Windmill bridge system safety assessment method based on KCBMA algorithm

Abstract

The invention discloses a KCBMA algorithm-based windmill bridge system safety assessment method, which relates to the technical field of windmill bridge coupling systems, combines a Kepler optimization algorithm (KOA) with a convolutional neural network-bidirectional long-short-term memory network (CNN-Bi-LSTM-MA) under a multi-head attention mechanism, adaptively searches an optimal hyper-parameter combination of the CNN-Bi-LSTM-MA network through the KOA, and provides a safety assessment method for a windmill bridge system. Constructing a neural network prediction model with dynamic adaptive capacity; the Bi-LSTM unit performs modeling by fusing the randomness characteristics of wind load excitation and system parameters, so that a numerical model can effectively represent the randomness of a wind-vehicle-bridge system and predict the random response of the wind-vehicle-bridge system. According to the method, the dynamic interaction among the wind-vehicle-bridge structures is integrated into the neural network model, the modeling time is remarkably shortened by using the KOA, the modeling accuracy is improved, the calculation cost is reduced, and the system response is more accurately predicted.

Description

Technical Field

[0001] The present invention relates to the technical field of windmill - bridge coupling systems, and particularly to a safety assessment method for a windmill - bridge system based on the KCBMA algorithm. Background Art

[0002] With the rapid development of high - speed railways, the phenomenon of vehicles crossing bridges in strong wind environments has attracted wide attention. Especially in the current technical background of pursuing fast and lightweight high - speed trains, cross - winds have become a key factor threatening the safety and stability of trains. In special environments such as deep valleys or sea - crossing and river - crossing bridges, this risk is particularly prominent. When a train travels on a long - span bridge affected by cross - winds, the high flexibility of the bridge may lead to strong interaction between the vehicle and the bridge, thereby reducing the running comfort of the train and threatening traffic safety. In addition, the coupled action of wind - induced excitation and track irregularity further increases the complexity of the dynamic analysis of the vehicle - bridge system. Therefore, it is very important to evaluate the stability and safety of the windmill - bridge system under cross - wind action.

[0003] In recent years, with the development of artificial intelligence technology, its application scope has expanded to various engineering fields, and the vehicle - bridge field is no exception. Compared with traditional methods, this technology can directly drive through data, thus avoiding complex modeling processes and significantly improving the operation efficiency. With the breakthrough progress of deep - learning algorithms, their applications in the field of random vibration analysis have shown a rapid growth trend. Neural networks can utilize their powerful feature extraction capabilities to study the dynamic response of structures under random loads. However, existing research generally ignores the influence of system uncertainty factors on vibration characteristics. The application of deep - learning technology in the dynamic analysis of vehicle - bridge systems still has obvious limitations. Taking traditional neural networks as an example, their network structures, combinations, and hyperparameter settings are all manually adjusted according to the training data model. As the core elements determining the model performance, the reasonable setting of hyperparameters is directly related to the prediction accuracy and calculation reliability. The manual adjustment method not only increases the modeling complexity and time cost but also easily produces empirical biases, resulting in the model being difficult to reach the optimal adaptation state. In the existing technology, although there are similar combined models such as CNN - LSTM that can improve the data - feature extraction ability to a certain extent, in complex application scenarios such as the windmill - bridge system, in addition to the problem of poor cross - scenario generalization caused by the need for manual adjustment of hyperparameters and the inability to adapt to the non - stationary characteristics of wind loads, there are also defects such as not designing a weight - allocation strategy for the local vibration modes of the vehicle - bridge system, a single module - stacking order, and ignoring the guiding role of spatial features in time - series prediction. Therefore, it is very meaningful to develop an intelligent hyperparameter - adjustment method and optimize the weight allocation and module order. Summary of the Invention

[0004] To address the above problems, the present invention provides a method for safety assessment of a windmill-bridge system based on the KCBMA algorithm, which combines the Kepler optimization algorithm (KOA) with a Convolutional Neural Network (CNN)-Bidirectional Long Short-Term Memory (Bi-LSTM)-Multi-Head Attention (MA) mechanism, namely KCBMA. The optimization ability of KOA is utilized to find the optimal hyperparameters for the model, and the MA mechanism is used to enhance the model's ability to capture key data features. Finally, a mapping relationship between wind speed, track irregularity excitation, and system dynamic response is established, enabling the establishment of an efficient and accurate prediction model for the wind-vehicle-bridge coupling system response. The specific technical solutions are as follows:

[0005] A method for safety assessment of a windmill-bridge system based on the KCBMA algorithm, comprising the following steps:

[0006] Step 1: Establish a vehicle-bridge coupling dynamics model using commercial finite element software; obtain wind speed time series data samples by spectral solution based on the wind spectrum, and calculate wind load time series data using the three-component force coefficient; generate track irregularity excitation time series data samples through the track spectrum.

[0007] Step 2: Input the calculated wind load time series data and track irregularity excitation time series data samples into the vehicle-bridge coupling dynamics model for buffeting analysis, and solve to obtain the windmill-bridge random response time series data samples.

