Axle coupling system reliability analysis method based on adaptive multi-task deep learning

Abstract

The invention relates to an axle coupling system reliability analysis method based on adaptive multi-task deep learning, and belongs to the technical field of rail transit infrastructure safety. Aiming at the problems that the vehicle and bridge response cannot be efficiently and synchronously predicted and the multi-task loss weight is difficult to adjust in the prior art, a self-adaptive multi-task learning model AMLM is provided. The model integrates an improved chimpanzee group optimization algorithm MGTO, a shared convolutional neural network CNN and a two-way state fusion gated long short-term memory network SFLSTM. Dynamically balancing the vehicle and bridge prediction task through a same variance uncertainty loss weighting strategy; and constructing an AMLM-PDEM framework in combination with a probability density evolution method PDEM. The method has the technical effects that axle response synchronization high-precision prediction is realized, multi-task weight distribution is autonomously optimized, the calculation efficiency and the modeling precision are remarkably improved, and an axle system time-varying reliability evaluation system is perfected.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of rail transit infrastructure safety, and relates to a vehicle-bridge coupling system reliability analysis method based on adaptive multi-task deep learning. BACKGROUND

[0002] Bridge structure is a core component of modern railway system and is crucial to ensure train operation safety. In-depth study of vehicle-bridge coupling vibration theory and reliability evaluation are the inevitable requirements to ensure the safe operation of railway transportation infrastructure. However, there is significant randomness in the geometric manufacturing precision, structural parameters and track irregularities of vehicles and bridges, which brings challenges to the reliability evaluation of vehicle-bridge interaction system. Under the joint action of multiple random factors, vehicle-bridge coupling vibration reliability analysis is of great significance to improve the safety of rail transportation infrastructure.

[0003] In recent years, various stochastic vibration analysis methods have been developed in the field of vehicle-bridge coupling, such as point estimation method, pseudo-excitation method, probability density evolution method and direct probability integral method. Yu et al. combined number theory method with probability density evolution method to study the stochastic vibration characteristics of three-dimensional train-bridge coupling system; Jiang et al. proposed an improved point estimation method combined with Karhunen-Loéve method to analyze the stochastic vibration of train-bridge system; Liu et al. used direct probability integral method to analyze the stochastic vibration of heavy-load ballast track vehicle-bridge system; Shang et al. introduced sparse polynomial chaos expansion to analyze the extreme response of vehicle-track-bridge coupling system under multiple random factors. Although the above methods have achieved remarkable results, the computational efficiency of vehicle-bridge coupling system still needs to be improved due to its time-varying characteristics.

[0004] With the development of artificial intelligence technology, deep learning models have made breakthroughs in natural language processing, computer vision and other fields. Some scholars have tried to apply them to vehicle-bridge coupling stochastic vibration analysis: Li et al. used Bayesian method to construct stochastic LSTM model; Li et al. proposed least squares generative adversarial network to predict bridge acceleration and track irregularity through vehicle and bogie acceleration; Yang et al. combined stochastic pseudo-excitation method with CNN-BiLSTM model to analyze the stochastic vibration of vehicle-bridge coupling system with uncertain parameters; Zhang et al. proposed an improved graph neural network to predict train safety indicators in multiple scenarios; Cheng et al. combined probability density evolution method with adaptive hybrid deep learning model and used variational modal decomposition to preprocess data; Yang et al. used CNN-bidirectional gated recurrent unit hybrid model to evaluate train safety under near-fault earthquakes; He et al. proposed a dynamic deep learning model by combining improved temporal convolution network with Gaussian process to predict stochastic response; Mao et al. constructed a Bayesian optimization deep learning model to analyze the stochastic vibration of vehicle-track-bridge coupling system.

[0005] However, existing surrogate models mostly focus on single task prediction, only predicting one of the vehicle response or the bridge response. In actual engineering, vehicle motion will exert dynamic load on the bridge, and bridge vibration will in turn affect the vehicle dynamic response, both of which are transmitted through contact point force and displacement to form a tightly coupled system. Predicting only a single system response cannot fully reveal the coupling mechanism of vehicle-bridge system, and simultaneously predicting vehicle and bridge responses is crucial for system reliability assessment. According to the current research status, there is a lack of research on simultaneously predicting vehicle and bridge responses considering random structural parameters and random track irregularity input. The core difficulty lies in that the prediction accuracy of the model is heavily dependent on the relative weight of different task losses, and it is extremely difficult to manually adjust the multi-task loss weight. SUMMARY

[0006] Therefore, the present application aims to provide a vehicle-bridge coupling system reliability analysis method based on adaptive multi-task deep learning, and proposes an adaptive multi-task learning model (AMLM) which integrates an improved GorillaTroops Optimizer (MGTO), a shared convolutional neural network (CNN) and two independent enhanced long short-term memory networks (LSTMs). Among them, the MGTO algorithm is used to determine the optimal hyperparameters of the model, thereby improving the performance and generalization ability of the model. Since there is a similar mapping relationship from track irregularity to vehicle and bridge response, a shared CNN model is used to extract the local fluctuation features of track irregularity, thereby reducing the complexity of the model. In order to further improve the ability of the model to capture long-term temporal dependencies, a new state fusion gate mechanism is proposed, which combines the LSTM unit state and input features. In addition, an adaptive task loss weighting strategy based on homoscedastic uncertainty is proposed to dynamically balance the learning process of multiple tasks. An additional temperature coefficient is used to control the uncertainty sensitivity and regularization strength to ensure that the adaptive learning strategy can achieve smooth adjustment. By comparing with the results of the Monte Carlo method (MCM) of the vehicle-bridge coupling system, the prediction accuracy of the proposed model is verified. Based on the proposed adaptive multi-task prediction framework embedded with PDEM, the reliability of the vehicle-bridge coupling system is systematically analyzed. By comparing with the results of traditional PDEM, the reliability of the AMLM-PDEM method is verified. In addition, by analyzing the performance of the proposed model under different vehicle speeds and noise intensities, the robustness of the proposed model is further verified.

