Calculation methods, media and equipment for post-seismic response and capacity of rail and bridge systems

Abstract

The present invention relates to the technical field of post-earthquake passage of rails and bridges, and specifically to a method, medium, and equipment for calculating the post-earthquake response and traffic capacity of a rail-bridge system. The method comprises: establishing a nonlinear simulation model of a high-speed railway system; calculating the residual irregularity of the track after the earthquake, constructing a characteristic curve of the residual irregularity of the track after the earthquake, and realizing rapid calculation of the post-earthquake response; establishing a nonlinear mapping model of a wheel-rail dynamic system based on a convolutional neural network; performing a Monte Carlo simulation on the quantitative index of the residual irregularity of the track and inputting it into the nonlinear mapping model of the wheel-rail dynamic system, calculating the dynamic response index of the train, and obtaining the post-earthquake traffic capacity of the train. The present invention establishes a reasonable calculation model based on the structural characteristics of the rail system, reducing time and economic costs; calculates the post-earthquake dynamic response through the nonlinear mapping model of the wheel-rail dynamic system, establishes the relationship between the residual deformation of the track after the earthquake and the dynamic response of the train, and obtains the post-earthquake traffic capacity of the rail-bridge system under different safety levels.

Description

Technical Field

[0001] The present invention relates to the technical field of post-earthquake traffic on rail bridges, and in particular to a method, medium and equipment for calculating the post-earthquake response and traffic capacity of a rail bridge system. Background Art

[0002] Some early studies explored the seismic performance of ballastless track-bridge systems through finite element simulation analysis and shaking table tests. For example, a three-dimensional coupled model of a high-speed railway track-bridge system, established using the finite element software ANSYS, and a shaking table test of the ballastless track-bridge system constructed using the experimental model filled the gaps in physical test data. Generally speaking, such studies can obtain relatively accurate structural response data through a combination of precise experiments and numerical simulations. However, complex experimental designs and elaborate finite element models often face significant time and cost challenges. Therefore, reducing computational time and costs through simplified modeling, parameter optimization, and scaled-down experiments is particularly important.

[0003] During post-earthquake rescue and reconstruction, ensuring the normal operation of high-speed railway trains is of vital importance. Based on the dynamic response research of the train-track-bridge system, track smoothness is considered a key factor in ensuring the safe operation of high-speed trains. Track smoothness can be evaluated using peak deduction methods, track quality index methods, and power spectrum density analysis methods, or by proposing target earthquake-induced track irregularities for specific structural systems and sites, and evaluating the track condition from a statistical perspective. However, the above studies mainly focus on CRTS I and CRTS II ballastless tracks, and most of them focus on the analysis at the track system level, ignoring the comprehensive consideration of trains, tracks, and bridges as a whole. They fail to fully explore the relationship between track smoothness and train dynamic response, making it difficult to provide reasonable and accurate guidance for safe post-earthquake driving.

[0004] Therefore, to evaluate the post-earthquake capacity of the CRTS III slab track-bridge system, the following key issues must be addressed: (1) Based on the structural characteristics of the track system, a reasonable calculation model must be proposed to reduce time and economic costs; (2) Based on the post-earthquake dynamic response of the track system, the distribution law of the post-earthquake residual deformation of the track must be clarified; (3) The mapping relationship between the post-earthquake residual deformation of the track and the dynamic response of the train must be established. Therefore, in order to solve the above key issues, it is necessary to propose an evaluation method that can systematically evaluate the track smoothness and post-earthquake capacity of the CRTS III slab track-bridge system. Summary of the Invention

[0005] The present invention aims to provide a method for systematically evaluating the track smoothness and post-earthquake capacity of a CRTS III slab track-bridge system. The specific technical solution is as follows:

[0006] A method for calculating post-seismic response and traffic capacity of a rail bridge system comprises the following steps:

[0007] S1: Establish a nonlinear simulation model for the high-speed railway system, which includes a simplified track-bridge system model and a coupled train-track-bridge system model;

[0008] S2: Calculate the post-earthquake track residual irregularity using the simplified track-bridge system model, construct a post-earthquake track residual irregularity characteristic curve using the residual irregularity database, and quickly predict the post-earthquake response of the track-bridge system using the post-earthquake track residual irregularity characteristic curve;

[0009] S4: Propose quantitative indicators of track residual irregularity and determine their distribution;

[0010] S5: Using the track residual irregularity quantification index and train speed as input and the post-earthquake train dynamic response index as output, a nonlinear mapping model of the wheel-rail dynamic system based on a convolutional neural network is established;

[0011] S6: performing a Monte Carlo simulation on the quantitative index of track residual irregularity according to the distribution of the quantitative index of track residual irregularity;

[0012] S7: The quantitative index of track residual irregularity obtained after Monte Carlo simulation is input into the nonlinear mapping model of the wheel-rail dynamic system to calculate the train dynamic response index, classify the train safety level, and obtain the post-earthquake traffic capacity of the train under different levels.