[0008] Step 3: Construct a KCBMA combined model, mainly including a KOA module and a CNN-Bi-LSTM-MA module. The KOA module is used to optimize the hyperparameters of the CNN-Bi-LSTM-MA module. The CNN sub-module in the CNN-Bi-LSTM-MA module is used to adaptively extract spatial local features and global abstract representations from the input time series data samples of wind speed and track irregularity excitation. The Bi-LSTM sub-module is used to capture the long-term dependencies between time series data points to achieve sequence-to-sequence prediction of the windmill-bridge system random response. The MA sub-module is used to simulate the dynamic correlation between different time steps in the time series data samples of wind speed and track irregularity excitation, and enhance the weights of key time step features.

[0009] Step 4: Use the time series data samples of wind speed and track irregularity excitation as input data, and the windmill-bridge random response time series data samples as output data, and bring them into the KCBMA combined model to find the optimal hyperparameters.

[0010] Step 5: Based on the optimal hyperparameters found by the KOA module, construct an accurate neural network model and train the neural network model with the input data and output data; after the training is completed, realize the prediction of the stochastic response of the windmill bridge system.

[0011] The beneficial effects of the present invention are:

[0012] The neural network model adopts a multi-module collaborative architecture. Through the deep combination of the feature extractor and the multi-head self-attention mechanism, it realizes the efficient modeling of the double inputs of wind speed and track irregularity excitation, and finally can accurately predict the stochastic response of the windmill bridge system. Each module closely cooperates to form an efficient data processing flow. The CNN is responsible for extracting spatial features from the original data. The multi-head self-attention mechanism enhances the representation of key features on this basis. The Bi-LSTM network further mines the time series information, and the KOA module dynamically adjusts the model parameters to optimize the performance. This combination not only makes full use of the advantages of each module, but also improves the model's understanding and prediction ability of the windmill bridge response data through the synergy between modules. Compared with the conventional single network structure, it has higher flexibility and adaptability, and can better handle various tasks in the windmill bridge system.

[0013] The core innovation of the present invention lies in the accurate prediction of the dynamic response of the windmill bridge system through a multi-module collaborative architecture. The specific technical integration is reflected in:

[0014] The dynamic coupling mechanism of KOA and deep learning: The hyperparameters of traditional neural networks rely on artificial experience, while KOA simulates the parameter space search through the planetary gravity model and dynamically adjusts the initial learning rate, the number of neurons, and the convolution kernel size of the Bi-LSTM in combination with the anti-predation mechanism to achieve the adaptive matching of hyperparameters and data features; combining the dynamic time step update rule of KOA with the time series prediction of Bi-LSTM enables the parameter optimization process to synchronously respond to the time-varying characteristics of the wind speed-track excitation.

[0015] The combination of CNN-Bi-LSTM-MA: The multi-layer convolution kernels of the CNN module can extract the local spatial patterns of the wind speed load in the windmill bridge system, solving the defect that the traditional LSTM can only process time series signals; the Bi-LSTM models the forward-backward dependence relationship of the bridge displacement, solving the problem of the lag effect of the wind vibration response in the wind-vehicle-bridge coupling system; the multi-head attention mechanism (MA) calculates the spatio-temporal weight matrix at the output end of the Bi-LSTM hidden layer, which can effectively focus on the pulsating wind load in the strong wind section and reduce the prediction error.

[0016] The present invention fully combines the Kepler optimization algorithm (KOA), convolutional neural network (CNN), bidirectional long short-term memory network (Bi-LSTM), and multi-head attention mechanism to construct a structural response prediction model for the windmill bridge system. This technology conducts targeted engineering adaptation for the data characteristics of the windmill bridge coupling system, establishes an optimal training model based on the best parameters, simplifies the establishment of vehicle models and bridge models through deep learning to achieve the purpose of shortening the calculation time, and can establish an uncertain model to accurately predict the responses of the uncertain vehicle-bridge system and improve the prediction accuracy. Description of the Drawings

[0017] Figure 1 It is a neural network architecture diagram.

[0018] Figure 2(a) is a curve graph of the fitness fitting function during the KOA search process.

[0019] Figure 2(b) is a process graph of the iterative optimization of the initial learning rate.

[0020] Figure 2(c) is a process graph of the iterative optimization of the convolution kernel size.

[0021] Figure 2(d) is a process graph of the iterative optimization of the number of neurons.

[0022] Figure 2(e) is a process graph of the iterative optimization of the planetary gravity.

[0023] Figure 2(f) is a process graph of the iterative optimization of the planetary mass.

[0024] Figure 3(a) is a trend graph of the total loss value (Loss) during the training process with the number of training epochs.

[0025] Figure 3(b) is a trend graph of the root-mean-square error (RMSE) during the training process with the number of training epochs.

[0026] Figure 3(c) is a loss convergence curve graph.

[0027] Figure 3(d) is a root-mean-square error convergence curve graph.

[0028] Figure 4(a) is a bridge lateral displacement response graph during vehicle driving.

[0029] Figure 4(b) is a bridge vertical displacement response graph during vehicle driving.

[0030] Figure 5(a) is a vehicle lateral acceleration response graph during vehicle driving.