[0007] To achieve the above purpose, the present application provides the following technical solutions:

[0008] A vehicle-bridge coupling system reliability analysis method based on adaptive multi-task deep learning, comprising the following steps:

[0009] S1. generating a sample set of random variables of a vehicle-bridge coupling system, the random variables including bridge structure parameters and track irregularity parameters;

[0010] S2. constructing a vehicle-bridge coupling physical model based on a Monte Carlo method MCM, calculating vehicle responses and bridge responses according to the sample set of random variables;

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

[0012] an improved gorilla group optimization algorithm MGTO for optimizing model hyperparameters;

[0013] a shared convolutional neural network CNN for extracting local features from track irregularity inputs;

[0014] two independent state fusion gated long short-term memory networks SFLSTM for predicting vehicle responses and bridge responses respectively;

[0015] an adaptive task weighting strategy based on homoscedastic uncertainty for dynamically balancing loss weights of vehicle and bridge responses;

[0016] S4. training the AMLM model using the calculation results of S2;

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

[0018] S6. calculating a reliability index of the vehicle-bridge coupling system based on the response probability density function.

[0019] Further, in the S1, the generating method of the sample set of random variables is:

[0020] initial point sets are generated by Sobol sequences;

[0021] the point sets are calibrated and transformed by combining the minimum GF-difference criterion with the Monte Carlo method, so that the probability distribution of each point meets the preset conditions.

[0022] Further, the shared convolutional neural network CNN includes:

[0023] an input layer receiving 4-channel data of track irregularities, including left rail vertical irregularities, right rail vertical irregularities, left rail lateral irregularities, and right rail lateral irregularities;

[0024] at least three convolution modules, each module containing a convolution layer Conv, a batch normalization layer BN, a ReLU activation function, and a maximum pooling layer MP in sequence;

[0025] The convolution kernel size of each convolution layer is 5, and the step is 2; the pooling kernel size of each max pooling layer is 2, and the step is 2. Further, the hidden state update formula of the state fusion gated long short-term memory network SFLSTM is:

[0026] h t =β·tanh(S t )+(1-β)·h t-1

[0027] wherein S t is the cell state at the current moment, h t-1 is the hidden state at the previous moment, and β is a weight coefficient generated by the state fusion gate g t , and the calculation formula is:

[0028] g t =σ(W g ·[x t ,S t ]+b g )

[0029] x t is the current input feature, W g and b g are the weight matrix and the bias term respectively, and σ represents the Sigmoid activation function.

[0030] Further, the total loss function of the adaptive task weighting strategy is defined as:

[0031]

[0032] wherein L i (W) is the mean square error loss of the vehicle response or the bridge response; i=1 for the vehicle response, and i=2 for the bridge response, σ i is a task-related learnable noise parameter, and T is a temperature coefficient for adjusting the loss weight balance strength.

[0033] Further, in the S5, the execution of the probability density evolution method PDEM includes:

[0034] The joint probability density function of the system response is calculated through the generalized probability density evolution equation:

[0035]

[0036] wherein p XΘ is the joint probability density function of the state vector X and the random variable Θ, is the system response change rate;

[0037] The equation is solved by using the double difference method.

[0038] Further, in the S6, the calculation method of the reliability index is:

[0039] According to the three standard deviation principle, the probability of the response falling in the interval [mu-3sigma, mu+3sigma] is taken as the time-varying reliability;

[0040] Where mu is the response mean, and sigma is the response standard deviation.

[0041] An adaptive multi-task deep learning system for reliability analysis of axle coupling systems, comprising:

[0042] A data generation module for generating a random variable sample set of the axle coupling system;

[0043] A physical calculation module for solving the axle coupling dynamics equation based on the Monte Carlo method MCM and outputting the vehicle and bridge responses;

[0044] An adaptive multi-task learning model AMLM, comprising:

[0045] An MGTO optimization unit for hyperparameter optimization;

[0046] A shared CNN unit for processing track irregularity input;

[0047] A double-path SFLSTM unit for outputting vehicle and bridge response prediction values respectively;

[0048] An adaptive weighting unit for dynamically adjusting the loss weight according to the homoscedastic uncertainty;

[0049] A PDEM evaluation module for calculating the response probability density function and the reliability index based on the AMLM prediction result.

[0050] Further, the architecture of the shared CNN unit comprises:

[0051] An input layer receiving a tensor with a dimension of 32x4x5000;

[0052] Three convolution modules connected in series, and the output tensor dimensions of each module are 32x8x2500, 32x16x624 and 32x32x156 respectively.

[0053] Further, the adaptive weighting unit controls the sensitivity of the noise parameter sigma i by the temperature coefficient T, and the update formula is:

[0054]

[0055] Where eta is the learning rate.

[0056] The present application has the following beneficial effects:

[0057] (1) The innovative use of shared feature extraction and dual-path independent time series modeling architecture enables the first simultaneous high-precision prediction of vehicle and bridge responses. By integrating the vehicle-bridge dynamic coupling mechanism, this overcomes the limitation of traditional single-task models that cannot fully reveal the interaction relationship between the systems, providing a more complete dynamic response data foundation for reliability assessment.

[0058] (2) A loss weighting strategy based on homoscedastic uncertainty is proposed, and a temperature coefficient is introduced to dynamically adjust the task weight distribution. This mechanism autonomously balances the learning process of vehicle and bridge prediction tasks, significantly reducing the model's dependence on manual parameter adjustment, effectively solving the weight sensitivity problem in multi-task learning, and improving the model's convergence speed and generalization ability.

[0059] (3) The improved gorilla swarm optimization algorithm enhances global search capabilities through the Cauchy inverse accumulation operator and the tangent flight operator, quickly obtaining the optimal model hyperparameters; the state fusion gating mechanism enhances the ability to model long-term dependencies by fusing cell states with input features. The two work together to ensure that the model maintains prediction accuracy while significantly reducing the computational resource consumption of traditional physical models.

[0060] (4) Deeply integrate the deep learning agent model with the probability density evolution method to establish an efficient solution path for the vehicle-bridge response probability density function. Through the generalized probability density evolution equation, the probability evolution law of the system response under random factors is accurately captured, and a time-varying reliability quantification index is constructed to provide a more reliable evaluation basis for the safe operation of rail transit infrastructure.

