A probability evaluation method for operation safety resilience of mountain wind-vehicle-bridge system

Abstract

This invention relates to the field of bridge engineering and traffic safety technology, and discloses a probabilistic assessment method for the operational safety resilience of a wind-vehicle-bridge system in mountainous areas. It introduces the Informer model as the core prediction module, maintaining a strong ability to capture long-term dependencies in long-term series while reducing computational complexity. The model is trained by constructing a loss function through quantile regression, driving the model to synchronously output the upper and lower bound prediction sequences of the derailment coefficient at specified quantiles, thereby directly forming a prediction interval for quantifying risk uncertainty. A parameter optimization strategy is employed to obtain the optimal prediction interval under different wind speed conditions, while ensuring the reliability of the preset prediction interval coverage, with the goal of minimizing the normalized interval width. This invention can efficiently and reliably complete long-term safety predictions, scientifically reflecting the changes in the safety risk level and resilience of the vehicle-bridge system under wind load excitation in mountainous areas, providing technical support for traffic safety early warning and resilience management.

Description

Technical Field

[0001] This invention relates to the field of bridge engineering and traffic safety technology, specifically a probabilistic assessment method for the operational safety resilience of a mountain wind-vehicle-bridge system. Background Technology

[0002] The wind-vehicle-bridge system is a complex high-order dynamic system involving multiple stochastic excitations such as wind loads, vehicle dynamic loads, and track irregularities. To ensure simulation accuracy and the stability of wheel-rail dynamic interaction calculations, numerical analysis typically requires extremely small step sizes, leading to the accumulation of thousands or even more calculation steps, forming a typical long-term analysis scenario. Therefore, to ensure the continuous safe operation of the vehicle-bridge system in complex mountainous environments for resilience management, developing a safety resilience assessment method that can efficiently and reliably handle such long-term, highly stochastic processes has become a key requirement in this field.

[0003] Currently, various methods have been proposed and applied for the random vibration analysis of vehicle-bridge systems. Traditional numerical methods, such as Monte Carlo simulation, probability density evolution, and pseudo-excitation methods, have achieved good results in theoretical research, but their computational cost typically increases exponentially with system complexity and accuracy requirements, making it difficult to meet the needs of efficient, real-time assessment in engineering practice. In recent years, with the rapid development of artificial intelligence technology, deep learning models have been introduced into this field, providing new approaches to handling high-dimensional and nonlinear problems. For example, some studies have combined temporal convolutional networks with Gaussian processes to construct surrogate models, or used the CNN-LSTM framework to characterize system uncertainties and predict random vibration responses. These methods have improved computational efficiency to some extent and have begun to focus on the probabilistic characteristics of the response. However, existing technologies, especially when applied to the operational safety resilience assessment of wind-vehicle-bridge systems, still have significant defects and shortcomings.

[0004] First, existing methods struggle to balance computational efficiency and accuracy in long-term forecasting. The safety resilience assessment of wind-vehicle-bridge systems is essentially a long-term series forecasting problem. Traditional finite element methods or numerical integration methods are computationally expensive when dealing with long sequences of thousands of steps. While common deep learning sequence models, such as recurrent neural networks and long short-term memory networks, are widely used, their structural characteristics make them ineffective at capturing long-term dependencies in ultra-long sequences. As the prediction step size increases, errors accumulate and propagate, leading to a significant decrease in prediction accuracy. Although some studies have attempted to handle long sequences through segmented generation, this method disrupts the continuity of the dynamic response process, potentially resulting in the loss of key extrema and important physical information, thus affecting the reliability of the safety assessment. The Transformer model addresses the long-term dependency problem through its self-attention mechanism, but its computational complexity is too high, requiring enormous computational resources and making low-cost deployment difficult in engineering practice.

[0005] Second, existing safety assessment methods are mostly limited to point predictions, failing to quantify the uncertainty of predictions and resulting in insufficient assessment of safety resilience. Current research on the safety resilience assessment of wind-vehicle-bridge systems based on artificial intelligence primarily focuses on deterministic point predictions of safety indicators such as derailment coefficients and wheel load reduction rates. However, due to the system being subjected to multiple strongly stochastic stimuli, its response itself exhibits significant uncertainty. Providing only a single predicted value cannot reflect the potential range of risk fluctuations, creating blind spots in engineering decision-making. This leads to an inability to know the reliability of the prediction results and the safety boundary under worst-case conditions, potentially resulting in untimely or overly conservative early warnings. Although interval prediction methods are maturely applied in fields such as wind power prediction, enabling intuitive quantification of risk through prediction intervals, related research has not yet applied them to the safety assessment of complex dynamic systems like wind-vehicle-bridge systems.