[0031] Figure 5(b) is a vehicle vertical acceleration response graph during vehicle driving.

[0032] Figure 6(a) is a prediction error (error) graph of the vehicle vertical acceleration under different numbers of samples.

[0033] Figure 6(b) is a prediction error (error) graph of the bridge vertical displacement under different numbers of samples.

[0034] Figure 7(a) is a power spectral density (PSD) graph of the bridge lateral displacement.

[0035] Figure 7(b) is a power spectral density (PSD) graph of the bridge vertical displacement.

[0036] Figure 7(c) is a power spectral density (PSD) graph of the vehicle lateral acceleration.

[0037] Figure 7(d) is a power spectral density (PSD) graph of the vehicle vertical acceleration.

[0038] Figure 8(a) is a prediction effect graph under Case 1.

[0039] Figure 8(b) is a prediction effect graph under Case 2.

[0040] Figure 8(c) is a prediction effect graph under Case 3.

[0041] Figure 8(d) is a prediction effect graph under Case 4.

[0042] Figure 9 It is a prediction error graph under 4 cases. Specific implementation manners

[0043] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0044] The present invention aims to establish an efficient and accurate prediction model for the response of the wind-vehicle-bridge coupling system to achieve the best prediction effect. To this end, the present invention is verified on a double-tower double-cable-plane cable-stayed bridge. Based on the concept described in this method, the KCBMA optimization algorithm (KOA-CNN-Bi-LSTM-MA) is designed and developed. Among them, the KOA module is used to search for optimal hyperparameters, and its anti-predation mechanism is used to improve the accuracy of the search. Then, the multi-head attention mechanism (MA) is used to optimize the position information in Bi-LSTM, thereby improving the performance of the model. The optimization algorithm uses the response samples calculated by the Monte Carlo Method (MCM) as the data set, and uses track irregularity excitation, wind speed excitation, and structural parameters as input data for training. The point-by-point prediction of the vehicle-bridge system response is realized through time series estimation in the Bi-LSTM layer. Using this method, the optimal parameters are obtained to establish the best training model. By deep learning, the establishment of a simplified vehicle model and a bridge model is achieved to shorten the calculation time. At the same time, an uncertain model can be established to accurately predict the response of the uncertain vehicle-bridge system and improve the prediction accuracy.

[0045] I. The technical solution adopted by the present invention is as follows:

[0046] Step 1: Establish a vehicle-bridge coupling dynamics model through commercial finite element software ANSYS and MIDAS. Verify the natural vibration frequency of the vehicle model and the natural vibration frequency of the bridge model according to the analysis, and verify the correctness of the bridge model according to the natural vibration frequency and mode of the bridge model obtained by calculation.

[0047] The bridge model is: (1); In the formula, represents the bridge mass matrix, represents the bridge damping matrix, represents the bridge stiffness matrix; represents the bridge acceleration, represents the bridge velocity, represents the bridge displacement response; represents the external force acting on the bridge.

[0048] The vehicle model is: (2); In the formula, is the mass matrix of the vehicle, is the damping matrix of the vehicle, is the stiffness matrix of the vehicle; represents the acceleration of the vehicle movement, represents the velocity of the vehicle movement, A displacement vector representing vehicle motion; is the excitation force or load acting on the vehicle.

[0049] Step 2: Obtain wind speed time series data samples using the spectral solution method through the wind spectrum, and then calculate the wind load time series data according to the wind speed samples using the three-component force coefficient.

[0050] Step 3: Use the German track irregularity power spectral density as the random excitation, and obtain the track irregularity excitation time series data samples through the spectral representation method.

[0051] Step 4: Input the calculated wind load and track irregularity excitation into the vehicle-bridge coupling system, and solve it through the Monte Carlo method to obtain the random response time series data samples of the wind-vehicle-bridge system.

[0052] Step 5: Construct the KCBMA combined model, whose structure is as Figure 1 shown. The KCBMA model architecture includes the Kepler Optimization Algorithm (KOA), Convolutional Neural Network (CNN), Bidirectional Long Short-Term Memory Network (Bi-LSTM), and Multi-Head Attention Mechanism (MA).

[0053] Figure 1 In, in the CNN feature extractor frame, a, b, and c respectively represent the category feature vectors generated after feature extraction; in the multi-head attention mechanism frame, W Q , W K , W V respectively represent the weight matrices for mapping the input features to the query, key, and value spaces; in the bidirectional LSTM neural network frame, X t represents the input at the current moment; X i and Vt in the KOA frame are the input information and the current state information respectively.

[0054] 1. Kepler Optimization Algorithm (KOA):

[0055] This module is used to find the optimal hyperparameters of the neural network model. Its core principle is that each planet and its position represent a candidate solution, which is randomly updated through an optimization process based on the current optimal solution (the sun). The distance between the planet (candidate solution) and the sun (current optimal solution) changes over time, and the planet's orbit is randomly selected based on the normal distribution. This property enables the KOA to efficiently explore and utilize the search space.

