A vehicle-bridge coupling system reliability analysis method based on adaptive multi-task deep learning

Abstract

The present application relates to a kind of vehicle-bridge coupling system reliability analysis method based on adaptive multi-task deep learning, belong to rail transit infrastructure safety technical field.For the problem that existing technology cannot efficiently and synchronously predict vehicle and bridge response, multi-task loss weight adjustment is difficult, adaptive multi-task learning model AMLM is proposed.The model integrates improved gorilla group optimization algorithm MGTO, shared convolutional neural network CNN and double-path state fusion gated long short-term memory network SFLSTM;Through the same variance uncertainty loss weighting strategy, the vehicle and bridge prediction tasks are dynamically balanced;Combined with probability density evolution method PDEM, AMLM-PDEM framework is constructed.The technical effects include: realizing synchronous high-precision prediction of vehicle-bridge response, autonomously optimizing multi-task weight distribution, significantly improving calculation efficiency and modeling accuracy, and perfecting the time-varying reliability evaluation system of vehicle-bridge system.

Description

Technical Field

[0001] This invention belongs to the field of rail transit infrastructure safety technology, and relates to a reliability analysis method for vehicle-bridge coupled systems based on adaptive multi-task deep learning. Background Technology

[0002] Bridge structures are a core component of modern railway systems and are crucial for ensuring train operation safety. In-depth research into vehicle-bridge coupled vibration theory and conducting reliability assessments are essential for ensuring the safe operation of railway infrastructure. However, vehicles and bridges exhibit significant randomness in terms of geometric manufacturing precision, structural parameters, and track irregularities, posing challenges to the reliability assessment of vehicle-bridge interaction systems. Under the combined influence of multiple random factors, vehicle-bridge coupled vibration reliability analysis is of great significance for improving the safety of rail transit infrastructure.

[0003] In recent years, various random vibration analysis methods have been developed in the field of vehicle-bridge coupling, such as point estimation, pseudo-excitation, probability density evolution, and direct probability integration. Yu et al. combined number theory methods with probability density evolution to study the random vibration characteristics of three-dimensional train-bridge coupled systems; Jiang et al. proposed an improved point estimation method, combining it with the Karhunen-Loéve method to conduct random vibration analysis of train-bridge systems; Liu et al. used the direct probability integration method to analyze the random vibration of heavy-load ballasted track vehicle-bridge systems; Shang et al. introduced sparse polynomial chaotic expansion to analyze the extreme response of vehicle-track-bridge coupled systems under multiple random factors. Although these methods have achieved significant results, their computational efficiency still needs improvement due to the time-varying characteristics of vehicle-bridge coupled systems.

[0004] With the development of artificial intelligence technology, deep learning models have made breakthroughs in fields such as natural language processing and computer vision. Some scholars have attempted to apply them to the analysis of random vibrations in vehicle-bridge coupled systems: Li et al. constructed a stochastic LSTM model using Bayesian methods; Li et al. proposed a least-squares generative adversarial network to predict bridge acceleration and track irregularities using vehicle and bogie accelerations; Yang et al. combined a stochastic pseudo-excitation method with a CNN-BiLSTM model to analyze the random vibrations of vehicle-bridge coupled systems with uncertain parameters; Zhang et al. proposed an improved graph neural network to predict vehicle safety indicators in multiple scenarios; Cheng et al. combined probability density evolution with an adaptive hybrid deep learning model and used variational mode decomposition to preprocess data; Yang et al. used a CNN-bidirectional gated recurrent unit hybrid model to evaluate vehicle safety during near-fault earthquakes; He et al. proposed a dynamic deep learning model that combined an improved temporal convolutional network with a Gaussian process to predict random responses; and Mao et al. constructed a Bayesian-optimized deep learning model to analyze the random vibrations of vehicle-track-bridge coupled systems.

[0005] However, existing surrogate models mostly focus on single-task prediction, forecasting only one of the vehicle or bridge responses. In practical engineering, vehicle motion imposes dynamic loads on the bridge, and bridge vibration, in turn, affects the vehicle's dynamic response; the two form a tightly coupled system through force and displacement transmission at contact points. Predicting only the response of a single system cannot fully reveal the vehicle-bridge coupling mechanism; simultaneously predicting both vehicle and bridge responses is crucial for system reliability assessment. Currently, research considering stochastic structural parameters and random track irregularities while simultaneously predicting vehicle and bridge responses is extremely scarce. The core challenge lies in the fact that the model's prediction accuracy heavily depends on the relative weights of the losses from different tasks, and manually adjusting the weights of these multi-task losses is extremely difficult. Summary of the Invention

[0006] In view of this, the purpose of this invention is to provide a reliability analysis method for vehicle-bridge coupled systems based on adaptive multi-task deep learning. An adaptive multi-task learning model (AMLM) is proposed, which integrates an improved Gorilla Troops Optimizer (MGTO), a shared convolutional neural network (CNN), and two independent enhanced long short-term memory networks (LSTM). The MGTO algorithm is used to determine the optimal hyperparameters of the model, thereby improving model performance and generalization ability. Given the similar mapping relationship between track irregularities and vehicle and bridge responses, a shared CNN model is used to extract local fluctuation features of track irregularities, thus reducing model complexity. To further improve the model's ability to capture long-term temporal dependencies, a novel state fusion gate mechanism is proposed, which combines LSTM unit states with input features. Furthermore, this invention proposes an adaptive task loss weighting strategy based on homoscedastic uncertainty to dynamically balance the learning process of multiple tasks. An additional temperature coefficient is used to control uncertainty sensitivity and regularization strength, ensuring that the adaptive learning strategy can achieve smooth adjustment. The prediction accuracy of the proposed model is verified by comparing results with those of the Monte Carlo method (MCM) for vehicle-bridge coupled systems. Based on the proposed adaptive multi-task prediction framework embedded with PDEM, the reliability of the vehicle-bridge coupling system was systematically analyzed. The reliability of the AMLM-PDEM method was verified by comparing the results with those of traditional PDEM. Furthermore, the robustness of the proposed model was further verified by analyzing its performance under different vehicle speeds and noise intensities.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A reliability analysis method for vehicle-bridge coupled systems based on adaptive multi-task deep learning includes the following steps:

[0009] S1. Generate a sample set of random variables for the vehicle-bridge coupling system, wherein the random variables include bridge structural parameters and track irregularity parameters;

[0010] S2. Construct a vehicle-bridge coupled physical model based on the Monte Carlo method (MCM), and calculate the vehicle response and bridge response based on the random variable sample set;

[0011] S3. Construct an adaptive multi-task learning model AMLM, the model comprising:

[0012] An improved gorilla population optimization algorithm, MGTO, is used to optimize model hyperparameters.