[0006] Third, even with the introduction of interval forecasting, constructing and optimizing the forecast interval remains a challenge. An ideal forecast interval needs to be as narrow as possible at a given confidence level (e.g., 95%) to improve accuracy, while ensuring sufficient coverage to guarantee reliability. In wind-vehicle-bridge systems, environmental conditions such as wind speed change dynamically, and fixed forecast interval parameters may not be suitable for all operating conditions, leading to excessively wide intervals (information redundancy) or insufficient coverage (risk underreporting) under certain conditions. Therefore, an optimization strategy is needed to automatically find the most accurate forecast interval while satisfying reliability constraints for different wind speed conditions, thereby scientifically reflecting different risk levels.

[0007] In summary, existing technologies have significant shortcomings in balancing long-term computational efficiency and accuracy, ensuring the sufficiency of uncertainty quantification and risk assessment, and optimizing the prediction interval when dealing with probabilistic assessments of the operational safety resilience of wind-mill-bridge systems. Summary of the Invention

[0008] To address the aforementioned problems, the present invention aims to provide a probabilistic assessment method for the operational safety resilience of a mountain wind-vehicle-bridge system. By introducing a probabilistic prediction model based on the Informer architecture and integrating quantile regression and parameter optimization strategies, it can efficiently and reliably complete long-term safety predictions. The width of its optimal prediction interval can scientifically reflect the changes in the safety risk level and resilience level of the vehicle-bridge system under mountain wind load excitation, thereby providing technical support for traffic safety early warning and resilience management. The technical solution is as follows:

[0009] A probabilistic assessment method for the operational safety resilience of a mountain wind-vehicle-bridge system includes the following steps: Step 1: Generate spatiotemporally correlated time-series data of pulsating wind speeds acting on the bridge structure and vehicles; Step 2: Construct a coupled dynamic model of the wind-vehicle-bridge system. Input the time series data of the pulsating wind speed and the track irregularity time history generated based on the standard track spectrum as external excitations into the coupled dynamic model, solve for the dynamic response of the vehicle, and extract the time series data of the derailment coefficient from it. Step 3: Use the time series data of fluctuating wind speed under different wind speed conditions and the average wind speed data of each time series as input features, and use the time series data of the corresponding calculated derailment coefficient as the target output. Align the data according to the time series to form sample data, and divide it into training set, validation set and test set. Step 4: Construct a deep learning network based on the Informer architecture as the core prediction module. The output layer of the core prediction module is configured to output the derailment coefficient time series of the left and right wheels under a preset quantile. Step 5: Construct a loss function based on quantile regression for model validation and model training when predicting intervals; Step 6: Train the deep learning network using the training set to obtain a probabilistic prediction model; the probabilistic prediction model is used to output the derailment coefficient prediction time series at multiple quantiles for the input pulsating wind speed time series data, wherein the upper quantile and lower quantile time series constitute the prediction interval. Step 7: Using the trained probabilistic prediction model, generate multiple derailment coefficient prediction interval samples for the input data of the target wind speed condition. Each sample includes an upper bound time series and a lower bound time series. Perform parameterized search optimization on the generated multiple derailment coefficient prediction interval samples to determine the optimal prediction interval under the target wind speed condition.

[0010] The beneficial effects of this invention are:

[0011] The probabilistic assessment method for the operational safety resilience of mountain wind-vehicle-bridge systems provided by this invention brings significant benefits by introducing a probabilistic prediction model based on the Informer architecture and integrating quantile regression and parameter optimization strategies.

[0012] First, this invention effectively solves the problem of balancing computational efficiency and prediction accuracy under long-term, stochastic excitation. By utilizing the ProbSparse self-attention mechanism of the Informer model, it significantly reduces computational complexity while accurately capturing long-term dependencies in thousands of time-series data points, achieving efficient and high-precision point prediction of the derailment coefficient.

[0013] Secondly, by constructing a loss function based on quantile regression, the model can generate predicted time series under preset quantile conditions and form a prediction interval under a specified reliability threshold. In this field, it realizes a quantitative assessment of the uncertainty of safety indicators, overcomes the limitation of insufficient risk assessment in point prediction methods, and provides more comprehensive risk information for decision-making.