[0056] During the optimization process, the following criteria are followed, and the fitness of each solution is calculated according to the objective function:

[0057] (1) The optimal solution in each iteration is used as the central star (the sun);

[0058] (2) The distance between the planet and the sun is dynamically adjusted according to the current time;

[0059] (3) The revolution period of the planet (candidate solution) is randomly selected according to the normal distribution;

[0060] (4) The orbital eccentricity of each planet is randomly selected within the range of 0 - 1.

[0061] During the calculation, the population size is determined by the following equation, and the candidate solutions are randomly distributed in the d - dimensional space. These candidate solutions represent the hyperparameters that need to be optimized and updated in the neural network model.

[0062] (3); In the formula, represents the population size (the set of candidate solution distributions) of the i - th candidate solution in the j - th hyperparameter in the space; d is the dimension of the hyperparameters to be optimized, corresponding to the types of hyperparameters that need to be optimized in the CNN - Bi - LSTM - MA module, including the convolutional kernel size, the number of Bi - LSTM neurons, and the initial learning rate; N represents the total number of candidate solutions in each type of hyperparameter dimension; and respectively represent the upper and lower bounds of the i - th solution in the j - th dimension; is a random number uniformly distributed within the interval [0, 1].

[0063] The KOA optimization algorithm simulates the search of the neural network hyperparameter space through the planetary gravitational model to update the hyperparameter combination, where the "sun" represents the optimal hyperparameter combination (with the highest fitness) in the current iteration; the "planet" represents other candidate hyperparameter combinations, which approach the optimal solution through gravitational force.

[0064] The planet moves in space due to its own mass and the gravitational force it receives, which requires defining the corresponding gravitational function.

[0065] (4); In the formula, represents the gravitational value received by the i - th candidate solution (planet) at time t, which is used to guide the candidate solution to approach the current optimal solution (sun); and respectively represent the normalized fitness values of the current optimal hyperparameter combination (sun) and other candidate hyperparameter combination solutions (planets); is the dynamic universal gravitational constant, which is related to the number of iterations to balance global search and local optimization; is a small value to prevent division by zero; is a numerical value randomly generated between 0 and 1, which is used to increase the diversity of the gravitational value and avoid local optima; Denote the normalized quality coefficient of the \(i\)-th candidate solution, which is used to adjust the weight of the gravitational value.

[0066] while is the normalized value of denote and the Euclidean distance between, which is defined as follows: (5); In the formula, and respectively denote the values of the \(j\)-th dimensional hyperparameter of the optimal solution and the candidate solution.

[0067] The distance between the selected random solution and the current solution affects the speed calculation, resulting in a reduced speed. This lack of solution diversity may reduce the probability of escaping from the local optimal solution due to insufficient mutation of the current solution. Therefore, it is necessary to define the speed (update speed of the hyperparameter combination) of the candidate solution (planet).

[0068] (6); In the formula, represents the speed of the candidate solution (planet), indicating the update direction and step size of the hyperparameter combination; and respectively represent the direction control factor and the complementary direction control factor, where ; and are randomly generated values (random perturbation factors) within the interval [0,1] to enhance search randomness; and respectively represent the dynamic decay perturbation factor and its vectorized extended form; and represent the position vectors of two selected candidate solutions, indicating different hyperparameter combinations; represents the normalized fitness difference; and represent binary scalars; and respectively represent the upper and lower bounds of the \(i\)-th hyperparameter candidate solution; and represent the upper and lower bound vectors of the hyperparameter candidate solution; is used to switch the search direction; 、 respectively represent the position vector of the current candidate solution and the position update decay factor.

[0069] According to the previous equation, the new position of each candidate solution (planet) far from the hyperparameter optimal solution (sun) will be updated through the flow mechanism.

[0070] (7); Wherein, represents the new position of candidate solution i at time t + 1; is the instantaneous velocity required for candidate solution i to reach the new position; is the sun-optimal position found so far; is used to switch the search direction; r is a random number drawn from the standard normal distribution; is a binary vector.

[0071] 2. Convolutional Neural Network (CNN):

[0072] This module adaptively extracts the spatial local features and global abstract representations of the input data through operations such as local perception, non-linearity, and pooling of multi-layer convolutional kernels. With its powerful feature extraction ability, it can effectively handle the high-dimensional characteristics of each time step in the input wind speed and track irregularity excitation time series.

[0073] CNN slides a convolutional kernel over each time step in the input wind speed and track irregularity excitation time series data to extract local features.

[0074] (8); Wherein, is the input sequence, is the convolutional kernel weight, is the bias, is the convolutional kernel size, is the output feature.

[0075] Non-linearity is introduced through the activation function (ReLU) to enhance the feature extraction and expression ability of CNN.

[0076] (9); Wherein, is the output feature extracted by the convolutional kernel.

[0077] The pooling layer is used for downsampling operations to reduce the dimension and retain significant features: (10); Wherein, is the output feature after pooling, representing the maximum value within the window; is the local feature value extracted previously; v is the index range of the pooling window, defining the feature extraction region; s is the stride, and k is the pooling window size.

