A safety assessment method for windmill bridge system based on KCBMA algorithm

Abstract

This invention discloses a windmill-bridge system safety assessment method based on the KCBMA algorithm. This method relates to the technical field of windmill-bridge coupled systems. The method combines the Kepler optimization algorithm (KOA) with a convolutional neural network-bidirectional long short-term memory network (CNN-Bi-LSTM-MA) with a multi-head attention mechanism. The KOA adaptively searches for the optimal hyperparameter combination of the CNN-Bi-LSTM-MA network to construct a neural network prediction model with dynamic adaptability. The Bi-LSTM unit integrates wind load excitation and the random characteristics of system parameters for modeling, enabling the numerical model to effectively characterize the randomness of the windmill-bridge system and predict its random response. This method integrates the dynamic interaction between the windmill-bridge structure into the neural network model. Using the KOA, the method significantly shortens modeling time, improves modeling accuracy, reduces computational costs, and provides more accurate predictions of system responses.

Description

Technical Field

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

[0002] With the rapid development of high-speed railways, the phenomenon of vehicles crossing bridges in strong winds has attracted widespread attention. Especially in the current technological context of pursuing fast, lightweight high-speed trains, crosswinds have become a key factor threatening train safety and stability. This risk is particularly prominent in special environments such as deep valleys or bridges across seas or rivers. When trains travel on long-span bridges affected by crosswinds, the high flexibility of the bridge may lead to strong interactions between the train and the bridge, reducing train comfort and threatening driving safety. In addition, the coupling of wind-induced excitation and track irregularities further complicates the dynamic analysis of the train-bridge system. Therefore, it is very important to evaluate the stability and safety of windmill-bridge systems under crosswinds.

[0003] In recent years, with the advancement of artificial intelligence (AI) technology, its application has expanded to various engineering fields, including axles. Compared to traditional methods, this technology can be directly data-driven, bypassing complex modeling processes and significantly improving computational efficiency. With breakthrough advances in deep learning algorithms, its application in random vibration analysis is rapidly growing. Neural networks can leverage their powerful feature extraction capabilities to study the dynamic response of structures under random loads. However, existing research generally ignores the impact of system uncertainty on vibration characteristics. The application of deep learning technology in the dynamic analysis of axle systems still has significant limitations. For example, traditional neural networks, their network structure, combination, and hyperparameter settings are all manually adjusted based on the training data model. As a core factor in determining model performance, the appropriate setting of hyperparameters is directly related to prediction accuracy and computational reliability. Manual adjustment not only increases modeling complexity and time costs, but is also prone to empirical bias, making it difficult to achieve optimal model fit. While existing technologies, such as CNN-LSTM, can improve data feature extraction to a certain extent, they face challenges in complex applications like windmill-bridge systems. These models require manual hyperparameter adjustment, resulting in poor cross-scenario generalization and an inability to adapt to the non-stationary nature of wind loads. Furthermore, they lack weight allocation strategies tailored to the local vibration modes of the bridge system, employ a single module stacking sequence, and ignore the guiding role of spatial features in time series prediction. Therefore, developing intelligent hyperparameter adjustment methods and optimizing weight allocation and module sequence is crucial. Summary of the Invention

[0004] To address the above issues, the present invention provides a windmill-bridge system safety assessment method based on the KCBMA algorithm. This method combines the Kepler optimization algorithm (KOA) with a convolutional neural network (CNN)-bidirectional long short-term memory (Bi-LSTM)-multi-head attention mechanism (MA), namely KCBMA. The KOA optimization capability 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. Ultimately, a mapping relationship is established between wind speed, track irregularity excitation, and the system's dynamic response, enabling the establishment of an efficient and accurate wind-mill-bridge coupled system response prediction model. The specific technical solution is as follows:

[0005] A windmill bridge system safety assessment method based on the KCBMA algorithm includes the following steps:

[0006] Step 1: Use commercial finite element software to establish a vehicle-bridge coupling dynamics model; use the spectral solution method based on the wind spectrum to obtain wind speed time series data samples, and use the three-force coefficient to calculate the wind load time series data; and use the track spectrum to generate track irregularity excitation time series data samples;

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

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

[0010] Step 5: Based on the optimal hyperparameters found by the KOA module, an accurate neural network model is constructed and trained using input and output data. After training, the random response of the windmill bridge system is predicted.

