. For each subset weight, the difference between the current gradient and the historical gradient is calculated, and a weighted subtractive averaging operation is performed to form an adjustment vector.

9. The wind turbine bridge coupling response analysis method according to claim 1, characterized in that, The steps for gradient information extraction and parameter updating based on a composite loss function include: The gradient of the composite loss function with respect to the network weight parameters is calculated using an automatic differentiation mechanism; The gradient calculation process involves multi-objective joint gradient backpropagation, which includes mean squared error, mean absolute error, and physical residual terms. According to the subtraction averaging optimization strategy, the corresponding gradient information is extracted for each sub-network weight subset, gradient difference calculation is performed, and the current gradient is subtracted from the historical gradient to form the gradient adjustment vector. The gradient adjustment vector is normalized to prevent gradient explosion or gradient vanishing problems, and weighted accumulation is performed in combination with momentum factor to improve the smoothness and convergence speed of gradient updates. Based on the adjusted gradient, the system calls the learning rate scheduler to adjust the current learning rate according to the preset learning rate dynamic adjustment rules, supporting step decay, cosine annealing and adaptive adjustment mechanisms.

10. The wind turbine bridge coupling response analysis method according to claim 1, characterized in that, The expression for the composite loss function, which integrates data-driven mean squared error and physical residuals, includes: An improved discretized model is established based on the dynamic equations of the train-bridge system, and the time-domain discrete equations are defined as follows: in, The discretized mass matrix; The damping matrix is ​​discretized. The discretized stiffness matrix; For the first The displacement vector at the time step; For the first The velocity vector at the time step; For the first The acceleration vector at the time step; For the first The force vector at the time step depends on the wind speed. and vehicle speed ; This is the wind speed vector; For vehicle speed parameters; For time step index; Substitute the displacement-velocity parameters from the hybrid predicted response into the discrete equation to calculate the weighted L1 norm physical residual term, and define the physical residual term: in, For the first The physical residual of the time step; For the improved weighted L1 norm; By integrating data-driven mean squared error and physical residuals, a composite loss function is constructed: in, This is the value of the composite loss function; The mean squared error is driven by data. These are dynamic weighting coefficients; This is the sum of the physical residuals for all time steps.

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