[0078] 3. Bidirectional Long Short-Term Memory Network (Bi-LSTM):

[0079] This module is used to capture the correlation between time series data points, achieve sequence-to-sequence prediction, and avoid the error accumulation problem existing in traditional feedforward neural networks. This bidirectional long short-term memory network overcomes the limitations of traditional LSTM networks in encoding past and future context time information, captures the forward and backward dependencies of the sequence through bidirectional time series processing, solves the long-term memory problem, and thus improves the understanding ability of sequence data. The gating mechanism of the LSTM unit includes a forget gate, an input gate, a cell update state, and an output gate. Among them:

[0080] Forget gate: determines what information to discard: (11); In the formula, is the input vector at time t; represents the output vector at time t - 1; and are the weight and bias of the forget gate respectively; is the sigmoid activation function.

[0081] Input gate: updates the cell state: , (12); In the formula, and are the weights in the input gate, and are the biases in the input gate; represents the candidate cell state; indicates which information needs to be updated.

[0082] Cell state update: (13); In the formula, represents the cell state at the current time t; represents the cell state at the previous time.

[0083] Output gate: generates the current hidden state: , (14); In the formula, and are the weight and bias of the output gate respectively; represents the output vector at time t.

[0084] Bi-LSTM processes the data bidirectionally, processes the sequence from the forward and the backward respectively, and merges the outputs: (15); Wherein, represents vector concatenation.

[0085] 4. Multi-Head Attention Mechanism (MA):

[0086] This module is used to simulate the correlation between different positions in the input sequence. It calculates the attention weights of each time step in the input wind speed and track irregularity excitation time series data relative to other time steps. Then, the input sequence is weighted and summed according to these weights, enabling the model to prioritize the processing of important information in different parts of the sequence. By using the attention mechanism, the model can more effectively focus on key data points when processing sequential data. This is particularly useful for analyzing the coupled response of vehicles and bridges, as the attention mechanism can capture the correlation between different time steps in the sequence.

[0087] The multi-head attention mechanism enhances the model's ability to capture richer features and context information by using multiple attention heads. These attention heads work in parallel, enabling the model to simultaneously focus on different dimensions of the input information. This approach can analyze data more comprehensively, as follows: (16); Wherein, are the transformation matrices of the query, key, and value of the m-th attention head, respectively.

[0088] The outputs from all attention heads are concatenated together and then undergo a final linear transformation and layer normalization. This process integrates the information learned from different subspaces and enhances the model's expressive power.

[0089] (17); Wherein, is the final output transformation matrix.

[0090] The multi-head attention mechanism enhances the model's parallel computing ability by processing multiple attention distributions in parallel and enables it to capture key features in the input information from multiple perspectives and dimensions. This significantly improves the model's expressive power and learning efficiency, making it an indispensable component in modern deep learning architectures.

[0091] Step 6: Use the calculated wind speed samples and track irregularity excitation samples as input data, and the random samples of windmill-bridge responses as output data, and input them into the KCBMA model to find the optimal hyperparameters.

[0092] Based on the hyperparameter update module KOA in the model, the hyperparameters are iteratively optimized according to the input data, and the fitness function is minimized to obtain the optimal hyperparameter combination. Among them, KOA optimizes three hyperparameters: the initial learning rate (Initial-Learn-Rate) of the bidirectional long short-term memory network, the number of neurons (Neuron count), and the kernel size (Kernel size). When the adaptation function does not reach the optimum, the process of finding hyperparameters continues until the maximum number of iterations is reached.

[0093] Step 7: Establish an accurate neural network model based on the optimal hyperparameters found by KOA, and train the CNN-Bi-LSTM-MA model with the input data and output data.

[0094] The neural network model starts with a CNN feature extraction network. First, it performs dual-channel parallel processing on the wind speed and track irregularity excitation. Through CNN convolution operations, it automatically learns the spatial features in the time series data of the wind speed and track irregularity excitation. The extracted spatial features then enter the MA sub-module. The MA sub-module contains multiple parallel attention heads. Each head calculates attention scores through query, key, and value weight matrices, weights different time steps in the feature sequence to capture the global dependencies between the spatial distribution and temporal evolution features, enhances important features such as extreme special wind speed features, and suppresses irrelevant features such as sensor noise and high-frequency vibrations. The features processed by the attention mechanism are divided into two parts and fed into the two Bi-LSTM networks of the Bi-LSTM sub-module respectively. The first Bi-LSTM contains N c layers, which are used to capture the long-term time dependencies of the input features. The second Bi-LSTM is a single layer, which further refines the feature representation, weights and screens the interactions of features within a local time window (such as sudden wind speed fluctuations and track transient impact responses), and suppresses short-term noise interference. The training process of the neural network model is continuously optimized through iterative gradient descent method to minimize the gradient value. Finally, according to the best hyperparameters determined by the KOA module and the key sequence feature weights optimized by the multi-head attention mechanism, the optimal neural network model is determined, and the optimal neural network model is used to predict the random response of the windmill bridge system to obtain the best result.

[0095] Step 8: After the training is completed, predict the random response of the windmill bridge system.