[0013] Preferably, the step S1 further comprises simplifying the simplified model of the track-bridge system in the following manner:

[0014] The equivalent elastic modulus of the track slab-self-compacting composite slab and base slab-box girder composite beams is calculated based on the composite beam theory and Euler-Bernoulli beam equation theory using the weighted average method. and the equivalent neutral axis position , the calculation formula is as follows:

[0015] ;

[0016] ;

[0017] Where, 、 and represent the elastic modulus, cross-sectional area and neutral axis position of the upper track structure respectively; 、 and They represent the elastic modulus, cross-sectional area and neutral axis position of the lower track structure respectively.

[0018] Preferably, when modeling the train, S1 makes the following assumptions:

[0019] Only the rigid body motion of the car body, bogie and wheelset is considered, and the elastic deformation of these components is ignored;

[0020] The car body, bogie and wheelset have three-axis symmetry in the inertial principal axis coordinate system;

[0021] The speed of the train is determined by the speed constraint, ignoring the influence of the power system.

[0022] Preferably, the post-earthquake track residual irregularity characteristic curve is constructed by the following method:

[0023] The random post-earthquake track residual irregularities in the residual irregularity database are recorded as signals ,right After windowing, discrete Fourier transform DFT is performed to obtain the space-frequency complex matrix The expression is as follows:

[0024] ;

[0025] Where, , represents the number of the residual track irregularity signal after the earthquake; , represents the number of the signal data point; represents spatial frequency; Indicates the serial number of the window function; Indicates the overlap ratio of the window function;

[0026] is the window function, and its expression is as follows:

[0027] ;

[0028] Where, is the length of the window function;

[0029] Using spatial coordinates replace , and introduce the evolution power spectral density Indicates different frequencies The signal energy within the range is expressed as follows: and The relationship between:

[0030] ;

[0031] Where, Indicates the interval between analysis points;

[0032] For the evolving power spectral density with non-stationary characteristics Perform logarithmic transformation and construct a logarithmic set ;

[0033] Using JB statistics Perform a test of statistical distribution and define the JB statistic as:

[0034] ;

[0035] Where, represents the sample size; and They represent the skewness coefficient and kurtosis coefficient of the sample, respectively, and are calculated by the following formula:

[0036] ;

[0037] ;

[0038] Where, represents the third-order central moment, represents the fourth-order central moment, represents the cube of the standard deviation, represents the fourth power of the standard deviation, represents the sample mean;

[0039] Defining a function ,when When , the evolution power spectral density The mean and variance are and Normal distribution, then:

[0040] ;

[0041] Where, represents the significance level; is the significance level The chi-square test critical value under ;

[0042] The upper bound of the confidence interval of the track residual irregularity characteristic curve is obtained by the following expression:

[0043] ;

[0044] ;

[0045] Where, represents the sample mean of track irregularity, Represents the standard normal distribution Quantile, represents the standard deviation of track irregularity samples;

[0046] Take the significance level The residual track irregularity characteristic curve after the earthquake based on the 95% probability guarantee rate was reconstructed by inverse discrete Fourier transform. .

[0047] Preferably, the track residual irregularity quantification index The calculation formula is as follows:

[0048] ;

[0049] Where, It means that the track remains uneven after the earthquake. Indicates the total mileage of rails.

[0050] Preferably, the nonlinear mapping model of the wheel-rail dynamic system based on convolutional neural network is specifically:

[0051] The input layer of the convolutional neural network receives two parameters: train speed and quantitative index of residual track irregularity. The output layer provides the predicted value of the post-earthquake train dynamic response index obtained by training the nonlinear mapping model of the wheel-rail dynamic system.

[0052] The residual track irregularities after the earthquake were input into the train-track-bridge system coupling model, with 80% of the total samples used as training samples and the remaining 20% as test samples.