[0014] Finally, through the proposed parameterized search optimization strategy, this invention can find the optimal prediction interval with the smallest interval width under different wind speed conditions while meeting preset reliability requirements (such as coverage ≥ 95%). This makes the prediction interval not only reliable but also accurate, and its width can scientifically and intuitively reflect the dynamic changes in risk level caused by wind speed changes. Thus, it provides an intelligent assessment tool for driving safety early warning that is both efficient, reliable and scientific. Attached Figure Description

[0015] Figure 1 This is a diagram of the model structure.

[0016] Figure 2 The graph shows the loss curve during the training process of the model in Example 1.

[0017] Figure 3(a) is a time series comparison of the derailment coefficient of the left wheel under the condition of an average wind speed of 10 m / s.

[0018] Figure 3(b) is a time series comparison of the right wheel derailment coefficient under the condition of an average wind speed of 10 m / s.

[0019] Figure 3(c) is a time series comparison of the derailment coefficient of the left wheel under the condition of an average wind speed of 20 m / s.

[0020] Figure 3(d) is a time series comparison of the right wheel derailment coefficient under the condition of an average wind speed of 20 m / s.

[0021] Figure 3(e) is a time series comparison of the derailment coefficient of the left wheel under the condition of an average wind speed of 30 m / s.

[0022] Figure 3(f) is a time series comparison of the right wheel derailment coefficient under the condition of an average wind speed of 30 m / s.

[0023] Figure 4 This is a training loss curve for the CNN-GRU model. Detailed Implementation

[0024] The purpose of this invention is to provide a probabilistic assessment method for the operational safety resilience of wind-wheel-bridge systems that is efficient, reliable, and can scientifically quantify risks.

[0025] To address the challenge of balancing efficiency and accuracy in long-term forecasting in existing technologies, this invention introduces the Informer model as the core forecasting module. Utilizing its adaptive sparse attention mechanism, it significantly reduces computational complexity while maintaining a strong ability to capture long-term dependencies in long-term series data. This allows for efficient processing of derailment coefficient time-series data spanning thousands of steps at a lower cost. The Informer model receives historical time-series data under different wind speed conditions as input and outputs corresponding time-series predictions of the derailment coefficient.

[0026] To address the problem of insufficient risk assessment in existing systems, this invention trains the Informer model by constructing a loss function through quantile regression, driving the model to synchronously output the upper and lower bound prediction sequences of the derailment coefficient at specified quantiles, thereby directly forming a prediction interval for quantifying uncertainty.

[0027] To obtain a prediction interval that achieves the optimal balance between reliability and accuracy, this invention proposes a parameter optimization strategy. The upper and lower quantiles of the prediction interval are used as adjustable parameters for optimization. For different wind speed conditions, the optimal combination of quantiles with the smallest interval width is adaptively found to meet the preset reliability requirements. This generates an optimal prediction interval that can scientifically reflect changes in risk level, so that the interval width can scientifically reflect the differences in risk level caused by changes in wind speed.

[0028] The specific implementation of the technical solution is as follows:

[0029] A probabilistic assessment method for the operational safety resilience of a mountain wind-vehicle-bridge system includes the following steps:

[0030] Step 1: Generate time-series data of fluctuating wind speeds with spatiotemporal correlation. Specifically, this includes: simulating and generating time histories of fluctuating wind speeds acting on bridge structures and vehicles based on a preset power spectrum model.

[0031] Harmonic synthesis was used to generate fluctuating wind speed time histories for multiple simulated points distributed along the bridge span to characterize the spatial correlation of wind loads. For moving vehicles, the simulated wind speed time histories corresponding to their bridge coordinate positions were interpolated to obtain instantaneous wind speed data synchronized with vehicle movement, which were then used as the fluctuating wind speed time histories acting on the vehicles.

[0032] Step 2: Construct a coupled dynamic model of the wind-vehicle-bridge system and obtain time-series data of the derailment coefficient. Specifically, this includes establishing a coupled system that includes a finite element model of the bridge and a multibody dynamic model of the vehicle.

[0033] The fluctuating wind speed time history generated in step 1, along with the track irregularity time history generated based on the standard track spectrum, are used as the external excitation input to the coupled dynamic model. By solving the dynamic differential equations of the system, the dynamic response of the vehicle under the combined excitation of wind and track irregularities is calculated, and the derailment coefficient time series data are extracted from it. The track irregularity time history is not used as a known input feature in the dataset for subsequent prediction models to reflect the uncertainties in actual engineering.

[0034] Step 3: Construct a dataset for model training and testing. Specifically, this includes using the different wind speed conditions data (pulsating wind speed time series and the average wind speed corresponding to that time series) generated in Step 1 as input features, and the derailment coefficient time series data calculated in Step 2 as the target output, aligning them by time series to form the sample data. All sample data are then divided into a training set, a validation set, and a test set in an 8:1:1 ratio for subsequent model training, optimization, and performance evaluation.