[0096] II. Case analysis:

[0097] To better verify and apply the optimization algorithm proposed in this paper, the KCBMA is applied to the model of a high-speed train crossing a cable-stayed bridge, and the research is carried out on the bridge coupling model under the excitation of random wind speed and random track irregularities. In this paper, a double-tower double-cable-plane cable-stayed bridge with a span combination of 81 + 162 + 432 + 162 + 81 m and a total main bridge length of 918 m is taken as the research object. The main girder adopts a single-box single-room concrete box girder structure, the structural damping ratio is 2%, the beam height is 3.5 m, the beam width is 24.5 m, cross-section partitions are set in the cable-stayed cable section, and the structural parameters of the finite element model of the bridge are shown in Table 1.

[0098] Table 1 Main parameters of the bridge structure 。

[0099] Combined with the design drawings, two software models are established for analysis. Their dynamic characteristics are basically in agreement, and the error is within the allowable range, as shown in Table 2.

[0100] Table 2 Verification of the bridge's natural vibration characteristics 。

[0101] The vehicle model adopts the German ICE high-speed train model, which consists of 8 carriages, and its specific parameters are shown in Table 3. The vehicle speed is set at 200 km / h and the wind speed is set at 10 m / s.

[0102] Table 3 Parameters of the elastically suspended vehicle model 。

[0103] The wind load and track irregularity samples are used as the input data of the KCBMA model, and the system responses calculated by the Monte Carlo method (MCM) are used as the training samples. Since the number of samples has increased significantly, the parameters of the Kepler optimization algorithm (KOA) need to be reset: a larger population size is set, where the number of search planets is set to 10 and the number of iterations is set to 5. Three hyperparameters are set during the optimization search process, namely the initial learning rate, neuron count, and kernel size of the bidirectional long short-term memory network (Bi-LSTM). Through the continuous search of the Kepler optimization algorithm (KOA), the best combination of the three hyperparameters is finally found after 5 iterations (10 populations per round), as shown in Table 4.

[0104] To better illustrate the search process, the fitness function curves and parameter optimization processes of each iteration are extracted, as shown in Figures 2(a) - 2(f). Each parameter tends to be stable after the first 3 iterations. Therefore, setting the number of iterations to 3 can not only meet the model optimization requirements but also significantly shorten the optimization time.

[0105] Optimal Hyperparameters of the Model in Table 4 。

[0106] The optimized neural network model was trained with 1000 sets of samples. The entire training process was optimized by the gradient descent method, ultimately minimizing the gradient value. To visually represent the training process, the root mean square error (RMSE) loss function was mainly plotted for characterization. As shown in Figures 3(a) - 3(d), the figures display the changing trends of the root mean square error (RMSE) and total loss (Loss) of the predicted data with the number of training cycles.

[0107] After training, the prediction results of the model were analyzed. The predicted values of the KCBMA method were compared and mutually verified with those of the Monte Carlo simulation (MCM) and the CNN - Bi - LSTM (CBL) model. For the bridge structure, vertical and lateral displacements were the key concerns, while for the vehicle system, vertical and lateral accelerations were of the utmost importance. The comparison results are shown in Figures 4(a) - 4(b) and Figures 5(a) - 5(b).

[0108] The changing trends of the root mean square error (RMSE) and mean square error (MSE) of vehicle acceleration and bridge displacement with the increase in the sample size are shown in Figures 6(a) - 6(b). The prediction error decreases as the sample size increases, and the MSE index is more stable. Figures 7(a) - 7(d) show the average power spectral density (PSD) of vehicle acceleration and bridge displacement, where the Monte Carlo simulation (MCM) is compared with the KCBMA method. The PSD curves of the two coincide highly, indicating that the proposed KCBMA method has similar accuracy to MCM.

[0109] Table 5 Comparison of Prediction Errors 。

[0110] Based on the prediction results of the bridge and the vehicle, the predicted values of the KCBMA method are closer to the Monte Carlo simulation (MCM), with smaller errors, and can meet the requirements of engineering applications. To more intuitively compare the prediction efficiency of KCBMA, Table 5 lists relevant performance indicators, including the root mean square error (RMSE), mean absolute error (MAE), mean relative percentage error (MRPE), training set accuracy, test set accuracy, and training time. Among them, the improvement in the test set accuracy is the most significant, increasing by more than 75% compared to the CBL method, and the training time is also shortened by 8.21%. It can be seen that KCBMA is optimized to varying degrees in all aspects compared with traditional neural network algorithms.

[0111] To verify the superiority of the proposed method, the proposed method is compared with CNN-Attention-Bi-LSTM (CABL) and CNN-Bi-LSTM (CBL). Given the significant advantages of the attention mechanism for long-time series data, the time-history displacement of the system response is used for verification. It should be noted that four step sizes of 0.02, 0.025, 0.03, and 0.04 are set for Cases 1 to 4 respectively (see Table 6 for details), and the other parameters remain unchanged. Since the total time remains unchanged and only the step size is changed, the response data lengths of each case are different, and the prediction results are shown in Figures 8(a) - 8(d).