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

[0012] This neural network model utilizes a multi-module collaborative architecture. Through the deep integration of a feature extractor and a multi-head self-attention mechanism, it achieves efficient modeling of the dual inputs of wind speed and track irregularity, ultimately enabling accurate prediction of the random responses of the windmill bridge system. The modules work closely together to form an efficient data processing pipeline. The CNN extracts spatial features from the raw data, while the multi-head self-attention mechanism enhances the representation of key features. The Bi-LSTM network further mines time series information, and the KOA module dynamically adjusts model parameters to optimize performance. This combination not only fully leverages the strengths of each module but also enhances the model's understanding and prediction capabilities of windmill bridge response data through inter-module synergy. Compared to conventional single-network structures, it offers greater flexibility and adaptability, enabling it to better handle the diverse tasks of windmill bridge systems.

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

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

[0015] The combination of CNN, Bi-LSTM, and MA: The multi-layer convolution kernels of the CNN module can extract the local spatial pattern of wind speed loads in the windmill-bridge system, overcoming the limitation of traditional LSTM that can only process time series signals. The Bi-LSTM models the forward-backward dependency of bridge displacement to address the lag effect of wind vibration response in the wind-vehicle-bridge coupled system. The multi-head attention mechanism (MA) calculates the spatiotemporal weight matrix at the output of the Bi-LSTM hidden layer, which can effectively focus on the fluctuating wind loads in strong wind sections and reduce prediction errors.

[0016] This paper leverages the Kepler Optimization Algorithm (KOA), Convolutional Neural Network (CNN), Bidirectional Long Short-Term Memory (Bi-LSTM), and a multi-head attention mechanism to construct a structural response prediction model for windmill-bridge systems. This technology provides targeted engineering adaptation to the data characteristics of the windmill-bridge coupled system, establishing an optimal training model based on optimal parameters. Deep learning simplifies the creation of vehicle and bridge models to shorten computation time. Furthermore, it establishes an uncertain model to accurately predict the response of the uncertain vehicle-bridge system, improving prediction accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 This is a diagram of the neural network architecture.

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

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

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

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

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

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

[0024] Figure 3 (a) shows the trend of the total loss value (Loss) changing with the number of training rounds during training.

[0025] Figure 3(b) shows the changing trend of the root mean square error (RMSE) with the number of training rounds during the training process.

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

[0027] Figure 3(d) is the RMS error convergence curve.

[0028] Figure 4(a) shows the lateral displacement response of the bridge during vehicle travel.

[0029] Figure 4(b) shows the vertical displacement response of the bridge during vehicle travel.

[0030] Figure 5 (a) shows the lateral acceleration response of the vehicle during its travel.

[0031] Figure 5(b) shows the vertical acceleration response of the vehicle during its travel.

[0032] Figure 6 (a) shows the prediction error of the vehicle vertical acceleration under different sample numbers.

[0033] Figure 6(b) shows the prediction error of the vertical displacement of the bridge under different sample numbers.

[0034] Figure 7(a) shows the power spectral density (PSD) of the bridge's lateral displacement.

[0035] Figure 7(b) shows the power spectrum density (PSD) of the vertical displacement of the bridge.

[0036] Figure 7(c) shows the power spectrum density (PSD) of the vehicle's lateral acceleration.

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

[0038] Figure 8(a) shows the prediction effect under Case 1.

[0039] Figure 8(b) shows the prediction effect under Case 2.

[0040] Figure 8(c) shows the prediction effect under Case 3.

[0041] Figure 8 (d) shows the prediction effect under Case 4.

[0042] Figure 9 The following are the prediction error diagrams for the four cases. DETAILED DESCRIPTION

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

[0044] This invention aims to establish an efficient and accurate prediction model for the response of a wind-vehicle-bridge coupled system, achieving optimal prediction results. To this end, the invention was validated on a twin-tower, twin-cable-plane cable-stayed bridge. Based on the concepts described in this method, a KCBMA optimization algorithm (KOA-CNN-Bi-LSTM-MA) was designed and developed. The KOA module searches for optimal hyperparameters, leveraging its anti-predator mechanism to improve search accuracy. A multi-head attention mechanism (MA) is then used to optimize the position information within the Bi-LSTM, thereby improving model performance. This optimization algorithm uses response samples calculated using the Monte Carlo method (MCM) as a dataset and is trained using track irregularity excitation, wind speed excitation, and structural parameters as input data. Time series estimation is used at the Bi-LSTM layer to achieve point-by-point prediction of the vehicle-bridge system response. This method uses the optimal parameters to establish an optimal training model. Deep learning simplifies the vehicle and bridge model development, reducing computation time. Furthermore, it can establish an uncertain model to accurately predict the uncertain vehicle-bridge system response, improving prediction accuracy.