[0013] A shared convolutional neural network (CNN) is used to extract local features from an input with an uneven track.

[0014] Two independent state-fused gated long short-term memory networks (SFLSTM) are used to predict vehicle response and bridge response, respectively.

[0015] An adaptive task weighting strategy based on homoscedastic uncertainty is used to dynamically balance the loss weights of vehicle and bridge responses.

[0016] S4. Use the calculation results of S2 to train the AMLM model;

[0017] S5. Embed the trained AMLM model into the probability density evolution method (PDEM) to predict the response probability density function of the vehicle-bridge coupling system;

[0018] S6. Based on the response probability density function, calculate the reliability index of the vehicle-bridge coupling system.

[0019] Furthermore, in S1, the method for generating the random variable sample set is as follows:

[0020] Generate an initial point set using the Sobol sequence;

[0021] By combining the minimization GF-difference criterion with the Monte Carlo method, the point set is calibrated and transformed so that the probability distribution of each point meets the preset conditions.

[0022] Furthermore, the shared convolutional neural network (CNN) includes:

[0023] The input layer receives four channels of track irregularities, including vertical irregularities on the left rail, vertical irregularities on the right rail, lateral irregularities on the left rail, and lateral irregularities on the right rail.

[0024] At least three convolutional modules, each of which contains a convolutional layer Conv, a batch normalization layer BN, a ReLU activation function, and a max pooling layer MP in sequence;

[0025] The kernel size of each convolutional layer is 5, and the stride is 2; the kernel size of each max pooling layer is 2, and the stride is 2.

[0026] Furthermore, the state fusion gated long short-term memory network SFLSTM includes:

[0027] State fusion gate This is used to fuse the current input features with the cell state, and its calculation formula is:

[0028]

[0029] in, For the current input features, This represents the current state of the cell. and These are the weight matrix and the bias term, respectively. This represents the Sigmoid activation function;

[0030] Hidden state The update formula is:

[0031]

[0032] in, The state that was hidden in the previous moment.

[0033] Furthermore, the total loss function of the adaptive task-weighted strategy is defined as:

[0034]

[0035] in, The mean square error loss is the loss for the vehicle response or bridge response. i When =1, it indicates a vehicle response. i When =2, it is the bridge response. For task-related learnable noise parameters, T This is a temperature coefficient used to adjust the strength of the loss weight balance.

[0036] Furthermore, in S5, the execution of the probability density evolution method (PDEM) includes:

[0037] The joint probability density function of the system response is calculated using the generalized probability density evolution equation:

[0038]

[0039] in, State vector X The joint probability density function with the random variable Θ, The rate of change of the system response;

[0040] The equation is solved using the bilateral difference method.

[0041] Furthermore, in step S6, the reliability index is calculated as follows:

[0042] According to the three-standard-deviation principle, the response falls within the interval [ μ 3 σ , μ +3 σ The probability within ] is used as the time-varying reliability;

[0043] Where μ is the mean of the response and σ is the standard deviation of the response.

[0044] An adaptive multi-task deep learning system for reliability analysis of vehicle-bridge coupled systems includes:

[0045] The data generation module is used to generate a sample set of random variables for the vehicle-bridge coupling system.

[0046] The physics calculation module solves the vehicle-bridge coupled dynamic equations based on the Monte Carlo method (MCM) and outputs the vehicle and bridge responses.

[0047] The adaptive multi-task learning model AMLM includes:

[0048] The MGTO optimization unit is used for hyperparameter optimization.

[0049] Shared CNN units handle inputs with uneven tracks;

[0050] Dual-channel SFLSTM unit, outputting vehicle and bridge response predictions respectively;

[0051] Adaptive weighted units dynamically adjust loss weights based on homoscedasticity uncertainty.

[0052] The PDEM evaluation module calculates the response probability density function and reliability index based on the AMLM prediction results.

[0053] Furthermore, the architecture of the shared CNN unit includes:

[0054] The input layer receives tensors with dimensions of 32×4×5000;

[0055] The three concatenated convolutional modules output tensors with dimensions of 32×8×2500, 32×16×624, and 32×32×156, respectively.

[0056] Furthermore, the adaptive weighting unit uses a temperature coefficient T Controlling noise parameters The sensitivity of the value is updated using the following formula:

[0057]

[0058] in This is the learning rate.

[0059] The beneficial effects of this invention are as follows:

[0060] (1) Innovatively adopting a shared feature extraction and dual-path independent temporal modeling architecture, it achieves high-precision synchronous prediction of vehicle response and bridge response for the first time. By integrating the vehicle-bridge dynamic coupling mechanism, it overcomes the shortcomings of traditional single-task models that cannot fully reveal the interaction relationship of the system, and provides a more complete dynamic response data foundation for reliability assessment.

[0061] (2) A loss weighting strategy based on homoscedasticity uncertainty is proposed, and a temperature coefficient is introduced to dynamically adjust the task weight allocation. This mechanism autonomously balances the learning process of vehicle and bridge prediction tasks, significantly reduces the model's dependence on manual parameter tuning, effectively solves the weight sensitivity problem in multi-task learning, and improves the model's convergence speed and generalization ability.

[0062] (3) The improved gorilla population optimization algorithm enhances global search capabilities by using the Cauchy inverse accumulation operator and the tangent flight operator to quickly obtain the optimal hyperparameters of the model; the state fusion gating mechanism strengthens the ability to model long-term dependencies by fusing cell states and input features. The synergy of the two enables the model to significantly reduce the computational resource consumption of traditional physical models while ensuring prediction accuracy.

[0063] (4) Deeply integrate the deep learning surrogate model with the probability density evolution method to establish an efficient solution path for the probability density function of the vehicle-bridge response. Accurately capture the probability evolution law of the system response under random factors through the generalized probability density evolution equation, construct a time-varying reliability quantification index, and provide a more reliable evaluation basis for the safe operation of rail transit infrastructure.