[0035] Step 4: Construct the Informer model as the core module for training. Specifically, this includes building a deep learning network based on the Informer model architecture as the core prediction module. The model includes at least an embedding layer, an encoder, a decoder, and an output layer.

[0036] (1) Embedding layer:

[0037] The embedding layer is used to receive and process the input pulsating wind speed time-series data. The original input of the model is the lateral wind speed acting on the vehicle (…). ) and vertical wind speed ( The time series of wind speeds in different directions is used. To eliminate the difference in magnitude between wind speeds in different directions and to ensure the numerical stability of the model during training, the wind speed data in different directions are first normalized by taking the maximum absolute value. Specifically, each value in the lateral wind speed sequence is divided by the maximum absolute value in the entire lateral wind speed dataset, and the same operation is performed on the vertical wind speed sequence.

[0038] ;

[0039] ;

[0040] in, This is the normalized lateral wind speed vector. This is time-series data for lateral wind speed. This represents the maximum absolute value of the transverse wind speed; This is the normalized vertical wind speed vector. This is time-series data of vertical wind speed. This represents the maximum absolute value of the vertical wind speed.

[0041] This normalization method maps the data to the [-1,1] interval while preserving the original data's sign (wind direction) information.

[0042] Then, along the time step dimension, the normalized lateral wind speed vector is... With vertical wind speed vector and the average wind speed of that time series (Constant time series) concatenated into a three-dimensional wind speed feature vector The concatenated 3D wind speed feature vector is mapped to a high-dimensional space through a learnable linear layer. Then, positional encoding is used to incorporate temporal concepts as a fourth dimension into the wind speed features. Finally, a Dropout layer is introduced as a regularization method. The definition of positional encoding is as follows:

[0043] ;

[0044] ;

[0045] in, Indicates the absolute position of the input data. i For the dimensions of the data, Let be the dimension of the high-dimensional space. and They represent the positions respectively. The second encoding vector i The first dimension (i.e., the even-numbered index dimension) and the second i +1 dimension (i.e., odd index dimension) encoded values.

[0046] (2) Encoder:

[0047] The encoder consists of multiple stacked encoder layers used to extract high-level temporal features from the input sequence. Each encoder layer contains a sparse self-attention mechanism sublayer and a feedforward neural network sublayer.

[0048] Among them, self-attention mechanism is a method for calculating the relationship between arbitrary positions within a sequence, which is achieved by querying a vector ( Q ), key vector ( K ) and value vector ( V Attention weights are assigned based on the similarity calculation of ( ). The sparse self-attention mechanism sublayer introduces a sparse mask matrix on top of the self-attention mechanism. This reduces the computational complexity from O(N²) of traditional attention mechanisms to O(N(logN)), thereby achieving efficient capture of long-range dependencies in long sequence data. Specifically, the calculation formula for the sparse self-attention mechanism sub-layer is:

[0049] ;

[0050] Where ⊙ represents the Hadamard product, The dimension for each attention head. Here K , Q and V Both are obtained by mapping the input data through a learnable linear layer, where the input data is the output data of the embedding layer.

[0051] The feedforward neural network sublayer is one of the core processing layers in the encoder. It consists of two sequentially stacked one-dimensional convolutional layers with a kernel size of 1. Each convolutional layer contains a ReLU activation function and a Dropout regularization function, used to enhance non-linear feature representation and prevent overfitting, respectively. The first convolutional layer reduces the dimension from... Expand to 4× The first layer uses a high-dimensional space to facilitate richer feature combinations; the second layer compresses the dimensions back to their original values, and this dimensional consistency ensures compatibility with residual connections.

[0052] (3) Decoder:

[0053] The decoder also consists of multiple stacked decoder layers used to generate a prediction sequence based on contextual information provided by the encoder. Each decoder layer contains a sparse self-attention mechanism sublayer, an attention sublayer for receiving the encoder output, and a feedforward neural network sublayer. The decoder generates the entire target prediction sequence in a single-step forward propagation manner to avoid the error accumulation problem caused by autoregressive decoding. It is important to note that the sparse self-attention mechanism sublayer of the decoder... K , Q and V Consistent with the encoder, the input data is obtained by mapping through a learnable linear layer, where... K , Q and V The input data used is all encoder output data. The attention sublayer, used to receive the encoder output... K The encoder's output data is used as the input data, but Q and V Input data and K The difference lies in the input data. To prevent the encoder from losing important information during computation, the original pulsating wind speed time series and the average wind speed to which that time series belongs are processed as input data. The processing method is as follows: 1) The normalized wind speed time series in the two directions are processed by average pooling; 2) The two processed wind speed time series are averaged to obtain an average time series; 3) This time series is concatenated with the average wind speed (constant time series) to which that time series belongs in the feature dimension. The concatenated data is the input data. Q and V Input data.