[0053] Perform independent normalization and scaling for each type of sample;

[0054] The feature extraction process gradually refines data features through a combination of a series of convolutional layers and pooling layers;

[0055] After multiple layers of convolution and pooling operations, the high-dimensional features are converted into one-dimensional vectors by the flatten layer, then passed through the dense layer, and finally predicted and outputted by a single neuron in the output layer;

[0056] Accurately minimize the loss function through the RAdam algorithm;

[0057] The error between the predicted value and the actual value is measured by the mean square error loss function;

[0058] The activation function selects the advanced nonlinear activation function PReLU.

[0059] Preferably, the S6 comprises the following steps:

[0060] Multiple quantitative indicators of track residual irregularity obtained from Monte Carlo simulation are input into the nonlinear mapping model of the wheel-rail dynamic system to calculate the train dynamic response indicators at different train speeds, and obtain the probability distribution diagram and cumulative probability curve of these train dynamic response indicators;

[0061] The train safety levels were divided according to the cumulative probability threshold, and the post-earthquake train capacity at different levels was obtained.

[0062] The present invention also provides a readable storage medium having computer program instructions stored thereon, which, when executed by a processor, implements the above-mentioned method for calculating the post-earthquake response and traffic capacity of a rail bridge system.

[0063] The present invention also provides an electronic device comprising: at least one processor, at least one memory, and computer program instructions stored in the memory. When the computer program instructions are executed by the processor, the method for calculating the post-seismic response and traffic capacity of a rail bridge system is performed.

[0064] The application of the technical solution of the present invention has the following beneficial effects:

[0065] A method for calculating the post-earthquake response and traffic capacity of a track-bridge system comprises: S1: establishing a nonlinear simulation model of a high-speed railway system, the model comprising a simplified track-bridge system model and a train-track-bridge system coupling model; S2: calculating post-earthquake track residual irregularity using the simplified track-bridge system model to obtain a residual irregularity database; constructing a post-earthquake track residual irregularity characteristic curve using the residual irregularity database, and rapidly predicting the post-earthquake response of the track-bridge system using the post-earthquake track residual irregularity characteristic curve; and S3: inputting random post-earthquake track residual irregularity and train speed from the residual irregularity database into the train-track-bridge system coupling model. , and obtain the post-earthquake train dynamic response index; S4: propose a quantitative index of track residual irregularity and determine its distribution; S5: take the quantitative index of residual irregularity and train speed as input and the post-earthquake train dynamic response index as output, and establish a nonlinear mapping model of the wheel-rail dynamic system based on a convolutional neural network; S6: According to the distribution of the quantitative index of track residual irregularity, perform Monte Carlo simulation on the quantitative index of track residual irregularity; S7: input the quantitative index of track residual irregularity obtained after the Monte Carlo simulation into the nonlinear mapping model of the wheel-rail dynamic system, calculate the train dynamic response index, divide the train safety level, and obtain the post-earthquake train capacity under different levels. This method establishes a reasonable calculation model based on the structural characteristics of the track system, reducing time and economic costs; calculates the post-earthquake dynamic response of the track system through the nonlinear mapping model of the wheel-rail dynamic system, establishes the mapping relationship between the post-earthquake track residual deformation and the train dynamic response, and obtains the post-earthquake capacity of the track-bridge system after the design earthquake and the rare earthquake under different safety levels.

[0066] In addition to the above-described objects, features and advantages, the present invention has other objects, features and advantages. The present invention will be further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are intended to explain the present invention and do not constitute an undue limitation of the present invention. In the accompanying drawings:

[0068] Figure 1 Schematic diagram of the flow of a method for calculating post-seismic response and traffic capacity of a rail bridge system according to an embodiment of the present invention;

[0069] Figure 2 is the probability distribution diagram of the lateral acceleration in this embodiment;

[0070] Figure 3 is the cumulative probability curve of lateral acceleration in this embodiment;

[0071] Figure 4The maximum cumulative probability of safe operation of trains at different speeds after an earthquake is designed in this embodiment;

[0072] Figure 5 is the maximum cumulative probability of safe train operation at different speeds after a rare earthquake in this embodiment. DETAILED DESCRIPTION

[0073] The embodiments of the present invention are described in detail below with reference to the accompanying drawings. However, the present invention can be implemented in many different ways as defined and covered by the claims.