[0112] Table 6 Different series durations 。

[0113] As Figure 9 shown, the prediction effects and accuracies of the KCBMA and CABL methods are the highest, and their prediction results highly coincide with the MCM. Taking Case 1 in Figure 9 as an example, the prediction error of the proposed method is 2.9486×10^-6, the prediction error of CABL is 3.7997×10^-5, while the maximum prediction error of CBL reaches 5.1651×10^-5, which is about 18 times that of the proposed method and 12 times that of CABL. This shows that the proposed method has significant advantages in long-time series prediction, and the error is within the engineering acceptable range.

[0114] The above research shows that the method based on KCBMA can effectively predict the coupled vibration response of the wind-turbine-bridge system. Compared with other network frameworks, its accuracy and efficiency in long-time series prediction have been significantly improved.

Claims

1. A safety assessment method for a windmill bridge system based on the KCBMA algorithm, characterized in that, It includes the following steps: Step 1: Establish a vehicle-bridge coupling dynamics model using commercial finite element software; obtain the wind speed time series data samples by the spectral method based on the wind spectrum, calculate the wind load time series data using the three-component force coefficient; generate the track irregularity excitation time series data samples through the track spectrum; Step 2: Input the calculated wind load time series data and the track irregularity excitation time series data samples into the vehicle-bridge coupling dynamics model for buffeting analysis, and solve to obtain the wind-vehicle-bridge random response time series data samples; Step 3: Construct a KCBMA combined model, mainly including a KOA module and a CNN-Bi-LSTM-MA module. The KOA module is used to optimize the hyperparameters of the CNN-Bi-LSTM-MA module; the CNN sub-module in the CNN-Bi-LSTM-MA module is used to adaptively extract the spatial local features and global abstract representations from the input time series data samples of wind speed and track irregularity excitation, the Bi-LSTM sub-module is used to capture the long-term dependencies between time series data points to achieve sequence-to-sequence prediction of the random response of the wind-vehicle-bridge system; the MA sub-module is used to simulate the dynamic correlations between different time steps in the wind speed and track irregularity excitation time series data samples and enhance the weights of the key time step features; Step 4: Take the time series data samples of wind speed and track irregularity excitation as input data, and the wind-vehicle-bridge random response time series data samples as output data, and bring them into the KCBMA combined model to find the optimal hyperparameters; Step 5: Based on the optimal hyperparameters found by the KOA module, construct an accurate neural network model, and train the neural network model with the input data and output data; after training, realize the prediction of the random response of the wind-vehicle-bridge system.

2. The safety assessment method of the windmill bridge system based on the KCBMA algorithm according to claim 1, wherein In the above Step 3, the KOA module adopts the Kepler optimization algorithm. During the optimization process, the fitness of each solution is calculated according to the objective function; during the calculation, the population size is determined by the following equation, and the candidate solutions regarded as planets are randomly distributed in the d-dimensional space; （1）； Wherein, represents the population size of the i-th candidate solution among the j-dimensional hyperparameters in space, that is, the set of candidate solution distributions; d is the dimension of the hyperparameters to be optimized, corresponding to the types of hyperparameters to be optimized in the CNN-Bi-LSTM-MA module, including the convolutional kernel size, the number of Bi-LSTM neurons, and the initial learning rate; N represents the total number of candidate solutions in each type of hyperparameter dimension; represents the upper bound of the i-th candidate solution in the j-th dimension, represents the lower bound of the i-th candidate solution in the j-th dimension; is a random number uniformly distributed within the interval [0, 1]; Define the gravitational function: （2）； In the formula, represents the gravitational value received by the i-th candidate solution at time t, which is used to guide the candidate solution to approach the current optimal solution; represents the normalized fitness value of the current optimal hyperparameter combination as the sun, represents the normalized fitness value of other candidate hyperparameter combination solutions as planets; is the dynamic gravitational constant; is a tiny value to prevent division by zero; is a randomly generated value between 0 and 1, which is used to increase the diversity of gravitational values and avoid local optima; represents the normalized mass coefficient of the i-th candidate solution, which is used to adjust the weight of the gravitational value; while is the normalized value, representing the Euclidean distance between the optimal solution and the candidate solution in the hyperparameter space, which is defined as follows: （3）； In the formula, and respectively represent the values of the j-th dimensional hyperparameters of the optimal solution and the candidate solution; Define the velocity of the candidate solution: （4）； In the formula, represents the velocity of the candidate solution, indicating the update direction and step size of the hyperparameter combination; represents the direction control factor, represents the complementary direction control factor, where ; and are randomly generated random perturbation factors within the interval [0,1], enhancing the search randomness; and represent the dynamic decay perturbation factor and its vectorized extended form respectively; and represent the position vectors of two selected candidate solutions, representing different hyperparameter combinations; represents the normalized fitness difference; and represent binary scalars; and represent the upper and lower bounds of the i-th hyperparameter candidate solution respectively; and represent the upper bound vector and lower bound vector of the hyperparameter candidate solution respectively; is used to switch the search direction; 、 represent the position vector of the current candidate solution and the position update decay factor respectively; According to the previous equation, the new position of each candidate solution far from the optimal solution of the hyperparameters will be updated through the flow mechanism; （5）； In the formula, represents the new position of candidate solution τ at time t + 1, represents the new position of candidate solution τ at time t; is the instantaneous velocity required for candidate solution τ to reach the new position; is the best position of the sun discovered so far; r is a random number drawn from the standard normal distribution, is a binary vector.