[0054] (4) Output layer:

[0055] The output layer, connected after the decoder, consists of a linear projection layer followed by a Softplus activation function layer. The linear projection layer maps the high-dimensional sequence representation of the decoder output to the target dimension, while the Softplus activation function layer maps the data to [0, +]. The invention first verifies the accuracy of the Informer model, outputting only two time series at this stage: the point prediction values ​​of the derailment coefficients for the left and right wheels of the vehicle. After verification, during the prediction interval stage, the output layer selects to output six time series: the derailment coefficient time series for the left and right wheels at preset quantiles (2.5%, 50%, 97.5%). The time series at the 97.5% and 2.5% quantiles serve as the upper and lower bounds of the prediction interval.

[0056] Step 5: Construct the loss function used for model validation and model training when predicting intervals.

[0057] A loss function based on quantile regression is constructed, and a deep learning network is trained using the training set to obtain a probabilistic prediction model. The probabilistic prediction model is used to output the derailment coefficient prediction time series under multiple quantiles for the input pulsating wind speed time series data, wherein the upper bound quantile and the lower bound quantile time series constitute the prediction interval.

[0058] Mean squared error loss was selected for model validation. MSE The calculation formula is as follows:

[0059] ;

[0060] in, For the actual target derailment coefficient timing, The target time series predicted by the model; This represents the number of data points in the time series.

[0061] When determining the prediction interval, a loss function based on quantile regression is used. Given quantiles... q (where 0 < q <1) Quantile loss function Defined as:

[0062] ;

[0063] in, Represents the residual, and = - ;Ⅱ(•) is the indicator function.

[0064] Step 6: Combine the Informer model and loss function, and train the model. The model structure diagram is shown below. Figure 1 As shown.

[0065] The training parameters are set as follows: During training, the Adam optimizer is used to minimize the objective function, with a learning rate of 0.0002 and L2 regularization achieved through a weight decay coefficient of 1e-5. The beta parameter is set to (0.5, 0.999). The batch size is set to 8, and the training epochs are 2000.

[0066] Step 7: Based on the trained probabilistic prediction model, generate and optimize prediction intervals. Specifically, this includes using the trained probabilistic prediction model to generate multiple derailment coefficient prediction interval samples for input data under different wind speed conditions. Each prediction interval consists of an upper bound time series and a lower bound time series, corresponding to the potential risk range under that wind speed condition.

[0067] To determine the optimal prediction interval from multiple generated prediction interval samples, a parameterized search optimization is performed. The specific optimization process is as follows: An adjustable quantile parameter *a* (where 0 ≤ *a* ≤ 1) is set. For each candidate value of the adjustable quantile parameter *a*, the following operations are performed: The *a*-th quantile is extracted from the set of upper bound sequences of all generated prediction interval samples, forming a shrunken upper bound sequence; simultaneously, the *1-a*-th quantile is extracted from the set of lower bound sequences, forming a shrunken lower bound sequence. Thus, each pair of (a, 1-a) parameters defines a definite candidate prediction interval.

[0068] A comprehensive evaluation criterion is constructed to quantify the quality of each candidate interval. This criterion considers at least two indicators: first, interval coverage, which is the proportion of the true value of the target derailment coefficient falling within the candidate interval; its value should not be lower than a preset reliability threshold. The upper and lower bounds of the predicted time series generated by the model correspond to the 97.5% and 2.5% quantiles, respectively, therefore its reliability threshold is 97.5% - 2.5% = 95%. Second, the normalized average interval width, used to measure the accuracy of the interval; the smaller the width, the more accurate the prediction. The comprehensive evaluation criterion is a function of the interval width and coverage constraint, and its optimization objective is to minimize the interval width while meeting the coverage requirement. The formulas for minimizing the interval width (PINAW) and interval coverage (PICP) are as follows:

[0069] ;

[0070] ;

[0071] in, It is a Boolean variable; This represents the number of samples used in the evaluation calculation; if the true value falls within the interval... =1, otherwise =0; and These represent the upper and lower bounds of the prediction interval at the prediction point, respectively. To predict the difference between the upper and lower bounds of the interval.