[0061] Other advantages, objects, and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art upon examination of the following description or may be learned from practice of the present invention. The objects and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below with reference to the accompanying drawings, in which:

[0063] Figure 1 Schematic diagram of vehicle-bridge coupling mechanical model;

[0064] Figure 2 Schematic diagram of the adaptive multi-task learning model for reliability analysis of stochastic vehicle-bridge coupling systems;

[0065] Figure 3 Schematic diagram of the convolutional network model;

[0066] Figure 4 Schematic diagram of LSTM model;

[0067] Figure 5 For the state fusion gated LSTM model;

[0068] Figure 6 For the calculation process of the AMLM-PDEM agent model;

[0069] Figure 7 For the 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) is the mean of the vehicle; Figure 7 (b) is the standard deviation of the vehicle; Figure 7 (c) is the mean of the bridge; Figure 7 (d) is the standard deviation of the vehicle;

[0070] Figure 8 For the comparison of vehicle and bridge performance indicators under different loss weight assignments; Figure 8 (a) is the root mean square error RMSE value; Figure 8 (b) is the coefficient of determination R 2 value;

[0071] Figure 9 For the comparison of the vehicle-bridge response acceleration results of AMLM-PDEM and PDEM; Figure 9 (a) is the mean of the train; Figure 9 (b) is the standard deviation of the train; Figure 9 (c) is the mean of the bridge; Figure 9 (d) is the standard deviation of the bridge;

[0072] Figure 10 For the surface and contour visualization of the probability density function PDF of vehicle acceleration; Figure 10 (a) is the PDF surface obtained by PDEM; Figure 10 (b) is the PDF surface predicted by AMLM-PDEM; Figure 10 (c) is the PDF contour obtained by PDEM; Figure 10 (d) is the PDF contour predicted by AMLM-PDEM;

[0073] Figure 11 For the surface and contour visualization of the probability density function PDF of bridge acceleration; Figure 11 (a) is the PDF surface obtained by PDEM; Figure 11 (b) is the PDF surface predicted by AMLM-PDEM; Figure 11 (c) is the PDF contour obtained by PDEM; Figure 11 (d) is the PDF contour predicted by AMLM-PDEM;

[0074] Figure 12Comparisons of the probability density function (PDF) and cumulative distribution function (CDF) results for vehicle and bridge accelerations; Figure 12 (a) for vehicle acceleration; Figure 12 (b) for bridge acceleration.

[0075] Figure 13 Probability density function (PDF) contours and surface plots for the acceleration response of the vehicle-bridge interaction (VBI) system; Figure 13 (a) for train acceleration; Figure 13 (b) for bridge acceleration. DETAILED DESCRIPTION

[0076] Other advantages and benefits of the present application will become apparent to those skilled in the art upon consideration of the disclosure herein. The present application can be embodied in other specific forms without departing from the spirit or essential characteristics thereof. Thus, the present disclosure is not intended to limit the application, as the described embodiments are presented merely as examples of the application. The features of the described embodiments can be combined in any combination without departing from the spirit or essential characteristics of the application.

[0077] The accompanying drawings are included to provide a further understanding of the application, and are incorporated in and constitute a part of this specification. The drawings illustrate embodiments of the application and, together with the description, serve to explain the principles of the application. In the drawings:

[0078] The same or similar components in the drawings of the embodiments of the present application correspond to the same or similar components; in the description of the present application, it should be understood that the orientation or position relationship indicated by the terms "upper", "lower", "left", "right", "front", "back", etc. is based on the orientation or position relationship shown in the drawings, and is only for the convenience of describing the present application and simplifying the description, and does not indicate or imply that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, therefore the terms describing the position relationship in the drawings are only for illustrative purposes, and cannot be understood as a limitation of the present application, for those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0079] 1 Vehicle-bridge interaction system prediction framework

[0080] 1.1 Mechanical model

[0081] A schematic diagram of the mechanical model of the vehicle-bridge interaction (VBI) system is shown in FIG. 1. Figure 1The present application adopts a 3x32m simply supported beam bridge, which is widely used in high-speed railways. The beam and the pier are modeled by the finite element method, and the main parameters are shown in Figure 1 The train is modeled as a multi-body system, which includes a car body, two bogies, and four wheelsets. The bodies are connected by primary and secondary suspension systems. The primary suspension system is used to connect the bogie and the wheelset, while the secondary suspension system is used to connect the car body and the bogie. The car body, the front bogie, and the rear bogie have five degrees of freedom (lateral, vertical, yaw, pitch, and roll), and each wheelset includes three degrees of freedom (lateral, vertical, and yaw). In general, the train model includes 27 degrees of freedom.

[0082] Based on the law of conservation of energy, the mass, stiffness, and damping matrices of the train can be easily obtained, while the mass and stiffness matrices of the bridge are established by the finite element method. In constructing the damping matrix of the bridge, the Rayleigh damping assumption is adopted. Finally, the dynamic equation of the vehicle-bridge interaction (VBI) system can be expressed as:

[0083]

[0084] where the subscripts v and b represent the vehicle and the bridge, respectively; the displacement, velocity, and acceleration vectors of the dynamic response are represented by X, and respectively; the mass, damping, stiffness, and external force matrices are represented by M, C, K, and F, respectively.

[0085] 1.2 Adaptive multi-task prediction model

[0086] The adaptive multi-task learning model (AMLM) proposed in the present application is trained based on the Monte Carlo method (MCM) results of vehicle-bridge interaction, which includes an improved gorilla troop optimizer, 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 probabilistic density evolution method (PDEM) model is shown, which is used for reliability evaluation of a stochastic vehicle-bridge interaction system. Each component will be introduced separately.

[0087] 1.2.1 Improved gorilla troop optimizer (MGTO)

[0088] Mostafa et al. proposed an improved gorilla group optimization (GTO) to enhance the population diversity and global search ability. In the natural environment, gorillas usually live in groups, which are generally composed of multiple adult females, a dominant male silverback gorilla, and their offspring. The behavior patterns of gorillas can be systematically divided into two different stages: exploration stage and exploitation stage.