[0045] 1. The technical solution steps adopted by the present invention are as follows:

[0046] Step 1: Use the commercial finite element software ANSYS and MIDAS to establish a vehicle-bridge coupled dynamic model. Verify the natural frequencies of the vehicle model and the bridge model based on analysis. Verify the correctness of the bridge model based on the calculated natural frequencies and modes of the bridge model.

[0047] The bridge model is:

[0048] (1);

[0049] Where, represents the bridge mass matrix, represents the bridge damping matrix, represents the bridge stiffness matrix; represents the bridge acceleration, represents the bridge speed, represents the displacement response of the bridge; Indicates the external force acting on the bridge.

[0050] The vehicle model is:

[0051] (2);

[0052] Where, is the mass matrix of the vehicle, is the vehicle's damping matrix, is the vehicle's stiffness matrix; represents the acceleration of the vehicle, Indicates the speed of the vehicle. The displacement vector representing the vehicle's motion; is the excitation force or load acting on the vehicle.

[0053] Step 2: Use the spectral solution method to obtain wind speed time series data samples through the wind spectrum, and then calculate the wind load time series data based on the wind speed samples using the three-force coefficient.

[0054] Step 3: Use the German track irregularity power spectrum density as random excitation and obtain track irregularity excitation time series data samples through spectral representation.

[0055] Step 4: Input the calculated wind load and track irregularity excitation into the vehicle-bridge coupling system and solve it using the Monte Carlo method to obtain the random response time series data samples of the windmill-bridge system.

[0056] Step 5: Construct the KCBMA combination model, whose structure is as follows Figure 1 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).

[0057] Figure 1 In the CNN feature extractor frame, a, b, and c represent the category feature vectors generated after feature extraction; in the multi-head attention mechanism frame, W Q 、W K 、W V Represents the weight matrix of the input feature mapping to the query, key, and value space respectively; in the bidirectional LSTM neural network frame, X t Indicates the input at the current moment; the X in the KOA frame i and Vt are input information and current state information respectively.

[0058] 1. Kepler Optimization Algorithm (KOA):

[0059] This module is used to find optimal hyperparameters for neural network models. Its core principle is that each planet and its position represents 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 planetary orbits are randomly selected based on a normal distribution. This feature enables KOA to efficiently explore and exploit the search space.

[0060] The following guidelines are followed during the optimization process, and the fitness of each solution is calculated based on the objective function:

[0061] (1) The optimal solution in each iteration is used as the central star (the sun);

[0062] (2) The distance between the planet and the sun is dynamically adjusted according to the current time;

[0063] (3) The orbital periods of the planets (candidate solutions) are randomly selected according to the normal distribution;

[0064] (4) The eccentricity of each planet's orbit is randomly selected in the range of 0-1.

[0065] 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.

[0066] (3);

[0067] Where, represents the population size (the set of candidate solution distributions) of the i-th candidate solution in the j-dimensional hyperparameter space; d is the dimension of the hyperparameter to be optimized, corresponding to the type of hyperparameter to be optimized in the CNN-Bi-LSTM-MA module, including the convolution 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 They represent the upper and lower bounds of the i-th solution in the j-th dimension respectively; is a random number uniformly distributed in the interval [0,1].

[0068] The KOA optimization algorithm simulates the search in the neural network hyperparameter space through a planetary gravity model to update the hyperparameter combination, where the "sun" represents the optimal hyperparameter combination (with the highest fitness) in the current iteration; the "planets" represent other candidate hyperparameter combinations, which approach the optimal solution through gravity.

[0069] Planets move in space due to their own mass and the gravitational force they experience, which requires the definition of a corresponding gravitational function.