[0064] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0065] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0066] Figure 1 This is a schematic diagram of the vehicle-axle coupling mechanics model;

[0067] Figure 2A schematic diagram of an adaptive multi-task learning model for reliability analysis of a stochastic vehicle-bridge coupled system;

[0068] Figure 3 This is a schematic diagram of a convolutional network model;

[0069] Figure 4 A schematic diagram of the LSTM model;

[0070] Figure 5 For state fusion gated LSTM models;

[0071] Figure 6 The computational process for the AMLM-PDEM proxy model;

[0072] Figure 7 A comparison of the acceleration responses obtained by the Monte Carlo method MCM and the proposed adaptive multi-task learning model AMLM framework; Figure 7 (a) represents the average number of vehicles; Figure 7 (b) represents the standard deviation of the vehicles; Figure 7 (c) represents the average value of the bridge; Figure 7 (d) represents the standard deviation of the vehicles;

[0073] Figure 8 A comparison of vehicle and bridge performance indicators under different loss weightings; Figure 8 (a) is the root mean square error (RMSE) value; Figure 8 (b) is the coefficient of determination R. 2 value;

[0074] Figure 9 Comparison of axle response acceleration results between AMLM-PDEM and PDEM; Figure 9 (a) represents the average value for each train; Figure 9 (b) represents the standard deviation of the train; Figure 9 (c) represents the average value for bridges; Figure 9 (d) represents the standard deviation of the bridge;

[0075] Figure 10 Visualization of the surface and contour lines of the probability density function PDF of vehicle acceleration; Figure 10 (a) is the PDF surface obtained from PDEM; Figure 10 (b) is the PDF surface predicted by AMLM-PDEM; Figure 10 (c) PDF contour lines obtained from PDEM; Figure 10 (d) PDF contour lines predicted by AMLM-PDEM;

[0076] Figure 11 Visualization of the probability density function PDF of bridge acceleration using surfaces and contour lines; Figure 11 (a) is the PDF surface obtained from PDEM; Figure 11 (b) is the PDF surface predicted by AMLM-PDEM; Figure 11 (c) PDF contour lines obtained from PDEM; Figure 11 (d) PDF contour lines predicted by AMLM-PDEM;

[0077] Figure 12 Comparison of probability density function (PDF) and cumulative distribution function (CDF) results for vehicle and bridge acceleration; Figure 12 (a) is the vehicle acceleration; Figure 12 (b) represents the bridge acceleration;

[0078] Figure 13 PDF surface and contour plot of the acceleration response of the vehicle-bridge coupled VBI system; Figure 13 (a) represents the train's acceleration; Figure 13 (b) represents the bridge acceleration. Detailed Implementation

[0079] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0080] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0081] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0082] 1. Prediction framework for vehicle-axle interaction system

[0083] 1.1 Mechanical Model

[0084] A schematic diagram of the mechanical model of a vehicle-axle coupling (VBI) system is shown below. Figure 1 As shown. This invention uses a 3×32m simply supported beam bridge, a combination widely used in high-speed railways. The beams and piers are modeled using the finite element method, and their main parameters are shown in [the diagram]. Figure 1 The train is modeled as a multi-rigid-body system, comprising a car body, two bogies, and four wheelsets. The rigid bodies are interconnected via primary and secondary suspension systems. The primary suspension connects the bogies to the wheelsets, while the secondary suspension connects the car body to the bogies. The car body, front bogie, and rear bogie each have five degrees of freedom (lateral, vertical, yaw, pitch, and roll), while each wheelset has three degrees of freedom (lateral, vertical, and yaw). In total, the train model contains 27 degrees of freedom.

[0085] Based on the law of conservation of energy, the mass, stiffness, and damping matrices of the train can be obtained relatively easily, while the mass and stiffness matrices of the bridge are established using the finite element method. The Rayleigh damping assumption is used when constructing the bridge's damping matrix. Finally, the dynamic equations of the vehicle-bridge coupled (VBI) system can be expressed as:

[0086]

[0087] Among them, subscript v and b Representing the vehicle and the bridge respectively; the displacement, velocity, and acceleration vectors of the dynamic response are respectively represented by... , and The mass, damping, stiffness, and external force matrices are represented by M, C, K, and F, respectively.

[0088] 1.2 Adaptive Multi-Task Prediction Model

[0089] The adaptive multi-task learning model (AMLM) proposed in this invention is trained based on the results of the vehicle-bridge coupled Monte Carlo method (MCM). The model includes an improved gorilla population optimization algorithm, a shared convolutional neural network (CNN), two independent improved long short-term memory networks (LSTM), and a self-adjusting task weighting strategy based on homoscedastic uncertainty. Figure 2 The overall structure of the proposed AMLM integrated with the Probability Density Evolution (PDEM) model is presented for reliability assessment of stochastic vehicle-bridge coupled systems. Each component will be described in detail below.

[0090] 1.2.1 Improved Gorilla Force Optimizer (MGTO)

[0091] Mostafa et al. proposed an improved Group Optimization (GTO) algorithm for gorillas to enhance population diversity and global search capabilities. In their natural environment, gorillas typically live in groups, which generally consist of multiple adult females, a dominant male silverback gorilla, and their offspring. Gorillas' behavioral patterns can be systematically divided into two distinct phases: the exploration phase and the development phase.

[0092] In the exploratory phase of the improved gorilla population optimization algorithm (MGTO), an elite back-learning strategy was introduced. This strategy significantly improved population diversity during the algorithm's initialization and update processes. Theoretically, each gorilla in the model represents a candidate solution, while the optimal solution is represented by the silverback gorilla, symbolizing the best solution in the solution space. The candidate position of each gorilla is defined as follows:

[0093]

[0094] Among them, the candidate position vector of the gorilla is U(t+1) , U(t) Indicates the current position; r 1. r 2. r 3 and rand It is a random variable located in the interval [0, 1]; symbol g This represents a scaling constant constrained between 0 and 1; This indicates a position randomly selected from the population; u b and l b These represent the upper and lower bounds of the search space, respectively. Iteration parameters. T , G and H The adjustment method is as follows:

[0095]

[0096] in r 4 is a value between 0 and 1, and this value is updated in each iteration; Iter Indicates the current iteration number; MaxIt Indicates the pre-set maximum number of iterations; variable l Z is an integer randomly selected between -1 and 1; Z represents a random number from the symmetric interval [-T, T].