[0072] The search space of the adjustable quantile parameter 'a' is traversed, and the comprehensive evaluation criterion value corresponding to each candidate interval is calculated. The adjustable quantile parameter 'a' that optimizes (i.e., minimizes) the comprehensive evaluation criterion value is selected. The upper bound sequence (the 'a' quantile of all upper bound samples) and the lower bound sequence (the '1-a' quantile of all lower bound samples) corresponding to the adjustable quantile parameter 'a' are finally determined as the optimal derailment coefficient prediction interval for this wind speed condition. This interval maximizes prediction accuracy while meeting preset reliability requirements, and its width scientifically reflects the risk level under this condition. The comprehensive evaluation criterion is the Coverage Width Criterion (CWC), and the formula is as follows:

[0073] ;

[0074] ;

[0075] In the formula, Typically, the default confidence level is set; in this example, it is 95%. The penalty parameter is used to evaluate PICP and The degree of deviation. In this embodiment... The value is 50. This is a penalty switch function; its purpose is to determine whether the actual coverage rate has reached the preset target. To achieve the preset credit level The actual predicted interval coverage rate is calculated below.

[0076] Example verification:

[0077] This case study analyzes a long-span concrete cable-stayed bridge. The bridge has a span arrangement of 60+135+250+135+60 meters, a total length of 640 meters, and adopts a symmetrical double-tower, five-span structure. The main beams, towers, and piers are all made of concrete, while the stay cables are made of high-strength steel strands. A bridge structural model was established based on the finite element method. The element type was selected according to the mechanical properties of each component: the main beams, towers, piers, and other major load-bearing components were discretized using beam elements to accurately reflect their mechanical behavior; the stay cables, which primarily bear axial tension, were simulated using tension-only beam elements; secondary dead loads such as the bridge deck pavement and guardrails were represented by additional mass elements. Based on these principles, a full-bridge spatial finite element model was established in the general-purpose finite element software ANSYS.

[0078] The vehicle model established in this embodiment is a seven-body dynamics model, mainly composed of a car body, two frames, and four wheelsets. The rigid bodies are connected by primary and secondary suspension systems, and the model's flexibility primarily originates from these two suspension systems. Specific components include axle box springs, air springs, vertical and lateral dampers, anti-roll torsion bars, anti-hunting dampers, and lateral stops. In terms of degree of freedom, each car body and steering frame component includes five degrees of freedom: lateral displacement, vertical displacement, yaw, pitching, and roll; each wheelset only considers two degrees of freedom: lateral displacement and yaw. Therefore, the entire vehicle system has a total of 23 degrees of freedom. The wheel-rail creep force is calculated using a numerical algorithm based on the simplified Kalker theory (FASTSIM), and the dynamic equations of the entire vehicle subsystem are constructed and solved within the framework of the finite element method.

[0079] (1) Example 1: Validation and accuracy comparison of the Informer model;

[0080] This example is for point prediction, and the mean squared error is used as the loss function during training. Figure 2 The loss curves during training are shown. As the training iterations converge, the validation loss is consistently slightly lower than the training loss, indicating a low risk of overfitting and demonstrating the model's strong generalization ability. Figures 3(a)-3(f) present a comparison between the predicted and actual values ​​of the derailment coefficient under fluctuating wind fields with average wind speeds of 10 m / s, 20 m / s, and 30 m / s. The model's predicted curves and the actual curves agree well, indicating that the established Informer model can effectively capture the main characteristics of the system response.

[0081] Compared to Model 1, which is the Transformer model, under the same computer configuration, the Transformer model cannot perform calculations due to insufficient memory, indicating that the Informer model's runtime environment is more friendly to engineering applications. Compared to the Transformer model, the Informer model does not require high-end computer CPUs, GPUs, or memory.

[0082] Comparison Model 2 is a CNN-GRU (Convolutional Neural Network-Gate Recurrent Unit) model, using the same dataset and identical parameter settings, including learning rate, number of training epochs, weight decay, L2 regularization, dropout rate, batch size, and epoch size. The CNN-GRU model contains three convolutional layers (with 32, 64, and 128 channels respectively) and two GRU layers (with 128 and 256 hidden layers respectively), and its input and output data preprocessing methods are consistent with the model used in this invention. Figure 4The training loss curve of the CNN-GRU model is shown. Compared with the model proposed in this paper, the model converges much slower and exhibits significant oscillations. For the dataset used in this invention, the model shows instability during training and exhibits typical overfitting characteristics. Table 1 compares the error metrics of the two models under different operating conditions. Overall, the model proposed in this embodiment outperforms the CNN-GRU model in evaluation metrics such as RMSE (Root Mean Square Error), MAE (Mean Absolute Error), and R² (coefficient of determination).