[0070] (4);

[0071] Where, Represents the gravitational force on the i-th candidate solution (planet) at time t, which is used to guide the candidate solution closer to the current optimal solution (the sun); and Represent the normalized fitness values of the current optimal hyperparameter combination (the sun) and other candidate hyperparameter combination solutions (planets); is the dynamic gravitational constant, which is related to the number of iterations to balance global search and local optimization; A tiny value to prevent division by zero; It is a randomly generated value between 0 and 1, used to increase the diversity of gravity values and avoid local optimality; Represents the normalized mass coefficient of the i-th candidate solution, which is used to adjust the weight of the gravity value.

[0072] and yes The normalized value of express and The Euclidean distance between is defined as follows:

[0073] (5);

[0074] Where, and Represent the values of the j-th dimension hyperparameters of the optimal solution and candidate solutions respectively.

[0075] The distance between the selected random solution and the current solution affects the velocity calculation, resulting in a decrease in velocity. This lack of solution diversity can reduce the chance of escaping the local optimum due to insufficient variation in the current solution. Therefore, it is necessary to define the velocity (the rate at which hyperparameter combinations are updated) for candidate solutions (planets).

[0076] (6);

[0077] Where, Represents the speed of the candidate solution (planet), indicating the update direction and step size of the hyperparameter combination; and represent the directional control factor and the complementary directional control factor respectively, where ; and is a randomly generated value (random perturbation factor) in the interval [0,1] to enhance the randomness of the search; and Respectively represent the dynamic attenuation disturbance factor and its vectorized expansion form; and The position vectors representing the two selected candidate solutions represent different hyperparameter combinations; represents the normalized fitness difference; and Represents a binary scalar; and Represent the upper and lower bounds of the candidate solution for the i-th hyperparameter respectively; and The vectors representing the upper and lower bounds of candidate hyperparameter solutions; Used to switch the search direction; 、 Represent the position vector and position update attenuation factor of the current candidate solution respectively.

[0078] According to the previous equation, the new position of each candidate solution (planet) that is far away from the optimal solution for the hyperparameters (the sun) will be updated through the flow mechanism.

[0079] (7);

[0080] Where, 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; This is the best position of the sun discovered so far; Used to switch the search direction; r is a random number drawn from the standard normal distribution; is a binary vector.

[0081] 2. Convolutional Neural Network (CNN):

[0082] This module adaptively extracts the spatial local features and global abstract representation of the input data through local perception, nonlinearity, and pooling operations of multi-layer convolution kernels. With its powerful feature extraction capabilities, it can effectively cope with the high-dimensional characteristics of each time step in the input wind speed and track irregularity excitation time series.

[0083] CNN extracts local features by sliding convolution kernels over each time step in the input wind speed and track irregularity excitation time series data.

[0084] (8);

[0085] Where, is the input sequence, is the convolution kernel weight, is the bias, is the convolution kernel size, is the output feature.

[0086] Nonlinearity is introduced through the activation function (ReLU) to enhance the expression ability of CNN feature extraction.

[0087] (9);

[0088] Where, is the output feature extracted by the convolution kernel.

[0089] Use the pooling layer to perform downsampling operations to reduce the dimension and retain significant features:

[0090] (10);

[0091] Where, is the output feature after pooling, indicating the maximum value in the window; is the local eigenvalue extracted previously; v is the index range of the pooling window, which defines the feature extraction area; s is the step size, and k is the pooling window size.

[0092] 3. Bidirectional Long Short-Term Memory Network (Bi-LSTM):

[0093] This module is used to capture the correlation between time series data points, enabling sequence-to-sequence prediction and avoiding the error accumulation problem found in traditional feedforward neural networks. This bidirectional long short-term memory network overcomes the limitations of traditional LSTM networks in encoding past and future contextual temporal information. By capturing the dependencies between sequences through bidirectional temporal processing, it solves the long-term memory problem and thus improves the ability to understand sequence data. The LSTM unit gating mechanism includes a forget gate, an input gate, a cell update state, and an output gate. Among them:

[0094] Forget gate: decides which information to discard:

[0095] (11);

[0096] Where, 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.

[0097] Input gate: Update cell state:

[0098] , (12);

[0099] Where, and is the weight in the input gate, and is the bias in the input gate; Indicates the candidate unit status; Indicates which information needs to be updated.

[0100] Cell status update:

[0101] (13);

[0102] Where, Represents the unit state at the current time t; Indicates the unit state at the previous moment.