[0089] In the exploration stage of the improved gorilla group optimization (MGTO), an elite reverse learning strategy is introduced. This strategy significantly improves the diversity of the population during the initialization and updating process of the algorithm. From a theoretical point of view, each gorilla in the model represents a candidate solution, while the optimal solution is represented by the silverback gorilla, which symbolizes the best solution in the solution space. The candidate position of each gorilla is defined as:

[0090]

[0091] where the gorilla candidate position vector is U(t+1), U(t) represents the current position; r1, r2, r3, and rand are random variables in the interval [0, 1]; the symbol g represents a scaling constant constrained between 0 and 1; U r represents a randomly selected position from the population; u b and l b represent the upper and lower limits of the search space, respectively. The adjustment method of the iteration parameters T, G, and H is as follows:

[0092]

[0093] where r4 is a value between 0 and 1, which is updated at each iteration; Iter represents the current iteration number; MaxIt represents the pre-set maximum iteration number; the variable l is a randomly selected integer between -1 and 1; Z represents a random number from the symmetric interval [-T, T].

[0094] In the exploitation stage, gorillas exhibit two main behavior strategies: following the silverback gorilla and competing for mating opportunities with adult females. To enhance the local exploitation ability, the improved gorilla group optimization (MGTO) introduces the Cauchy inverse cumulative distribution operator and the tangent flight operator. These two operators work together to optimize search results, enabling the algorithm to efficiently navigate the solution space and converge to the optimal or near-optimal solution. This integration not only fully utilizes the natural behavior patterns of gorillas but also enhances the overall performance and effectiveness of the algorithm in solving complex optimization problems. The position update formula for gorillas following the silverback gorilla is as follows:

[0095]

[0096] where N gor represents the number of gorillas; X silverback represents the position of silverback gorillas; c is a random number uniformly distributed in the interval [0, 1] obtained by the inverse cumulative distribution operator.

[0097] The position of gorillas competing for an adult female can be represented as:

[0098]

[0099] where Q represents the force; ξ is a random variable with a value range between 0 and 1; the function tan() corresponds to the tangent flight operator; h represents another random variable uniformly distributed in the interval [0, 1].

[0100] The synergistic integration of these two operators significantly improves the convergence dynamic performance of the improved gorilla group optimization algorithm (MGTO) and optimizes the search trajectory. The program framework of MGTO is described in detail in Algorithm 1.

[0101] Algorithm 1 Steps of improved gorilla group optimization algorithm (MGTO)

[0102] 1. Initialize parameters: population size N pop , maximum number of iterations N max and parameters of gorilla group optimization algorithm (GTO).

[0103] 2. Generate initial population: generate initial gorilla population U i (i = 1, 2, …, Npop).

[0104] 3. While N max do:

[0105] 4. Update the current population using the elite backward learning (ELBO) strategy.

[0106] 5. Calculate the fitness value of gorillas.

[0107] 6. Update parameters T and G according to formula (3).

[0108] 7. Update the position of gorillas according to formula (2) and select silverback gorillas.

[0109] 8. For each gorilla (U i ):

[0110] 9. If |C| > > w:

[0111] 10. Update the position of gorillas according to formula (4).

[0112] 11. Else:

[0113] 12. Update the position of the gorilla according to equation (5).

[0114] 13. end if.

[0115] 14. end for.

[0116] 15. end while.

[0117] 16. Return the result: return silverback gorilla U Silverback and its optimal fitness value.

[0118] 1.2.2 Convolutional Neural Network Model (CNN)

[0119] Convolutional Neural Networks (CNNs) have become the dominant model for feature extraction from time series data, spanning a variety of scenarios such as images and audio signals. In this invention, a CNN model is designed to extract local features of track irregularities. The structural architecture of the convolutional neural network is shown in Figure 3 As shown in Figure 3 , a typical CNN framework consists of a series of hierarchical operations, where each convolution (Conv) layer is followed by batch normalization (BN) to stabilize training and improve convergence speed. Subsequently, a rectified linear unit activation function is deployed to introduce nonlinearity, enabling the modeling of complex and abstract data representations. To achieve the best balance between computational efficiency and generalization performance, a max-pooling (MP) layer is introduced. By downsampling the 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 retains the most salient spatial features, ensuring that key information is preserved while redundant data is discarded. The sequential arrangement of convolution (Conv), batch normalization (BN), rectified linear unit (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 ability, making it an efficient tool for extracting important features from track irregularity data.

[0120] The mathematical expression of the convolution operation is as follows:

[0121]

[0122] where j represents the index of the output channel; N in represents the number of input channels; κ represents the size of the convolution kernel; s represents the step size of the convolution filter; w n,k represents the kth weight in the filter related to the nth input channel; b (j) represents the bias term of the jth output channel; χ represents the size of the padding; x n,tRepresents the element of the input channel at the corresponding position t.

[0123] Table 1 lists the architectural parameters of the convolutional neural network (CNN) and their corresponding data dimensions. The model input consists of a four-channel track irregularity signal, consisting of vertical and lateral irregularity samples for the left and right tracks. During training, each batch consists of 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 convolution kernel of size 5, while each maximum pooling layer uses a pooling kernel of size 2. Both convolution and pooling operations use a stride of 2.

[0124] Table 1

[0125] Layer Name Input Size Output Size Kernel Size Stride Activation Function Conv_1 + BN_1 32×4×5000 32×8×2500 8×4×5 2 ReLU MP_1 32×8×2500 32×8×1250 2 2 / Conv_2 + BN_2 32×8×1250 32×16×624 16×8×5 2 ReLU MP_2 32×16×624 32×16×312 2 2 / Conv_3 + BN_3 32×16×312 32×32×156 32×16×5 2 ReLU MP_3 32×32×156 32×32×78 2 2 /

[0126] 1.2.3 State Fusion Gated Long Short-Term Memory Model (SFLSTM)

[0127] The Long Short-Term Memory (LSTM) model is an improved Recurrent Neural Network (RNN) that aims to solve the vanishing gradient problem often faced by traditional RNNs. It has become a commonly used model for capturing long-term dependencies in time series data. The architecture of LSTM is as follows: Figure 4 shown.