[0083] Table 1 Comparison of Prediction Results .

[0084] (2) Example 2: Interval prediction effect;

[0085] This embodiment employs a loss function based on quantile regression for interval estimation. Quantile regression does not rely on specific distribution assumptions and can directly fit the quantiles of the dataset, effectively preserving extreme values ​​with low probability of occurrence but significant numerical performance, thus better meeting the needs of safety risk assessment. The prediction interval evaluation parameters generated using the method in this paper are shown in Table 2. The coverage ratio (PICP) of the optimal prediction interval all exceed 0.95, meeting the preset 95% confidence interval requirement and demonstrating good reliability.

[0086] Table 2 Evaluation parameters for the optimal prediction interval of the derailment coefficient .

[0087] In summary, this invention provides a probabilistic assessment method for the operational safety resilience of a mountainous wind-vehicle-bridge system. Addressing the challenges of balancing computational efficiency and prediction accuracy in traditional methods, and the difficulty of effectively handling the long-term temporal characteristics of the system's random response using existing deep learning methods, this invention constructs a method that integrates an Informer model and a quantile regression loss function to predict the long-term sequence of derailment coefficients within uncertain intervals. Simultaneously, a parameter optimization strategy is employed to minimize the normalized interval width under different wind speed conditions, while ensuring the reliability of the preset prediction interval coverage. This method can efficiently and reliably complete long-term safety predictions, and the width of its optimal prediction interval can scientifically reflect the changes in the safety risk level and resilience of the vehicle-bridge system under mountainous wind load excitation, thus providing technical support for traffic safety early warning and resilience management. Example 1 demonstrates that the Informer model outperforms the commonly used CNN-GRU model in terms of generation performance and is superior to the Transformer model in terms of computational environment friendliness. Example 2, combining a quantile regression-based loss function and parameter optimization strategy, uses interval prediction to overcome the deficiency of commonly used point prediction in providing a sufficient range for safety risk assessment.

Claims

1. A probabilistic assessment method for the operational safety resilience of a mountain wind-vehicle-bridge system, characterized in that, Includes the following steps: Step 1: Generate spatiotemporally correlated time-series data of pulsating wind speeds acting on the bridge structure and vehicles; Step 2: Construct a coupled dynamic model of the wind-vehicle-bridge system. Input the time series data of the pulsating wind speed and the track irregularity time history generated based on the standard track spectrum as external excitations into the coupled dynamic model, solve for the dynamic response of the vehicle, and extract the time series data of the derailment coefficient from it. Step 3: Use the time series data of fluctuating wind speed under different wind speed conditions and the average wind speed data of each time series as input features, and use the time series data of the corresponding calculated derailment coefficient as the target output. Align the data according to the time series to form sample data, and divide it into training set, validation set and test set. Step 4: Construct a deep learning network based on the Informer architecture as the core prediction module. The output layer of the core prediction module is configured to output the derailment coefficient time series of the left and right wheels under a preset quantile. Step 5: Construct a loss function based on quantile regression for model validation and model training when predicting intervals; Step 6: Train the deep learning network using the training set to obtain a probabilistic prediction model; the probabilistic prediction model is used to output the derailment coefficient prediction time series at multiple quantiles for the input pulsating wind speed time series data, wherein the upper quantile and lower quantile time series constitute the prediction interval. Step 7: Using the trained probabilistic prediction model, generate multiple derailment coefficient prediction interval samples for the input data of the target wind speed condition. Each sample includes an upper bound time series and a lower bound time series. Perform parameterized search optimization on the generated multiple derailment coefficient prediction interval samples to determine the optimal prediction interval under the target wind speed condition.