[0103] Output gate: generates the current hidden state:

[0104] , (14);

[0105] Where, and are the weight and bias of the output gate respectively; Represents the output vector at time t.

[0106] Bi-LSTM processes data bidirectionally, from forward to and backward Process the sequence and merge the output:

[0107] (15);

[0108] Where, Represents vector concatenation.

[0109] 4. Multi-head Attention Mechanism (MA):

[0110] This module models the correlation between different locations in the input sequence. It calculates attention weights for each time step relative to other time steps in the input wind speed and track irregularity stimulus time series data. These weights are then used to perform a weighted sum of the input sequence, enabling the model to prioritize important information from 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 captures the correlation between different time steps in the sequence.

[0111] The multi-head attention mechanism enhances the model's ability to capture richer features and contextual information by using multiple attention heads. These attention heads work in parallel, allowing the model to focus on different dimensions of the input information simultaneously. This approach enables a more comprehensive analysis of the data, as follows:

[0112] (16);

[0113] in, are the transformation matrices of query, key, and value of the mth attention head, respectively.

[0114] The outputs from all attention heads are concatenated and then subjected to a final linear transformation and layer normalization. This process integrates information learned from different subspaces and enhances the expressive power of the model.

[0115] (17);

[0116] in, is the final output transformation matrix.

[0117] The multi-head attention mechanism enhances the model's parallel computing capabilities by processing multiple attention distributions in parallel, enabling it to capture key features of input information from multiple angles and dimensions. This significantly improves the model's expressiveness and learning efficiency, making it an indispensable component of modern deep learning architectures.

[0118] Step 6: Use the calculated wind speed samples and track irregularity excitation samples as input data, and the windmill bridge response random samples as output data, and bring them into the KCBMA model to find the optimal hyperparameters.

[0119] Based on the model's hyperparameter update module, KOA, iteratively optimizes hyperparameters based on input data, minimizing the fitness function to obtain the optimal hyperparameter combination. 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 convolution kernel size (Kernel size). If the fitness function does not reach the optimal value, the hyperparameter search process continues until the maximum number of iterations is reached.

[0120] Step 7: Build an accurate neural network model based on the optimal hyperparameters found by KOA, and train the CNN-Bi-LSTM-MA model using input and output data.

[0121] The neural network model takes the CNN feature extraction network as the starting point, first performs dual-channel parallel processing on wind speed and track irregularity excitations, and automatically learns the spatial features in the time series data of wind speed and track irregularity excitations through CNN convolution operations. The extracted spatial features then enter the MA submodule; the MA submodule contains multiple parallel attention heads, each of which calculates the attention score through the query, key and value weight matrix, and weights the different time steps in the feature sequence to capture the global dependency between spatial distribution and temporal evolution features, enhance important features such as extreme special wind speed features, and suppress irrelevant features such as sensor noise, high-frequency vibration and other interference; the features processed by the attention mechanism are divided into two parts and sent to the two Bi-LSTM networks of the Bi-LSTM submodule respectively; the first Bi-LSTM contains N clayer, used to capture the long-term temporal dependencies of input features; the second Bi-LSTM is a single layer, which further refines the feature representation and performs weighted screening on the interactions of features within the local time window (such as sudden wind speed fluctuations and track transient impact responses) to suppress short-term noise interference; the training process of the neural network model is continuously optimized through iterations of the gradient descent method to minimize the gradient value; finally, the optimal neural network model is determined based on the optimal hyperparameters determined by the KOA module and the key sequence feature weights optimized by the multi-head attention mechanism, and the optimal neural network model is used to predict the random response of the windmill bridge system to obtain the best results.

[0122] Step 8: After training is completed, the random response of the windmill-bridge system is predicted.

[0123] 2. Example analysis:

[0124] To better validate and apply the optimization algorithm proposed in this paper, the KCBMA was applied to a model of a high-speed train crossing a cable-stayed bridge. The study was conducted within a coupled bridge model under the excitation of random wind speeds and random track irregularities. This study examined a twin-tower, twin-cable-plane cable-stayed bridge with a span configuration of 81+162+432+162+81 meters and a total main bridge length of 918 meters. The main girder utilizes a single-chamber concrete box girder structure with a structural damping ratio of 2%, a beam height of 3.5 meters, and a beam width of 24.5 meters. Sectional diaphragms are installed in the cable-stayed sections. The structural parameters of the finite element model of the bridge are shown in Table 1.