[0097] During the development phase, gorillas exhibited two main behavioral strategies: following silverback gorillas and competing for mating opportunities with adult females. To enhance local development capabilities, the Improved Goat Population Optimization Algorithm (MGTO) introduced the Cauchy inverse cumulative distribution operator and the tangent flight operator. These two operators work synergistically to optimize search results, enabling the algorithm to efficiently navigate the solution space and converge to an optimal or near-optimal solution. This integration not only fully utilizes the gorillas' natural behavioral patterns but also leverages mathematical operators to improve the algorithm's overall performance and effectiveness in solving complex optimization problems. The position update formula for gorillas following silverback gorillas is as follows:

[0098]

[0099] in, N gor Indicates the number of gorillas; Indicates the location of the silverback gorilla; c These are random numbers that are uniformly distributed in the interval [0,1] and are obtained through the inverse cumulative distribution operator.

[0100] The competition among gorillas for the position of an adult female can be represented as follows:

[0101]

[0102] in, Q Indicates force; ξ Let be a random variable whose value ranges from 0 to 1; the function tan() corresponds to the tangent fly-by operator; h Let represent another random variable that is uniformly distributed in the interval [0,1].

[0103] The synergistic integration of these two operators significantly improves the convergence dynamics of the improved Goat Population Optimization (MGTO) algorithm and optimizes the search trajectory. The procedural framework of MGTO is described in detail in Algorithm 1.

[0104] The steps of Algorithm 1, the Improved Gorilla Population Optimization Algorithm (MGTO)

[0105] 1. Initialization parameters: Population size N pop Maximum number of iterations N max And the parameters of the Gorillas Group Optimization (GTO) algorithm.

[0106] 2. Generate the initial population: Generate the initial gorilla population. U i ( i =1,2,…, N pop).

[0107] 3. While t < N max do:

[0108] 4. Apply the Elite Backward Learning (ELBO) strategy to update the current population.

[0109] 5. Calculate the fitness value of the gorilla.

[0110] 6. Update the parameters according to formula (3) T and G .

[0111] 7. Update the gorilla's position according to formula (2) and select the silverback gorilla.

[0112] 8. for each gorilla ( U i ):

[0113] 9.if :

[0114] 10. Update the gorilla's position according to formula (4).

[0115] 11.else:

[0116] 12. Update the gorilla's position according to formula (5).

[0117] 13.end if.

[0118] 14. end for.

[0119] 15. end while.

[0120] 16. Return result: Return to Silverback Gorilla U Silverback And its optimal fitness value.

[0121] 1.2.2 Convolutional Neural Network Model (CNN)

[0122] Convolutional Neural Networks (CNNs) have become the mainstream model for extracting features from time-series data, covering various scenarios such as images and audio signals. In this invention, a CNN model is designed to extract local features from uneven tracks. The structural architecture of the convolutional neural network is as follows: Figure 3 As shown. Figure 3As shown, a typical CNN framework comprises a series of hierarchical operations, where each convolutional (Conv) layer is followed by batch normalization (BN) to stabilize training and improve convergence speed. Subsequently, a modified linear unit (ReLU) activation function is deployed to introduce non-linearity, enabling the modeling of complex and abstract data representations. To achieve the optimal balance between computational efficiency and generalization performance, a max pooling (MP) layer is introduced. By downsampling feature maps, this layer not only reduces computational complexity but also effectively prevents model overfitting. Through this dimensionality reduction operation, the max pooling layer selectively preserves the most salient spatial features, ensuring that key information is retained while discarding redundant data. The sequential arrangement of convolution (Conv), batch normalization (BN), modified linear units (ReLU), and max pooling (MP) constitutes a mature and effective architectural pattern. This modular design not only simplifies the computational process but also significantly enhances the network's predictive power, making it an efficient tool for extracting important features from data with uneven trajectory.

[0123] The mathematical expression for convolution is as follows:

[0124]

[0125] Where j represents the index of the output channel; N in Indicates the number of input channels; represents the size of the convolution kernel; s represents the stride of the convolution filter; w n,k b represents the k-th weight in the filter associated with the n-th input channel; (j) This represents the bias term for the j-th output channel; Indicates the size of the fill; x n,t This represents the element at position t in the input channel.

[0126] Table 1 lists the architectural parameters of the Convolutional Neural Network (CNN) and their corresponding data dimensions. The model's input consists of track irregularity signals with four channels, representing vertical and lateral irregularity samples from the left and right tracks. During training, each batch comprises 32 samples, and the length of each individual signal sequence is set to 5000. This length precisely corresponds to the actual physical distance traveled by the train, ensuring that the data reflects real-world operating conditions. Each convolutional layer uses a kernel of size 5, while each max-pooling layer uses a kernel of size 2. Both convolutional and pooling operations use a stride of 2.

[0127] Table 1

[0128]

[0129] 1.2.3 State Fusion Gated Long Short-Term Memory Model (SFLSTM)

[0130] Long Short-Term Memory (LSTM) networks are an improved type of recurrent neural network (RNN) designed to address the vanishing gradient problem often faced by traditional RNNs. They have become a commonly used model for capturing long-term dependencies in time-series data. The architecture of LSTM is as follows: Figure 4 As shown.

[0131] Forgotten Gate f t Regulates the cell state at the previous moment S t The proportion of information retained in section 1 is calculated using the following formula:

[0132]

[0133] in, σ This represents the Sigmoid activation function; W and b These represent the weight matrix and the bias term, respectively. x t This represents the input at the current moment; h t 1 indicates the hidden state in the previous moment.

[0134] Input gate i t It plays a crucial regulatory role in determining how much new information is incorporated into the cell state at any given moment. Simultaneously, a candidate cell state is generated. This represents newly emerging potential information. The formulas for calculating the input gate and candidate cell state are as follows:

[0135]

[0136] Where tanh represents the hyperbolic tangent function.