[0128] Forget Gate f t Regulates the cell state S at the previous moment t-1 The proportion of information retained in the , is calculated as follows:

[0129] f t =σ(W f ·[h t-1 ,x t ]+b f ) (7)

[0130] Where σ represents the Sigmoid activation function; W and b represent the weight matrix and bias term respectively; x t Indicates the input at the current moment; h t-1 Represents the hidden state at the previous moment.

[0131] Input gate i t It plays a key regulatory role in determining how much new information is incorporated into the cell state at the current moment. At the same time, a candidate cell state is generated. As a representative of the emerging potential information. The calculation formulas for the input gate and candidate cell state are:

[0132] i t =σ(W i ·[ht-1 ,x t ]+b i ) (8)

[0133]

[0134] where tanh denotes the hyperbolic tangent function.

[0135] Cell state S t As the memory component of LSTM, it is updated by combining the influence of the forget gate and the input gate, and its formula is:

[0136]

[0137] Finally, the output gate o t decides which part of the cell state is used as the hidden state h t to be presented. h t The calculation formula is:

[0138] o t = σ(W o · [h t-1 ,x t ]+b o ) (11)

[0139]

[0140] Although the long short-term memory (LSTM) model performs well in capturing dependencies within time series data, it has limitations in capturing dependencies when dealing with particularly long time series data, such as vehicle and bridge responses at high sampling frequencies. To address this challenge, the present invention proposes a state fusion gating mechanism combined with the LSTM model, namely the state fusion long short-term memory model (SFLSTM), to enhance the prediction ability of vehicle-bridge dynamic response. The proposed SFLSTM model cooperatively integrates the cell state and input features of LSTM to optimize time series feature learning. The architecture of the state fusion gating long short-term memory model is shown in Figure 5 Compared with the traditional LSTM model, there are mainly two differences:

[0141] (1) Inside the LSTM unit, the state fusion gate g t is designed by concatenating the current input x t and the cell state S t , and the state fusion gate signal is defined as follows:

[0142] g t = σ(W g · [x t , S t ]+b g) (13)

[0143] (2) In traditional LSTM, the hidden state is directly obtained by multiplying the output gate with the hyperbolic tangent result of the cell state, as shown in equation (12). In contrast, SFLSTM adopts a weighted combination of the cell state and the previous hidden state to obtain its hidden state, effectively solving problems such as limited modeling of long-range dependencies. The specific update method is represented as:

[0144]

[0145] 1.2.4 Adaptive task weight method

[0146] To balance the training process between different tasks, the present application adopts a multi-task loss function formula based on the Gaussian likelihood maximization principle of homoscedastic uncertainty. The purpose is to reasonably balance the contribution of each task in the training process, optimize the performance of the model on multiple tasks, and thus improve the generalization ability of the model to different targets.

[0147] Suppose the proposed model is represented as f W (x), where W represents a set of learnable parameters, and x represents input features. The model aims to simultaneously output responses for vehicles and bridges, denoted as and Under the dual-task learning framework, the mean square error (MSE) loss corresponding to the vehicle and bridge responses is represented as L1(W) and L2(W), respectively.

[0148] For individual regression tasks, it is assumed that the model output follows a Gaussian distribution, and its probability density function (PDF) is defined as follows:

[0149]

[0150] where represents the observation noise parameter related to the task, which is a learnable scalar that can effectively capture the inherent random uncertainty related to the task.

[0151] Suppose the prediction outputs of the two tasks are statistically independent of each other, then the joint probability distribution p(y1,y2∣f W (x)) can be decomposed into the product of the probability density functions specific to each task, expressed as follows:

[0152]

[0153] In maximum likelihood inference, the maximization of the joint likelihood is equivalent to the minimization of the negative log-likelihood, expressed as:

[0154]

[0155] Therefore, maximizing the joint likelihood can be derived as:

[0156]

[0157] To improve the efficiency of parameter updating during optimization, a new variable α is introduced as a substitute for ε. Under the assumption , formula (18) can be rewritten as:

[0158]

[0159] It is worth noting that a helper hyperparameter, the temperature coefficient T, is introduced to adjust the trade-off between exploration and exploitation in uncertainty multi-task learning. The corresponding update formula is as follows:

[0160]

[0161] In multi-task learning, the losses generated by different tasks usually have different magnitudes. The temperature coefficient T, as a helper parameter, plays a key role in balancing the contributions of α1 and α2 to the total loss. By scaling the logarithmic variance, it effectively prevents the uncertainty of any single task from excessively affecting the weighted proportion in the early stages. This approach makes the gradient updates between different tasks more fair, promoting a more harmonious training process. The detailed operation framework of the adaptive task weighting method is systematically elaborated in Algorithm 2.

[0162] Algorithm 2 Steps of adaptive task weighting method

[0163] 1. Initialize parameters: set the temperature coefficient T, initialize the model parameters W, and initialize the noise parameter ε.

[0164] 2. For each training cycle epoch {1, 2, …, num_epochs}:

[0165] 3. For each training batch:

[0166] 4. Forward propagation: calculate the predicted values of vehicles and bridges and

[0167] 5. Calculate task-specific loss: calculate the loss L1(W) and L2(W) of vehicles and bridges respectively.

[0168] 6. Calculate the loss based on the total likelihood: calculate the total loss L(W) using formula (20).

[0169] 7. Backpropagation: calculate the gradient and update W and ε i .

[0170] 8.end for.

[0171] 9. Calculate the validation loss on the validation set.

[0172] 10. Check the early stopping condition: if the validation loss is less than the threshold, stop training.

[0173] 11.end for.

[0174] 12. Return the optimized model parameters W and noise parameters ε i .

[0175] 2 Probability Density Evolution Method Based on Adaptive Multi-Task Agent Model

[0176] 2.1 Random vehicle-bridge coupling dynamics method

[0177] Due to the uncertainty of track irregularities and axle parameters, formula (1) can be restated as follows:

[0178]

[0179] Where Θ represents a random variable. In the present invention, the bridge parameters and track irregularity random variables Specifically expressed as:

[0180]

[0181] in, represents a random variable related to the elastic modulus of the bridge, which is assumed to obey a normal distribution; n p Represents the number of discrete points in space; and represent the random spatial frequency and random phase of the track irregularity, respectively, and are both assumed to obey uniform distribution.