[0125] Table 1 Main parameters of bridge structure

[0126] .

[0127] Combined with the design drawings, two software models were used for modeling and analysis. The dynamic characteristics of the two were basically consistent, and the error was within the allowable range, as shown in Table 2.

[0128] Table 2 Verification of bridge natural vibration characteristics

[0129] .

[0130] The vehicle model adopts the German ICE high-speed train model, which consists of 8 carriages. Its specific parameters are shown in Table 3. The speed is set to 200 km / h and the wind speed is 10 m / s.

[0131] Table 3 Parameters of elastic suspension vehicle model

[0132] .

[0133] Wind load and track irregularity samples were used as input data for the KCBMA model, and the system responses calculated using the Monte Carlo method (MCM) were used as training samples. Due to the significant increase in the sample size, the parameters of the Kepler Optimization Algorithm (KOA) needed to be reset: a larger population size was set, with the number of search planets (Search Planets) set to 10 and the number of iterations set to 5. Three hyperparameters were set during the optimization search: the initial learning rate (Initial-Learn-Rate), the number of neurons (Neuron count), and the kernel size (Kernel size) of the bidirectional long short-term memory (Bi-LSTM) network. Through continuous search using the Kepler Optimization Algorithm (KOA), the optimal combination of these three hyperparameters was found after five iterations (10 populations per round), as shown in Table 4.

[0134] To better illustrate the search process, the fitness function curves and parameter optimization process for each iteration are extracted, as shown in Figures 2(a)-2(f). The parameters tend to stabilize after the first three iterations. Therefore, setting the number of iterations to 3 can both meet the model optimization requirements and significantly shorten the optimization time.

[0135] Table 4 Optimal hyperparameters of the model

[0136] .

[0137] The optimized neural network model was trained using 1000 sets of samples. The entire training process was optimized using gradient descent, ultimately minimizing the gradient. To visualize the training process, the root mean square error (RMSE) loss function was plotted. Figures 3(a)-3(d) show the root mean square error (RMSE) and total loss of the predicted data over the training cycle.

[0138] After training, the model's prediction results were analyzed. The KCBMA predictions were compared and validated with those from the Monte Carlo simulation (MCM) and CNN-Bi-LSTM (CBL) models. The bridge structure focused on vertical and lateral displacements, while the vehicle system focused on vertical and lateral accelerations. The comparison results are shown in Figures 4(a)-4(b) and 5(a)-5(b).

[0139] Figures 6(a) and 6(b) show the root mean square error (RMSE) and mean square error (MSE) of vehicle acceleration and bridge displacement as the sample size increases. The prediction error decreases with increasing sample size, and the MSE indicator exhibits more stable performance. Figures 7(a) and 7(d) show the average power spectral density (PSD) of vehicle acceleration and bridge displacement, comparing the Monte Carlo simulation (MCM) with the KCBMA method. The PSD curves of the two methods closely overlap, indicating that the proposed KCBMA method and MCM have similar accuracy.

[0140] Table 5 Comparison of prediction errors

[0141] .

[0142] Based on the prediction results for bridges and vehicles, the KCBMA method's predictions are closer to Monte Carlo simulations (MCMs) with lower errors, meeting engineering application requirements. To more directly compare KCBMA's prediction efficiency, Table 5 lists relevant performance metrics, including root mean square error (RMSE), mean absolute error (MAE), mean relative percentage error (MRPE), training set accuracy, test set accuracy, and training time. The test set accuracy improved most significantly, exceeding 75% compared to the CBL method, while training time was also reduced by 8.21%. This shows that KCBMA offers various advantages over traditional neural network algorithms.

[0143] To verify the superiority of the proposed method, it was 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-shifting of the system response was used for verification. It should be noted that in Cases 1 to 4, four step sizes of 0.02, 0.025, 0.03, and 0.04 were set, respectively (see Table 6 for details), while all other parameters remained unchanged. Since the total time remained unchanged, only the step size was changed, the length of the response data in each case varied. The prediction results are shown in Figures 8(a) to 8(d).

[0144] Table 6 Different series lengths

[0145] .

[0146] like Figure 9 As shown in Figure 2, KCBMA and CABL methods have the highest prediction effect and accuracy, and their prediction results are highly consistent with MCM. Figure 9Taking Case 1 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, and 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-term time series prediction, and the error is within the acceptable range for engineering.