[0137] Cell state S t As the memory component of the LSTM, it is updated by combining the effects of the forget gate and the input gate, and its formula is as follows:

[0138]

[0139] Finally, the output gate o t Determine which part of the cell state is the hidden state. h t Presented. h t The calculation formula is:

[0140]

[0141] While Long Short-Term Memory (LSTM) models excel at capturing dependencies within time-series data, they exhibit limitations when dealing with exceptionally long time-series data, such as vehicle and bridge responses at high sampling frequencies. To address this challenge, this invention proposes a state fusion gating mechanism combining LSTM models, namely the State Fusion Long Short-Term Memory (SFLSTM) model, to enhance the predictive ability for vehicle-bridge dynamic responses. The proposed SFLSTM model synergistically integrates the cell state and input features of the LSTM to optimize temporal feature learning. The architecture of the State Fusion Gated Long Short-Term Memory model is as follows: Figure 5 As shown. Compared with the traditional LSTM model, there are two main differences:

[0142] (1) Inside the LSTM unit, by using the current input x t With cell state S t Design a state fusion gate by splicing together components. g t The state fusion gate signal is defined as follows:

[0143]

[0144] (2) In traditional LSTM, the hidden state is obtained directly by multiplying the output gate by the hyperbolic tangent of the cell state, as shown in Equation (12). In contrast, SFLSTM uses a weighted combination of the cell state and the previous hidden state to obtain its hidden state, effectively solving problems such as limited ability to model long-range dependencies. The specific update method is expressed as follows:

[0145]

[0146] 1.2.4 Adaptive Task Weighting Method

[0147] To achieve a balance in the training process across different tasks, this invention employs a multi-task loss function formula based on the principle of maximizing Gaussian likelihood with homoscedastic uncertainty. The aim is to optimize the model's performance across multiple tasks by reasonably balancing the contributions of each task during training, thereby improving the model's generalization ability to different objectives.

[0148] Assume the proposed model is represented as f W ( x ),in W Represents the set of learnable parameters. x This represents the input features. The model aims to simultaneously output the responses of the vehicle and the bridge, denoted as... and In the dual-task learning framework, the mean square error (MSE) losses corresponding to the vehicle and bridge responses are respectively expressed as: L 1 (W) and L 2 (W) .

[0149] For a standalone regression task, assuming the model output follows a Gaussian distribution, its probability density function (PDF) is defined as follows:

[0150]

[0151] in, This represents the observation noise parameter associated with the task. It is a learnable scalar that can effectively capture the inherent random uncertainties associated with the task.

[0152] Assuming the predicted outputs of these two tasks are statistically independent, then the joint probability distribution... It can be decomposed into a product of probability density functions specific to each task, as shown in the following expression:

[0153]

[0154] In maximum likelihood inference, maximizing the joint likelihood is equivalent to minimizing the negative log-likelihood, expressed as:

[0155]

[0156] Therefore, maximizing the joint likelihood can be derived as:

[0157]

[0158] To improve the efficiency of parameter update during optimization, a new variable is introduced. As The substitution, in the assumption , In this case, formula (18) can be rewritten as:

[0159]

[0160] It is worth noting that an auxiliary hyperparameter, the temperature coefficient T, is introduced to adjust the trade-off between exploration and exploitation in uncertain multi-task learning. The corresponding update formula is as follows:

[0161]

[0162] In multi-task learning, the losses generated by different tasks typically have different magnitudes. The temperature coefficient T, as an auxiliary parameter, is used in equilibrium... and It plays a crucial role in contributing to the total loss. By scaling the log-variance, it effectively prevents the uncertainty of any single task from excessively influencing the weighting in the early stages. This method makes gradient updates more equitable across different tasks, promoting a more harmonious training process. The detailed operational framework of the adaptive task weighting method is systematically described in Algorithm 2.

[0163] Steps of Algorithm 2 Adaptive Task Weighting Method

[0164] 1. Initialize parameters: Set the temperature coefficient T Initialize model parameters W and initial noise parameters .

[0165] 2. For each training epoch {1, 2, ..., num_epochs}:

[0166] 3. For each training batch:

[0167] 4. Forward propagation: Calculates predicted values ​​for vehicles and bridges. and .

[0168] 5. Calculate task-specific losses: Calculate the losses for vehicles and bridges separately. L 1( W )and L 2( W ).

[0169] 6. Calculate the loss based on total likelihood: Calculate the total loss using formula (20). L ( W ).

[0170] 7. Backpropagation: Calculate gradients and update W and .

[0171] 8. end for.

[0172] 9. Calculate the validation loss on the validation set.

[0173] 10. Check early stopping conditions: If the validation loss is less than the threshold, then stop training.

[0174] 11.end for.

[0175] 12. Return the optimized model parameters W and noise parameters .

[0176] 2. Probability Density Evolution Method Based on Adaptive Multi-Task Agent Model

[0177] 2.1 Stochastic Vehicle-Axle Coupled Dynamics Method

[0178] Due to track irregularities and the uncertainty of axle parameters, formula (1) can be restated as follows:

[0179]

[0180] in, This represents a random variable. In this invention, bridge parameters are considered. and orbital irregularity random variables Specifically, it is expressed as:

[0181]

[0182] in, Let represent a random variable related to the elastic modulus of the bridge, assuming it follows a normal distribution; n p Indicates the number of discrete points in space; and Let F represent the random spatial frequency and random phase of the orbital irregularity, respectively, both of which are assumed to follow a uniform distribution.

[0183] 2.2 Site Selection Strategy

[0184] In stochastic analysis of vehicle-bridge coupled (VBI) systems based on the probability density evolution (PDEM) method, generating a set of highly accurate discrete representative points is a crucial first step. This invention employs a hybrid approach, combining the minimization of the GF-difference criterion with the Monte Carlo method (MCM) to select a representative point set with minimal approximation error. The specific operational framework is detailed in Algorithm 3.

[0185] Algorithm 3:

[0186] Step 1: Using Sobol sequences Obtain the initial point set :

[0187]

[0188] in, Let represent the inverse cumulative distribution function (CDF) of the i-th dimension.

[0189] Step 2: Pair the point set Each dimension is calibrated to ensure consistency with [the target]. n The probabilities of each point being related are roughly equal:

[0190]

[0191] Step 3: Perform further transformations on the point set to reduce GF-discrepancy:

[0192]

[0193] in, This represents the probability of allocation. This represents the volume of a representative point.