2. The probabilistic assessment method for the operational safety resilience of a mountain wind-vehicle-bridge system according to claim 1, characterized in that, In step 4, the core prediction module includes an embedding layer, an encoder, a decoder, and an output layer; 1) The embedded layer is used to receive and process the input pulsating wind speed time-series data, including the lateral wind speed acting on the vehicle. With vertical wind speed Time series; The horizontal and vertical wind speed sequences are normalized by taking the maximum absolute value, as shown below: ； ； in, This is the normalized lateral wind speed vector. This is time-series data for lateral wind speed. This represents the maximum absolute value of the transverse wind speed; This is the normalized vertical wind speed vector. This is time-series data of vertical wind speed. This represents the maximum absolute value of the vertical wind speed. Along the time step dimension, the normalized lateral wind speed vector With vertical wind speed vector and the average wind speed corresponding to the time series Concatenate into a three-dimensional wind speed feature vector The concatenated 3D wind speed feature vector is mapped to a high-dimensional space through a learnable linear layer. Then, positional encoding is used to incorporate temporal concepts as a fourth dimension into the 3D wind speed feature vector. Finally, a Dropout layer is introduced as a regularization method. The definition of positional encoding is as follows: ； ； in, Indicates the absolute position of the input data. i For the dimensions of the data, Let be the dimension of the higher-dimensional space; and These represent the absolute positions. The second encoding vector i The second dimension and the second i +1 dimension of encoded values; 2) The encoder comprises multiple stacked encoder layers for extracting high-level temporal features from the input sequence; each encoder layer contains a sparse self-attention mechanism sublayer and a feedforward neural network sublayer; The sparse self-attention mechanism sublayer Based on the self-attention mechanism, a sparse mask matrix is ​​introduced, and its calculation formula is as follows: ； Where ⊙ represents the Hadamard product; Q and V These are the query vector and the value vector, respectively. K The key vector; M It is a sparse mask matrix; Dimensions for each attention head; Softmax The function is used to calculate attention weights; This is the transpose of the key vector; The feedforward neural network sublayer comprises two sequentially stacked one-dimensional convolutional layers with a kernel size of 1. Each convolutional layer contains a ReLU activation function and a Dropout regularization; the first convolutional layer reduces the dimension from... Expand to 4× The first layer uses a high-dimensional space to facilitate richer feature combinations; the second layer compresses the dimensions back to their original values ​​to ensure compatibility with residual connections through dimensional consistency. 3) The decoder includes multiple stacked decoder layers for generating a prediction sequence based on the context information provided by the encoder; each decoder layer includes a sparse self-attention mechanism sublayer, an attention sublayer for receiving the encoder output, and a feedforward neural network sublayer; the decoder generates the entire target prediction sequence in a single-step forward propagation manner to avoid the error accumulation problem caused by autoregressive decoding. 4) The output layer, connected after the decoder, includes a linear projection layer and a Softplus activation function layer; the linear projection layer maps the high-dimensional sequence representation output by the decoder to the target dimension; the Softplus activation function layer maps the data to [0, + ] interval.

3. The probabilistic assessment method for the operational safety resilience of a mountain wind-wheel-bridge system according to claim 1, characterized in that, In step 5, during model validation, mean squared error loss is selected. MSE The calculation formula is as follows: ； in, For the actual target derailment coefficient timing, The target time series predicted by the model; This represents the number of data points in the time series. When determining the prediction interval, a loss function based on quantile regression is selected; given the quantile... q , where 0 < q <1, quantile loss function Defined as: ； in, Represents the residual, and = - ;Ⅱ(•) is the indicator function.

4. The probabilistic assessment method for the operational safety resilience of a mountain wind-wheel-bridge system according to claim 1, characterized in that, In step 7, determining the optimal prediction interval under the target wind speed condition specifically involves: Step 7.1: Set an adjustable quantile parameter a. For each candidate value of the adjustable quantile parameter a, perform the following operations: extract the a-th quantile from the upper bound sequence set of all prediction interval samples as the shrunken upper bound sequence; at the same time, extract the 1-a-th quantile from the lower bound sequence set as the shrunken lower bound sequence; each pair (a, 1-a) forms a candidate prediction interval. Step 7.2: Construct a comprehensive evaluation criterion based on interval coverage and interval width, select the adjustable quantile parameter a that minimizes the interval width under the condition of satisfying the preset coverage threshold, and determine the upper and lower boundary sequences corresponding to the adjustable quantile parameter a as the optimal derailment coefficient prediction interval under the wind speed condition. The formulas for calculating Minimum Interval Width (PINAW) and Interval Coverage (PICP) are as follows: ； ； in, It is a Boolean variable; This represents the number of samples used in the evaluation calculation; if the true value falls within the interval... =1, otherwise =0; and These represent the upper and lower bounds of the prediction interval at the prediction point, respectively. To predict the difference between the upper and lower bounds of the interval; The comprehensive evaluation criterion, also known as the coverage width criterion (CWC), is expressed by the following formula: ； ； in, To preset the credit level; This is a penalty switch function, whose purpose is to determine whether the actual coverage rate has reached the preset target; For penalty parameters; To achieve the preset credit level The actual predicted interval coverage rate is calculated below.

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