[0147] The above research shows that the KCBMA method can effectively predict the coupled vibration response of the wind-vehicle-bridge system. Compared with other network frameworks, it has significantly improved the accuracy and efficiency in long-term prediction.

Claims

1. A windmill bridge system safety assessment method based on the KCBMA algorithm, characterized in that: The following steps are involved: Step 1: Use commercial finite element software to establish a vehicle-bridge coupling dynamics model; use the spectral solution method based on the wind spectrum to obtain wind speed time series data samples, and use the three-force coefficient to calculate the wind load time series data; and use the track spectrum to generate track irregularity excitation time series data samples; Step 2: Input the calculated wind load time series data and track irregularity excitation time series data samples into the vehicle-bridge coupled dynamic model for buffeting analysis, and obtain the windmill-bridge random response time series data samples; Step 3: Construct a KCBMA combined model, which includes 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 submodule in the CNN-Bi-LSTM-MA module is used to adaptively extract spatial local features and global abstract representations from the input wind speed and track irregularity excitation time series data samples. The Bi-LSTM submodule is used to capture the long-term dependencies between time series data points and achieve sequence-to-sequence prediction of the random response of the windmill bridge system. The MA submodule is used to simulate the dynamic correlation between different time steps in the wind speed and track irregularity excitation time series data samples and enhance the weight of key time step features. Step 4: Use the time series data samples of wind speed and track irregularity excitation as input data and the time series data samples of windmill bridge random response as output data to find the optimal hyperparameters in the KCBMA combination model; Step 5: Based on the optimal hyperparameters found by the KOA module, an accurate neural network model is constructed and trained using input and output data. After training, the random response of the windmill bridge system is predicted. The neural network model training in step 4 is specifically as follows: Step 4.1: After the KOA module completes hyperparameter optimization, it trains a neural network model based on the dataset. Starting with the CNN submodule feature extraction network, the neural network model first performs dual-channel parallel processing of wind speed and track irregularity excitations. The CNN convolution operation automatically learns the spatial features in the wind speed and track irregularity excitation time series data. The obtained spatial features are then fed into the MA submodule. Step 4.2: The MA submodule contains multiple parallel attention heads. Each head calculates an attention score using the query, key, and value weight matrices, weighting different time steps in the feature sequence to capture the global dependency between spatial distribution and temporal evolution features, enhancing important features such as extreme wind speed features and suppressing irrelevant features such as 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 submodule respectively; the first Bi-LSTM contains N c The first layer is used to capture the long-term temporal dependencies of input features. The second Bi-LSTM layer is a single layer that further refines the feature representation and performs weighted screening of feature interactions within a local time window to suppress short-term noise interference. Features within the local time window include sudden wind speed fluctuations and track transient impact responses. The training process of the neural network model is optimized through continuous iteration using the gradient descent method to minimize the gradient value. Step 4.4: Determine the optimal neural network model based on the optimal hyperparameters determined by the KOA module and the key sequence feature weights optimized by the multi-head attention mechanism, and use the optimal neural network model to predict the random response of the windmill bridge system to obtain the best results.