[0194] 2.3 Probability Density Evolution Method

[0195] Let the state space vector be X, then formula (21) can be transformed into:

[0196]

[0197] Matrix A and B are defined as follows:

[0198]

[0199] For a conserved dynamic system, its dynamic response is entirely determined by the solution to equation (21). This solution can be expressed as relevant parameters. Therefore, given that it is a function of , we can make the following reasonable assumption:

[0200]

[0201] Where H(·) represents the transfer function of the dynamic response; .

[0202] because Including all random factors within the system, the system is a probability-conserving system. Based on the principle of probability conservation, the generalized probability density evolution equation (GPDEE) can be constructed as follows:

[0203]

[0204] in This represents a vector of random variables.

[0205] The initial conditions for formula (30) are:

[0206]

[0207] in, This represents a definite initial vector. This represents the Dirac function.

[0208] Finally, formula (30) is solved using the bilateral difference method. The joint probability density function (PDF) of the vehicle-bridge coupled (VBI) system response can be expressed as:

[0209]

[0210] The reliability of the system response falling within the safe interval [lb, ub] at time t can be expressed as:

[0211]

[0212] in, l b and u b These represent the lower and upper limits of the interval, respectively.

[0213] 2.4 AMLM-PDEM Calculation Process

[0214] The AMLM-PDEM architecture proposed in this invention comprises a carefully designed four-stage framework capable of accurately predicting and comprehensively evaluating the response of stochastic vehicle-bridge coupled (VBI) systems. The flowchart of the AMLM-PDEM model is shown below. Figure 6 As shown, its computational process and key components are illustrated.

[0215] Phase 1:

[0216] A set of random variables is generated by combining the GF-residual strategy with the Monte Carlo method (MCM). These random variables were then used to numerically solve the vehicle-bridge coupled random vibration equation of formula (21).

[0217] Phase Two:

[0218] The proposed MGTO-CNN-SFLSTM model is trained to predict the dynamic response of the VBI system. This model outputs the predicted responses for the vehicle and the bridge, respectively denoted as... and Loss functions for vehicles and bridges L 1 (W) and L 2 (W) They are calculated separately. The weight parameters are adjusted through negative feedback from an adaptive task-weighted strategy. The total loss function is calculated based on formula (20), and the prediction accuracy of the model is optimized by balancing the loss contributions of the two tasks.

[0219] Phase Three:

[0220] The iterative training process continues until a predefined convergence criterion is met. Once convergence is achieved, the proposed AMLM model is used to predict the response of VBI systems under different stochastic factors.

[0221] Phase Four:

[0222] At this stage, the reliability of the vehicle-bridge response under multiple uncertain random factors is evaluated by calculating the generalized probability density evolution equation (GPDEE) expressed by formula (30). The reliability results provide a comprehensive description of the system response probability information, which facilitates the understanding of the variation law of the vehicle-bridge random response under different random factors.

[0223] 3. Model Accuracy Verification

[0224] 3.1 Data Preparation

[0225] In this invention, a high-speed railway vehicle-bridge coupling (VBI) system is selected as a case study to evaluate the accuracy and efficiency of the proposed adaptive multi-task learning model (AMLM). For example... Figure 1 As shown. The bridge studied is a three-span simply supported beam bridge, with each span being 32 meters long. The bridge and piers were modeled using beam elements based on the finite element method. Rayleigh damping was introduced to account for damping effects. The key structural parameters of the bridge and piers are shown in [the diagram]. Figure 1 The values ​​are given in Table 2. Furthermore, the bridge parameters are considered as random variables following a Gaussian distribution.

[0226] The train model comprises two power cars and six trailer cars, representing a typical vehicle configuration on China's high-speed railways. The train travels at a constant speed of 300 km / h, with the vehicles having traveled 50 meters ahead on the track embankment to ensure a stable response when entering bridges. A German low-interference track spectrum was used, and track irregularity samples were generated through harmonic synthesis. The spatial frequency range of the track irregularities is 0.01×2π to 1×2π rad / m. The number of randomly representative points for the track irregularities was set to 300, considering 50 spatial frequency components.

[0227] Table 2

[0228]

[0229] To comprehensively evaluate the predictive fidelity of the alternative models, four metrics were used: mean absolute error (MAE), root mean square error (RMSE), symmetric mean absolute percentage error (SMAPE), and coefficient of determination (R²). 2 The mathematical definitions of these indicators are as follows:

[0230]

[0231] Where m represents the total number of sample points; y i and These represent the actual value and the predicted value, respectively. This represents the average value of the observed sample.

[0232] 3.2 Comparison of axle dynamic response

[0233] The acceleration responses of vehicles and bridges obtained from 300 Monte Carlo method (MCM) samples and the proposed adaptive multi-task learning model (AMLM) framework have been... Figure 7 The diagram is shown in the image. It is worth noting that the AMLM framework has the ability to simultaneously predict the acceleration and displacement responses of a vehicle-bridge coupled (VBI) system. Given that the acceleration of the VBI system is closely related to train operation safety and passenger comfort, this invention, for simplicity, focuses on predicting the vertical acceleration of both the vehicle and the bridge. Figure 7 As shown, Figure 7 (a) represents the average number of vehicles; Figure 7 (b) represents the standard deviation of the vehicles; Figure 7 (c) represents the average value of the bridge; Figure 7 (d) represents the standard deviation of the vehicle; the predicted mean and standard deviation responses are highly consistent with the baseline MCM results, validating the superior accuracy of AMLM in simultaneously estimating vehicle and bridge responses. The 300 MCM samples were computed using a MATLAB program developed on a PC equipped with a 13th-generation Intel Core i9-13900K CPU and an NVIDIA GeForce RTX 4070 GPU, with a computation time of 34,200 seconds. In contrast, the total time for database construction, AMLM training, and inference on new samples was only 10,800 seconds. This reflects a significant improvement in computational efficiency, achieving approximately a 3.17x speedup.

[0234] To further clarify the effectiveness of the adaptive weighting strategy based on homoscedasticity, Figure 8 Evaluation metrics for multi-task prediction results under various fixed weight assignments are presented. Figure 8 (a) is the root mean square error (RMSE) value; Figure 8 (b) represents the coefficient of determination R², where the sum of the loss weights for vehicles and bridges is constrained to 1. The results show that, in the dual-task framework, the prediction accuracy of the vehicle and bridge responses is highly sensitive to the distribution of the loss weights. For example, when both vehicle and bridge weights are assigned a weight of 0.5, the root mean square error (RMSE) of the bridge acceleration response is relatively low. Conversely, when the vehicle loss weight is set to 0.8 and the bridge loss weight is 0.2, the RMSE of the vehicle acceleration response reaches its minimum. These findings highlight the difficulty of achieving a balanced and optimal prediction performance for both tasks using a static weighting scheme, thus emphasizing the importance of dynamic, driven adjustment mechanisms.