[0182] 2.2 Site selection strategy

[0183] Generating a set of highly accurate discrete representative points is a crucial first step in the stochastic analysis of vehicle-bridge interaction (VBI) systems using the probability density evolution method (PDEM). This paper employs a hybrid approach that combines minimizing the GF-discrepancy criterion with the Monte Carlo method (MCM) to select a representative point set with minimal approximation error. The detailed operational framework is detailed in Algorithm 3.

[0184] Algorithm 3:

[0185] Step 1: Go through the Sobol sequence Get the initialization point set x q ={(x q,1 ,xq,2 ,…,x q,s ),q = 1,2,...,n}:

[0186] x m,i = F i -1 (u m,i ) (23)

[0187] where F i -1 (·) denotes the inverse cumulative distribution function (CDF) of the i-th dimension.

[0188] Step 2: Calibrate each dimension of the point set x q to ensure that the probabilities associated with the n points are approximately equal:

[0189]

[0190] Step 3: Further transform the point set to reduce the GF-discrepancy:

[0191]

[0192] where p denotes the assigned probability, and V denotes the volume of the representative point.

[0193] 2.3 Probability density evolution method

[0194] Let the state space vector be X, then formula (21) can be converted to:

[0195]

[0196] where the matrices A and B are defined as follows:

[0197]

[0198] For a conservative dynamic system, its dynamic response is completely determined by the solution of formula (21). Since the solution can be expressed as a function of the relevant parameters Θ, the following reasonable assumption can be made:

[0199]

[0200] where H(·) represents the transfer function of the dynamic response;

[0201] Since Θ contains all the random factors in the system, the system is a probability-conservative system. Based on the principle of probability conservation, the generalized probability density evolution equation (GPDEE) can be constructed as follows:

[0202]

[0203] where denotes a random variable vector.

[0204] The initial condition of formula (30) is:

[0205]

[0206] where z0denotes the determined initial vector, and δ(·) denotes the Dirac function.

[0207] Finally, formula (30) is solved by the double difference method. The response joint probability density function (PDF) of the vehicle-bridge interaction (VBI) system can finally be expressed as:

[0208]

[0209] The reliability of the system response falling within the safety interval [lb, ub] at time t can be expressed as:

[0210]

[0211] where lband ubdenote the lower limit and the upper limit of the interval, respectively. b and u b denote the lower limit and the upper limit of the interval, respectively.

[0212] 2.4 AMLM-PDEM calculation process

[0213] The AMLM-PDEM architecture proposed in the present application comprises a four-stage framework, which is carefully designed to accurately predict and comprehensively evaluate the response of a random vehicle-bridge interaction (VBI) system. The flowchart of the AMLM-PDEM model is shown in Figure 6 , which shows its calculation process and key components.

[0214] First stage:

[0215] A set of random variables These random variables are then used to numerically solve the vehicle-bridge coupling random vibration equation of formula (21).

[0216] Second stage:

[0217] The proposed MGTO-CNN-SFLSTM model is trained to predict the dynamic response of the VBI system, which outputs the predicted responses of the vehicle and the bridge, denoted as and The loss functions L1(W) and L2(W) of the vehicle and the bridge are calculated, respectively. The weight parameter a is adjusted by negative feedback with an adaptive task weighting strategy. iThe total loss function is calculated based on equation (20) to optimize the prediction accuracy of the model by balancing the loss contribution of the two tasks.

[0218] Third stage:

[0219] The iterative training process continues until a predefined convergence criterion is met. Once convergence is reached, the proposed AMLM model is used to predict the response of the VBI system under different random factors.

[0220] Fourth stage:

[0221] In this stage, the reliability of the vehicle-bridge interaction system under multiple uncertain random factors is evaluated by calculating the generalized probability density evolution equation (GPDEE) represented by equation (30). The reliability results provide a comprehensive description of the system response probability information, facilitating the understanding of the variation of the vehicle-bridge random response under the action of different random factors.

[0222] 3 Model accuracy verification

[0223] 3.1 Data preparation

[0224] In this invention, a high-speed railway vehicle-bridge interaction (VBI) system case is selected to evaluate the accuracy and efficiency of the proposed adaptive multi-task learning model (AMLM), as shown in Figure 1 The bridge studied is a three-span simply supported beam bridge, with each span being 32 meters long. The bridge and piers are modeled using beam elements based on the finite element method. To consider the damping effect, Rayleigh damping is introduced. The key structural parameters of the bridge and piers are given in Figure 1 . In addition, the bridge parameters are considered as random variables following a Gaussian distribution, and the specific values are shown in Table 2.

[0225] The train model consists of two powered cars and six trailer cars, representing the typical vehicle configuration on Chinese high-speed railways. The train travels at a constant speed of 300 kilometers per hour, and the vehicles travel on the roadbed for 50 meters in advance to ensure stable response when entering the bridge. The German low disturbance track spectrum is used, and the track irregularity samples are generated by the harmonic synthesis method. The spatial frequency range of the track irregularity is 0.01×2π-1×2π rad / m. The number of random representative points of the track irregularity is set to 300, considering 50 spatial frequency components.

[0226] Table 2

[0227] Parameter Distribution Unit Mean Coefficient of Variation Elasticity Model Gaussian Pa 3.55 x 10 10 ]]> 0.05 Damping Ratio Gaussian / 0.03 0.05 Density Gaussian kg / m 2500 0.04

[0228] To comprehensively evaluate the prediction fidelity of surrogate models, four metrics are adopted: mean absolute error (MAE), root mean square error (RMSE), symmetric mean absolute percentage error (SMAPE), and coefficient of determination (R 2 )2. These metrics are mathematically defined as follows:

[0229]

[0230] where m denotes the total number of sample points; y i and represent the true and predicted values, respectively; denotes the mean value of observed samples.