2. A windmill bridge system safety assessment method based on the KCBMA algorithm according to claim 1, characterized in that: In step 3, the KOA module uses 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 for planets are randomly distributed in the d-dimensional space. （1）； Where, represents the population size of the i-th candidate solution in the j-dimensional hyperparameter space, that is, the distribution set of candidate solutions; d is the dimension of the hyperparameter to be optimized, corresponding to the type of hyperparameter to be optimized in the CNN-Bi-LSTM-MA module, including the convolution 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 in the interval [0,1]; Define the gravity function: （2）； Where, It represents the gravitational force on the i-th candidate solution at time t, which is used to guide the candidate solution closer to the current optimal solution; represents the normalized fitness value of the current optimal hyperparameter combination as the sun, represents the normalized fitness values of other candidate hyperparameter combination solutions as planets; is the dynamic gravitational constant; A tiny value to prevent division by zero; It is a randomly generated value between 0 and 1, used to increase the diversity of gravity values and avoid local optimality; represents the normalized mass coefficient of the i-th candidate solution, which is used to adjust the weight of the gravity value; and yes The normalized value of It represents the Euclidean distance between the optimal solution and the candidate solution in the hyperparameter space and is defined as follows: （3）； Where, and Represent the values of the j-th dimension hyperparameters of the optimal solution and candidate solution respectively; Define the speed of candidate solutions: （4）； Where, Represents the speed of the candidate solution and indicates the update direction and step size of the hyperparameter combination; represents the direction control factor, represents the complementary direction control factor, where ; and is a random perturbation factor randomly generated in the interval [0,1] to enhance the randomness of the search; and Respectively represent the dynamic attenuation disturbance factor and its vectorized expansion form; and The position vectors representing the two selected candidate solutions represent different hyperparameter combinations; represents the normalized fitness difference; and Represents a binary scalar; and Represent the upper and lower bounds of the candidate solution for the i-th hyperparameter respectively; and Represent the upper bound vector and lower bound vector of the candidate solutions for the hyperparameters respectively; Used to switch the search direction; 、 Represent the position vector and position update attenuation factor of the current candidate solution respectively; According to the previous equation, the new position of each candidate solution that is far away from the optimal solution of the hyperparameters will be updated through the flow mechanism; （5）； Where, represents the new position of the candidate solution τ at time t+1, represents the new position of the candidate solution τ at time t; is the instantaneous velocity required for the candidate solution τ to reach the new position; is the optimal position of the sun found so far; r is a random number drawn from a standard normal distribution, is a binary vector.

3. A windmill bridge system safety assessment method based on the KCBMA algorithm according to claim 2, characterized in that: In step 3, the CNN submodule uses a convolution kernel to slide on each time step in the input wind speed and track irregularity excitation time series data to extract the input wind speed and track irregularity excitation local features, as shown in the following formula: （6）； Where, is the input sequence, is the convolution kernel weight, is the bias, is the convolution kernel size, is the output feature; Nonlinearity is introduced through the activation function ReLU to enhance the CNN feature extraction expression ability: （7）； Where, Output features extracted by the convolution kernel; The output features are downsampled using the pooling layer to reduce the extracted feature dimensions and retain significant features, as shown in the following formula: （8）； Where, is the output feature after pooling, indicating the maximum value in the window; is the local eigenvalue extracted previously; v is the index range of the pooling window, which defines the feature extraction area; s is the step size, and k is the pooling window size.

4. A windmill bridge system safety assessment method based on the KCBMA algorithm according to claim 3, characterized in that: In step 2, the LSTM unit gating mechanism in the Bi-LSTM includes a forget gate, an input gate, a cell update state, and an output gate; wherein: Forget Gate f t : Decide which information to discard, expressed as: （9）； Where, 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）； Where, and is the weight in the input gate; and is the bias in the input gate; Indicates the candidate unit status; Indicates which information needs to be updated; The cell state is updated as: （11）； Where, Represents the unit state at the current time t; Indicates the unit state at the previous moment; Output gate O t : Generate the current hidden state, expressed as: , （12）； Where, is the weight of the output gate, is the bias of the output gate; represents the output vector at time t; The Bi-LSTM submodule processes the data bidirectionally, and backward Process the sequence and merge the output: （13）； Where, Represents vector concatenation.

5. A windmill bridge system safety assessment method based on the KCBMA algorithm according to claim 4, characterized in that: In step 2, the MA submodule calculates the attention weight of each time step relative to other time steps in the input time series data of wind speed and track irregularity excitation; then, the input sequence is weighted summed according to the attention weight, so that the model can prioritize important information in different parts of the sequence; specifically, as follows: （14）； in, is the mth attention head, are the queries of the mth attention head respectively. ,key Sum The transformation matrix of The outputs from all attention heads are concatenated together, followed by a final linear transformation and layer normalization. （15）； in, is the final output transformation matrix.

6. A windmill bridge system safety assessment method based on the KCBMA algorithm according to claim 1, characterized in that: In step 3, the KOA optimization algorithm is used to iteratively optimize the hyperparameters according to the input data, and minimize the fitness function to obtain the optimal hyperparameter combination, wherein the KOA optimization algorithm optimizes three hyperparameters: the initial learning rate of the bidirectional long short-term memory network, the number of neurons, and the convolution kernel size; when the fitness function does not reach the optimal value, the process of finding the hyperparameters continues until the maximum number of iterations is reached.

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