[0235] Table 3 presents a comparison of the prediction error indices for vehicle and bridge acceleration responses under fixed weight allocation and the proposed AMLM. The results further highlight the significant sensitivity of the multi-task prediction model to the specific task loss weight distribution. By employing an adaptive weight update strategy, the limitations of the static weight scheme are overcome, thereby significantly improving prediction accuracy.

[0236] Table 3

[0237]

[0238] 3.3 Results of Random Vibration Analysis

[0239] This invention verifies the prediction accuracy of the model by comparing the dynamic response results predicted by the proposed adaptive multi-task learning model and the probability density evolution method (AMLM-PDEM) framework with the results obtained by the traditional PDEM method. Figure 9 The mean and standard deviation of the dynamic response of vehicles and bridges are shown. Figure 9 (a) represents the average value for each train; Figure 9 (b) represents the standard deviation of the train; Figure 9 (c) represents the average value for bridges; Figure 9 (d) represents the standard deviation of the bridge. The predicted mean responses of vehicles and bridges are in high agreement with the results of the Monte Carlo method (MCM). However, there are slight differences in the standard deviations of the predicted responses.

[0240] Figure 10 and Figure 11 The spatiotemporal evolution of the probability density function (PDF) of the vehicle and bridge responses is shown respectively. Figure 10 (a) is the PDF surface obtained from PDEM; Figure 10 (b) is the PDF surface predicted by AMLM-PDEM; Figure 10 (c) PDF contour lines obtained from PDEM; Figure 10 (d) PDF contour lines predicted by AMLM-PDEM; Figure 11 (a) is the PDF surface obtained from PDEM; Figure 11 (b) is the PDF surface predicted by AMLM-PDEM; Figure 11 (c) PDF contour lines obtained from PDEM; Figure 11(d) PDF contour lines predicted by AMLM-PDEM; the results are presented in the form of 3D surface plots and contour plots, which are derived based on the proposed AMLM-PDEM method and the traditional PDEM method. Clearly, the PDF curves of vehicle and bridge vertical acceleration predicted by AMLM-PDEM show significant consistency with the curves generated by the traditional mechanics-based PDEM. Notably, the proposed AMLM-PDEM method achieves considerable prediction accuracy while significantly reducing the computational burden. Specifically, only 200 samples are needed to construct the database, compared to 300 samples required by the traditional PDEM, significantly reducing the sample size and further highlighting the superiority of the AMLM-PDEM framework in capturing the probabilistic characteristics of dynamic responses.

[0241] Figure 12 The probability density function (PDF) and cumulative distribution function (CDF) of the vertical acceleration response of the vehicle and the bridge at time 1.5 seconds were compared. Figure 12 (a) is the vehicle acceleration; Figure 12 (b) Bridge acceleration. The results show that the PDF and CDF curves obtained from the proposed AMLM-PDEM framework are in high agreement with those calculated by the traditional PDEM method. These findings strongly demonstrate the robustness and high prediction accuracy of the AMLM-PDEM framework, thus verifying its reliability as a stochastic vibration analysis method for vehicle-bridge coupled (VBI) systems.

[0242] 4. Reliability Analysis of the Dynamic Response of the Axle System

[0243] The probabilistic evolution process of the acceleration response of the vehicle-bridge coupled (VBI) system predicted by the proposed adaptive multi-task learning model and the probability density evolution method (AMLM-PDEM) has been applied in [the following context is missing from the original text]. Figure 13 Draw in the middle, Figure 13 (a) represents the train's acceleration; Figure 13 (b) Bridge acceleration. Probabilistic characteristics are visualized using surface plots and contour plots of the time-varying probability density function (PDF), accompanied by time-history curves with mean ± 3 standard deviations (Std). Figure 13 As shown, when a vehicle crosses the bridge, the PDF surface of the bridge's vertical acceleration exhibits significant periodic fluctuations. Simultaneously, the three-dimensional PDF surface of the vehicle acceleration resembles undulating terrain, showing significant oscillations centered at zero. Notably, most PDF values ​​of the train and bridge responses are confined within the mean ± 3 standard deviations. Based on the three-standard-deviation principle, the time-varying average reliability of train and bridge accelerations is calculated to be 0.9932 and 0.9977, respectively.

[0244] This invention proposes a novel adaptive multi-task learning framework for efficiently and accurately predicting the responses of vehicles and bridges simultaneously under stochastic stimuli and parameter uncertainties. The framework synergistically integrates an improved gorilla swarm optimization algorithm (MGTO), a shared convolutional neural network (CNN), and two enhanced long short-term memory (LSTM) network architectures with state fusion gates. This integration enables the simultaneous prediction of the dynamic responses of vehicles and bridges. To address the inherent task imbalance problem in multi-task learning, this invention proposes a self-adjusting loss weighting strategy. Guided by homoscedastic uncertainty and temperature regularization, this strategy effectively achieves a dynamic balance among multiple prediction objectives. Furthermore, combining the adaptive multi-task learning model (AMLM) with the probability density evolution method (PDEM) allows for a more refined characterization of the probabilistic behavior of the dynamic response of vehicle-bridge coupled (VBI) systems. The main conclusions of this invention are as follows:

[0245] (1) The proposed adaptive multi-task learning model demonstrates superior accuracy in predicting vehicle and bridge acceleration responses. Compared with traditional methods that rely on manual loss weight allocation, it significantly reduces the root mean square error (RMSE) by 30%-70%.

[0246] (2) The introduced State Fusion Long Short-Term Memory (SFLSTM) architecture effectively captures long-term temporal dependencies by fusing cell states with simultaneous input information. In addition, the AMLM-PDEM framework reduces computational cost by 3 to 4 times compared to traditional PDEM methods while maintaining satisfactory accuracy.

[0247] (3) The probability density function (PDF) values ​​of the train and bridge responses are mostly distributed within the range of mean ± 3 standard deviations (Std). According to the three standard deviations principle, the time-varying average reliability of train and bridge accelerations are 0.9932 and 0.9977, respectively.