3. The safety assessment method of the windmill bridge system based on the KCBMA algorithm according to claim 2, characterized in that, In the above Step 3, the CNN sub-module slides the convolutional kernel at each time step in the input time series data of wind speed and track irregularity excitation to extract the local features of the input wind speed and track irregularity excitation, as shown in the following formula: （6）； In the formula, is the input sequence, is the convolutional kernel weight, is the bias, is the convolutional kernel size, is the output feature; Introduce nonlinearity through the activation function ReLU to enhance the feature extraction and expression ability of CNN: （7）； In the formula, is the output feature extracted by the convolution kernel; Adopt a pooling layer to perform downsampling operation on the output features, reduce the dimension of the extracted features and retain the significant features, as shown in the following formula: （8）； wherein, is the output feature after pooling, representing the maximum value within the window; is the local feature value extracted previously; v is the index range of the pooling window, defining the feature extraction region; s is the stride, and k is the pooling window size.

4. The safety assessment method of the windmill bridge system based on the KCBMA algorithm according to claim 3, characterized in that, In the above Step 2, the LSTM cell gating mechanism in Bi-LSTM includes a forget gate, an input gate, a cell update state, and an output gate; among them: Forget gate f t : Determines which information to discard, expressed as: （9）； In the formula, is the input vector at time t; represents the output vector at time t - 1; and are the weight and bias of the forget gate respectively; is the sigmoid activation function; Input gate: Update the cell state, expressed as: , （10）； wherein, and are the weights in the input gate; and are the biases in the input gate; represents the candidate cell state; indicates which information needs to be updated; Cell state update, expressed as: （11）； In the formula, represents the unit state at the current moment t; represents the unit state at the previous moment; Output gate O t : Generates the current hidden state, expressed as: , （12）； wherein, is the weight of the output gate, is the bias of the output gate; represents the output vector at time t; The Bi-LSTM sub-module processes the data bidirectionally, processing the sequence forward and backward respectively, and merging the outputs: （13）； In the formula, represents vector concatenation.

5. The safety assessment method for a windmill bridge system based on the KCBMA algorithm according to claim 4, wherein, In step 2, the MA sub-module calculates the attention weights of each time step in the time series data of the input wind speed and track irregularity excitation relative to other time steps; then, based on the attention weights, the input sequence is weighted and summed, enabling the model to preferentially process important information in different parts of the sequence; specifically as follows: （14）； Among them, is the m-th attention head, are the query , key and value transformation matrices of the m-th attention head respectively; The outputs from all attention heads are concatenated together and then undergo a final linear transformation and layer normalization; （15）； Among them, is the final output transformation matrix.

6. The safety assessment method of the windmill bridge system based on the KCBMA algorithm according to claim 1, wherein, In step 3, the KOA optimization algorithm is used to iteratively optimize hyperparameters based on the input data, minimizing the fitness function to obtain the optimal hyperparameter combination. The KOA optimization algorithm optimizes three hyperparameters: the initial learning rate, the number of neurons, and the convolutional kernel size of the bidirectional long short-term memory network. When the adaptation function does not reach the optimum, the process of searching for hyperparameters continues until the maximum number of iterations is reached.

7. A safety assessment method for a windmill bridge system based on the KCBMA algorithm according to claim 1, characterized in that, The specific training of the neural network model in step 4 is as follows: Step 4.1: After the KOA module completes hyperparameter optimization, the neural network model is trained based on the dataset. The neural network model starts with the CNN sub-module feature extraction network. First, the wind speed and track irregularity excitation are processed in a two-channel parallel manner. Through CNN convolution operations, the spatial features in the time series data of the wind speed and track irregularity excitation are automatically learned, and the obtained spatial features then enter the MA sub-module; Step 4.2: The MA sub-module contains multiple parallel attention heads. Each head calculates attention scores through query, key, and value weight matrices, weights different time steps in the feature sequence to capture the global dependencies between spatial distribution and temporal evolution features, enhances important features including extreme special wind speed features, and suppresses irrelevant features including sensor noise and high-frequency vibration interference; Step 4.3: The features processed by the attention mechanism are divided into two parts and fed into the two Bi-LSTM networks of the Bi-LSTM sub-module respectively; the first Bi-LSTM contains N c layers, which are used to capture the long-term temporal dependencies of the input features; the second Bi-LSTM is a single layer, which further refines the feature representation, weights and screens the feature interactions within the local time window, suppresses short-term noise interference, and the features within the local time window include sudden wind speed fluctuations and track transient shock responses; the training process of the neural network model is continuously optimized through iterative gradient descent method to minimize the gradient value; Step 4.4: Based on the optimal hyperparameters determined by the KOA module and the key sequence feature weights optimized by the multi-head attention mechanism, the optimal neural network model is determined, and the optimal neural network model is used to predict the random response of the windmill bridge system to obtain the best result.

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