[0231] 3.2 Comparison of vehicle bridge dynamic responses

[0232] The acceleration responses of the vehicle and bridge obtained from 300 Monte Carlo method (MCM) samples and the proposed adaptive multi-task learning model (AMLM) framework are plotted in Figure 7 . It is worth noting that the AMLM framework is capable of simultaneously predicting the acceleration and displacement responses of the vehicle-bridge interaction (VBI) system. Given that the acceleration of the VBI system is closely related to train operation safety and passenger comfort, the present invention focuses on predicting the vertical acceleration of the vehicle and bridge for simplicity. As shown in Figure 7 , Figure 7 (a) is the mean value of the vehicle; Figure 7 (b) is the standard deviation of the vehicle; Figure 7 (c) is the mean value of the bridge; Figure 7 (d) is the standard deviation of the vehicle; the predicted mean and standard deviation responses are highly consistent with the baseline MCM results, verifying the superior accuracy of the AMLM in simultaneously estimating the vehicle and bridge responses. The 300 MCM samples are calculated based on a MATLAB program developed on a personal computer equipped with a 13th generation Intel Core i9-13900K CPU and NVIDIA GeForce RTX 4070 GPU, and the computation time is 34200 seconds. In comparison, the total time spent on building the database, AMLM training, and inference on new samples is only 10800 seconds. This reflects a significant improvement in computational efficiency, achieving a speedup of approximately 3.17 times.

[0233] To further illustrate the effectiveness of the adaptive weighting strategy based on homoscedasticity, Figure 8 the evaluation metrics of multi-task prediction results under various fixed weight assignments are shown, Figure 8 (a) is the root mean square error RMSE value; Figure 8(b) is the coefficient of determination R2value; where the sum of the loss weights of the vehicle and the bridge is constrained to 1. The results show that the prediction accuracy of the vehicle and the bridge responses in the dual-task framework is highly sensitive to the distribution of the loss weights. For example, when the weights of the vehicle and the bridge are both assigned as 0.5, the root mean square error (RMSE) of the bridge acceleration response is relatively low. In contrast, when the loss weight of the vehicle is set as 0.8 and the loss weight of the bridge is 0.2, the RMSE of the vehicle acceleration response reaches the minimum. These findings highlight the difficulty of achieving balanced and optimal prediction performance for both tasks using the static weight scheme, thereby emphasizing the importance of the dynamic, driving adjustment mechanism.

[0234] Table 3 presents the comparative results of the prediction error indicators of the vehicle and the bridge acceleration responses under the fixed weight assignment and the proposed AMLM. The results further emphasize the significant sensitivity of the multi-task prediction model to the distribution of the specific task loss weights. By the adaptive weight updating strategy, the limitations of the static weight scheme are overcome, thereby significantly improving the prediction accuracy.

[0235] Table 3

[0236]

[0237] 3.3 Random vibration analysis results

[0238] The prediction accuracy of the model is verified by comparing the dynamic response results predicted by the proposed adaptive multi-task learning model with 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 vehicle and the bridge dynamic responses are shown, Figure 9 (a) is the train mean; Figure 9 (b) is the train standard deviation; Figure 9 (c) is the bridge mean; Figure 9 (d) is the bridge standard deviation. The predicted mean responses of the vehicle and the bridge are highly consistent with the Monte Carlo method (MCM) results. However, there is a slight difference in the standard deviation of the predicted responses.

[0239] Figure 10 and Figure 11 The spatiotemporal evolution of the probability density function (PDF) of the vehicle and the bridge responses, respectively, is shown. Figure 10 (a) is the PDF surface obtained by PDEM; Figure 10 (b) is the PDF surface predicted by AMLM-PDEM; Figure 10 (c) is the PDF contour obtained by PDEM; Figure 10 (d) is the PDF contour predicted by AMLM-PDEM; Figure 11 (a) is the PDF surface obtained by PDEM;Figure 11 (b) is the PDF surface predicted by AMLM-PDEM; Figure 11 (c) is the PDF contour obtained by PDEM; Figure 11 (d) is the PDF contour predicted by AMLM-PDEM; The results are presented in the form of three-dimensional surface plots and contour plots, which are obtained based on the proposed AMLM-PDEM method and the traditional PDEM method. Obviously, the PDF curves of vehicle and bridge vertical acceleration predicted by AMLM-PDEM exhibit significant consistency with the curves generated by the traditional mechanics-based PDEM. It is worth noting that the proposed AMLM-PDEM method achieves comparable prediction accuracy while significantly reducing the computational burden. Specifically, only 200 samples are needed to construct the database, which is a significant reduction compared to the 300 samples required by the traditional PDEM, further highlighting the superiority of the AMLM-PDEM framework in capturing the probabilistic characteristics of dynamic responses.

[0240] Figure 12 The probability density function (PDF) and cumulative distribution function (CDF) of the vehicle and bridge vertical acceleration responses at 1.5 seconds are compared. Figure 12 (a) is the vehicle acceleration; Figure 12 (b) is the bridge acceleration. The results show that the PDF and CDF curves obtained by the proposed AMLM-PDEM framework exhibit high consistency with the results calculated by the traditional PDEM method. These findings strongly demonstrate the robustness and high prediction accuracy of the AMLM-PDEM framework, thereby verifying its reliability as a random vibration analysis of vehicle-bridge interaction (VBI) systems.

[0241] 4 Reliability analysis of vehicle-bridge system dynamic responses

[0242] The probabilistic evolution process of vehicle-bridge interaction (VBI) system acceleration responses predicted by the proposed adaptive multi-task learning model and probability density evolution method (AMLM-PDEM) has been plotted in Figure 13 , Figure 13 (a) is the train acceleration; Figure 13 (b) is the bridge acceleration. The probabilistic characteristics are visualized by surface plots and contour plots of the time-varying probability density function (PDF), with the mean ± 3 times the standard deviation (Std) time history curves. As Figure 13As shown, the PDF surface of the bridge vertical acceleration exhibits significant periodic fluctuations as the vehicle drives over the bridge. Meanwhile, the three-dimensional PDF surface of the vehicle acceleration resembles a rolling terrain with significant oscillations centered around zero. It is worth noting that most of the PDF values of both train and bridge responses are confined within the mean ± 3 standard deviation band. According to the three-sigma rule, the time-varying average reliabilities of train and bridge accelerations are calculated as 0.9932 and 0.9977, respectively.