[0248] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A reliability analysis method for vehicle-bridge coupled systems based on adaptive multi-task deep learning, characterized in that: Includes the following steps: S1. Generate a sample set of random variables for the vehicle-bridge coupling system, wherein the random variables include bridge structural parameters and track irregularity parameters; S2. Construct a vehicle-bridge coupled physical model based on the Monte Carlo method (MCM), and calculate the vehicle response and bridge response based on the random variable sample set; S3. Construct an adaptive multi-task learning model AMLM, the model comprising: An improved gorilla population optimization algorithm, MGTO, is used to optimize model hyperparameters. During the exploration phase, MGTO introduces an elite back-learning strategy to update the population and updates gorilla candidate positions using the following formula: in, u b and l b These represent the upper and lower limits of the search space, respectively. r 1. r 2. r 3 and rand It is a random variable located in the interval [0,1]. g This represents a scaling constant constrained between 0 and 1. U ( t () indicates the current position. U r ( t () indicates a position randomly selected from the population. U ( t+1 ) represents the candidate position vector of the gorilla; T , G and H Indicates the iteration parameters; A shared convolutional neural network (CNN) is used to extract local features from an input with an uneven track. Two independent state fusion-gated long short-term memory (SFLSTM) networks are used to predict vehicle responses and bridge responses, respectively. The SFLSTM network comprises: State fusion gate This is used to fuse the current input features with the cell state, and its calculation formula is: in, For the current input features, This represents the current state of the cell. and These are the weight matrix and the bias term, respectively. This represents the Sigmoid activation function; Hidden state The update formula is: in, The state was hidden in the previous moment; An adaptive task-weighted strategy based on homoscedastic uncertainty is used to dynamically balance the loss weights of vehicle and bridge responses; the total loss function of the adaptive task-weighted strategy is defined as: in, The mean square error loss is the loss for the vehicle response or bridge response. W Represents the set of learnable parameters; i When =1, it indicates a vehicle response. i When =2, it is the bridge response. For task-related learnable noise parameters, T This is a temperature coefficient used to adjust the strength of the loss weight balance. S4. Use the calculation results of S2 to train the AMLM model; S5. Embed the trained AMLM model into the probability density evolution method (PDEM) to predict the response probability density function of the vehicle-bridge coupling system; S6. Based on the response probability density function, calculate the reliability index of the vehicle-bridge coupling system.

2. The reliability analysis method for vehicle-bridge coupling system based on adaptive multi-task deep learning according to claim 1, characterized in that: In S1, the method for generating the random variable sample set is as follows: Generate an initial point set using the Sobol sequence; By combining the minimization GF-difference criterion with the Monte Carlo method, the point set is calibrated and transformed so that the probability distribution of each point meets the preset conditions.

3. The reliability analysis method for vehicle-bridge coupling system based on adaptive multi-task deep learning according to claim 1, characterized in that: The shared convolutional neural network (CNN) includes: The input layer receives four channels of track irregularities, including vertical irregularities on the left rail, vertical irregularities on the right rail, lateral irregularities on the left rail, and lateral irregularities on the right rail. At least three convolutional modules, each of which contains a convolutional layer Conv, a batch normalization layer BN, a ReLU activation function, and a max pooling layer MP in sequence; The kernel size of each convolutional layer is 5, and the stride is 2; the kernel size of each max pooling layer is 2, and the stride is 2.

4. The reliability analysis method for vehicle-bridge coupling system based on adaptive multi-task deep learning according to claim 1, characterized in that: In step S5, the execution of the probability density evolution method (PDEM) includes: The joint probability density function of the system response is calculated using the generalized probability density evolution equation: in, State vector X The joint probability density function with the random variable Θ, x State vector X The value of , θ Let Θ be the value of the random variable. t For time, The rate of change of the system response; The equation is solved using the bilateral difference method.

5. The reliability analysis method for vehicle-bridge coupling system based on adaptive multi-task deep learning according to claim 1, characterized in that: In S6, the reliability index is calculated as follows: According to the three-standard-deviation principle, the response falls within the interval [ μ- 3 σ , μ +3 σ The probability within ] is used as the time-varying reliability; Where μ is the mean of the response and σ is the standard deviation of the response.

6. An adaptive multi-task deep learning system for reliability analysis of vehicle-bridge coupled systems, characterized in that: include: The data generation module is used to generate a sample set of random variables for the vehicle-bridge coupling system. The physics calculation module solves the vehicle-bridge coupled dynamic equations based on the Monte Carlo method (MCM) and outputs the vehicle and bridge responses. The adaptive multi-task learning model AMLM includes: The MGTO optimization unit is used for hyperparameter optimization. Shared CNN units handle inputs with uneven tracks; The dual-channel SFLSTM unit outputs predicted vehicle and bridge responses respectively; the hidden state update formula in the SFLSTM unit is: in, This represents the current state of the cell. The state was hidden in the previous moment. For state fusion gate The generated weighting coefficients are calculated using the following formula: For the current input features, and These are the weight matrix and the bias term, respectively. This represents the Sigmoid activation function; An adaptive weighting unit dynamically adjusts the loss weights based on homoscedasticity uncertainty; the total loss function in the adaptive weighting unit is defined as: in, The mean square error loss is the loss for the vehicle response or bridge response. W Represents the set of learnable parameters; i When =1, it indicates a vehicle response. i When =2, it is the bridge response. For task-related learnable noise parameters, T This is a temperature coefficient used to adjust the strength of the loss weight balance. The PDEM evaluation module calculates the response probability density function and reliability index based on the AMLM prediction results.

7. The adaptive multi-task deep learning system for reliability analysis of vehicle-bridge coupling systems according to claim 6, characterized in that: The architecture of the shared CNN unit includes: The input layer receives tensors with dimensions of 32×4×5000; The three concatenated convolutional modules output tensors with dimensions of 32×8×2500, 32×16×624, and 32×32×156, respectively.

8. The adaptive multi-task deep learning system for reliability analysis of vehicle-bridge coupling systems according to claim 6, characterized in that: The adaptive weighting unit uses a temperature coefficient T Controlling noise parameters The sensitivity of the value is updated using the following formula: in For learning rate, W This represents the set of learnable parameters.

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