[0243] The present application proposes a novel adaptive multi-task learning framework for efficiently and accurately predicting the responses of both vehicle and bridge simultaneously under random excitation and parametric uncertainty. The framework integrates the modified gorilla group optimization (MGTO), shared convolutional neural network (CNN), and two enhanced long short-term memory networks (LSTM) with state fusion gate mechanisms. This integration makes it possible to simultaneously predict the dynamic responses of both vehicle and bridge. To address the inherent task imbalance problem in multi-task learning, the present application proposes a self-adjusting loss weighting strategy. Under the guidance of homoscedastic uncertainty and temperature regularization, this strategy effectively achieves dynamic balance among multiple prediction objectives. In addition, the combination of adaptive multi-task learning model (AMLM) and probability density evolution method (PDEM) enables a more refined characterization of the probabilistic behavior of vehicle-bridge interaction (VBI) system dynamic responses. The main conclusions of the present application are as follows:

[0244] (1) The proposed adaptive multi-task learning model exhibits superior accuracy in predicting the acceleration responses of both vehicle and bridge. Compared to traditional methods that rely on manual loss weight distribution, it significantly reduces the root mean square error (RMSE) by 30%-70%.

[0245] (2) The introduced state fusion long short-term memory network (SFLSTM) architecture effectively captures long-term temporal dependencies by fusing cell states with simultaneous input information. In addition, the AMLM-PDEM framework reduces the computational cost by 3-4 times compared to traditional PDEM methods while maintaining satisfactory accuracy.

[0246] (3) The probability density function (PDF) values of both train and bridge responses are mostly distributed within the mean ± 3 standard deviation (Std) range. According to the three-sigma rule, the time-varying average reliabilities of train and bridge accelerations are 0.9932 and 0.9977, respectively.

[0247] Finally, it is to be explained that the above embodiments are only used to illustrate the technical solutions of the present application but not to limit the present application. Although the present application is described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present application can be modified or equivalently replaced without departing from the purpose and scope of the technical solutions, and all should be covered in the scope of the claims of the present application.

Claims

1. A reliability analysis method for a vehicle-bridge coupling system based on adaptive multi-task deep learning, characterized by: The following steps are involved: S1. Generate a sample set of random variables for the vehicle-bridge coupling system, wherein the random variables include bridge structure parameters and track irregularity parameters; S2. Constructing a vehicle-bridge coupling physical model based on the Monte Carlo method MCM, and calculating the vehicle response and bridge response according to the random variable sample set; S3. Construct an adaptive multi-task learning model AMLM, the model including: Improved gorilla group optimization algorithm MGTO, used to optimize model hyperparameters; A shared convolutional neural network (CNN) is used to extract local features from track irregularity input; Two independent state fusion gated long short-term memory networks (SFLSTMs) are used to predict vehicle response and bridge response respectively; An adaptive task weighting strategy based on homoscedastic uncertainty is used to dynamically balance the loss weights of vehicle and bridge responses; S4 uses 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. Calculate the reliability index of the vehicle-bridge coupling system based on the response probability density function.

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

3. The vehicle-bridge coupling system reliability analysis method based on adaptive multi-task deep learning according to claim 1 is characterized by: The shared convolutional neural network CNN includes: The input layer receives 4-channel track irregularity data, including left track vertical irregularity, right track vertical irregularity, left track lateral irregularity, and right track lateral irregularity. At least three convolution modules, each module contains a convolution layer Conv, a batch normalization layer BN, a ReLU activation function and a maximum pooling layer MP in sequence; The convolution kernel size of each convolution layer is 5 and the stride is 2; the pooling kernel size of each maximum pooling layer is 2 and the stride is 2.

4. The vehicle-bridge coupling system reliability analysis method based on adaptive multi-task deep learning according to claim 1 is characterized by: The hidden state update formula of the state fusion gated long short-term memory network SFLSTM is: h t =β·tanh(S t )+(1-β)·h t-1 Among them, S t is the cell state at the current moment, h t-1 is the hidden state at the previous moment, β is the state fusion gate g t The generated weight coefficient is calculated as follows: g t =σ(W g ·[x t ,S t ]+b g ) x t is the current input feature, W g and b g are the weight matrix and bias term respectively, and σ represents the Sigmoid activation function.

5. The vehicle-bridge coupling system reliability analysis method based on adaptive multi-task deep learning according to claim 1 is characterized by: The total loss function of the adaptive task weighted strategy is defined as: Among them, L i (W) is the mean square error loss of vehicle response or bridge response; when i = 1, it is vehicle response, when i = 2, it is bridge response, σ i is a task-related learnable noise parameter, and T is the temperature coefficient, which is used to adjust the loss weight balance strength.

6. The vehicle-bridge coupling system reliability analysis method based on adaptive multi-task deep learning according to claim 1 is characterized by: In S5, the execution of the probability density evolution method (PDEM) includes: The joint probability density function of the system response is calculated by the generalized probability density evolution equation: Among them, p XΘ is the joint probability density function of the state vector X and the random variable Θ, is the system response change rate; The equations are solved using the double difference method.

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

8. An adaptive multi-task deep learning system for vehicle-bridge coupling system reliability analysis, characterized by: include: A data generation module, used to generate a random variable sample set of the vehicle-bridge coupling system; The physical calculation module solves the vehicle-bridge coupled dynamic equations based on the Monte Carlo method (MCM) and outputs the vehicle and bridge responses. Adaptive multi-task learning model AMLM, including: MGTO optimization unit, used for hyperparameter optimization; Shared CNN unit to process track irregularity input; Dual-path SFLSTM units output vehicle and bridge response predictions respectively; Adaptive weighting unit, dynamically adjusts loss weights based on homoscedastic uncertainty; The PDEM evaluation module calculates the response probability density function and reliability index based on the AMLM prediction results.

9. The adaptive multi-task deep learning system for vehicle-bridge coupling system reliability analysis according to claim 8, characterized in that: The architecture of the shared CNN unit includes: The input layer receives a tensor of size 32×4×5000; There are three concatenated convolutional modules, and the output tensor dimensions of each module are 32×8×2500, 32×16×624, and 32×32×156 respectively.

10. The adaptive multi-task deep learning system for vehicle-bridge coupling system reliability analysis according to claim 8, characterized in that: The adaptive weighting unit controls the noise parameter σ through the temperature coefficient T i The sensitivity of , its update formula is: Where η is the learning rate.

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