[0074] In one embodiment, see Figure 1 A method for calculating the post-seismic response and traffic capacity of a track-bridge system includes the following steps:

[0075] S1: Establish a nonlinear simulation model for the high-speed railway system, which includes a simplified track-bridge system model and a coupled train-track-bridge system model;

[0076] The simplified model of the track-bridge system is simplified as follows:

[0077] The equivalent elastic modulus of the track slab-self-compacting composite slab and base slab-box girder composite beams is calculated based on the composite beam theory and Euler-Bernoulli beam equation theory using the weighted average method. and the equivalent neutral axis position , the calculation formula is as follows:

[0078] ;

[0079] ;

[0080] Where, 、 and represent the elastic modulus, cross-sectional area and neutral axis position of the upper track structure respectively; 、 and They represent the elastic modulus, cross-sectional area and neutral axis position of the lower track structure respectively.

[0081] Based on the theory of multi-body dynamics and train-track-bridge interaction, a system dynamic response calculation program was established for the train-track-bridge system coupling model using the numerical programming software MATLAB. When modeling the train, the following assumptions were made:

[0082] Only the rigid body motion of the car body, bogie and wheelset is considered, and the elastic deformation of these components is ignored;

[0083] The car body, bogie and wheelset have three-axis symmetry in the inertial principal axis coordinate system;

[0084] The speed of the train is determined by the speed constraint, ignoring the influence of the power system.

[0085] S2: Calculate the post-earthquake track residual irregularity using the simplified track-bridge system model, construct a post-earthquake track residual irregularity characteristic curve using the residual irregularity database, and quickly predict the post-earthquake response of the track-bridge system using the post-earthquake track residual irregularity characteristic curve;

[0086] The post-earthquake track residual irregularity characteristic curve is constructed by the following method:

[0087] The random residual track irregularities after the earthquake are recorded as signals ,right After windowing, discrete Fourier transform DFT is performed to obtain a space-frequency complex matrix The expression is as follows:

[0088] ;

[0089] Where, , represents the number of the residual track irregularity signal after the earthquake; , represents the number of the signal data point; represents spatial frequency; Indicates the serial number of the window function; Indicates the overlap ratio of the window function;

[0090] is the window function, and its expression is as follows:

[0091] ;

[0092] Where, is the length of the window function;

[0093] Using spatial coordinates replace , and introduce the evolution power spectral density Indicates different frequencies The signal energy within the range is expressed as follows: and The relationship between:

[0094] ;

[0095] Where, Indicates the interval between analysis points;

[0096] For the evolving power spectral density with non-stationary characteristics Perform logarithmic transformation and construct a logarithmic set ;

[0097] Using JB statistics Perform a test of statistical distribution and define the JB statistic as:

[0098] ;

[0099] Where, represents the sample size; and They represent the skewness coefficient and kurtosis coefficient of the sample, respectively, and are calculated by the following formula:

[0100] ;

[0101] ;

[0102] Where, represents the third-order central moment, represents the fourth-order central moment, represents the cube of the standard deviation, represents the fourth power of the standard deviation, represents the sample mean;

[0103] Defining a function ,when When , the evolution power spectral density The mean and variance are and Normal distribution, then:

[0104] ;

[0105] Where, represents the significance level; is the significance level The chi-square test critical value under ;

[0106] The upper bound of the confidence interval of the track residual irregularity characteristic curve is obtained by the following expression:

[0107] ;

[0108] ;

[0109] Where, represents the sample mean of track irregularity, Represents the standard normal distribution Quantile, represents the standard deviation of track irregularity samples;

[0110] Take the significance level The residual track irregularity characteristic curve after the earthquake based on the 95% probability guarantee rate was reconstructed by inverse discrete Fourier transform. .

[0111] Track residual irregularity is usually presented as a curve that varies with mileage, and it is not possible to directly calculate the sensitivity coefficient.

[0112] S3: The random post-earthquake track residual irregularities and train speeds in the residual irregularity database are input into the train-track-bridge system coupling model to obtain the post-earthquake train dynamic response index;

[0113] S4: Propose a quantitative index of track residual unevenness, as shown below: , which is used to quantify the track smoothness. According to the residual irregularity after the earthquake, the distribution characteristics of the track residual irregularity quantitative index are set to log-normal distribution.

[0114] The track residual irregularity quantitative index The calculation formula is as follows:

[0115] ;

[0116] Where, It means that the track remains uneven after the earthquake. Indicates the total mileage of rails.

[0117] S5: Using the track residual irregularity quantification index and train speed as input and the post-earthquake train dynamic response index as output, a nonlinear mapping model of the wheel-rail dynamic system based on a convolutional neural network is established;

[0118] A typical CNN structure includes input, output and multiple hidden layers;

[0119] The input layer of the convolutional neural network receives two parameters: train speed and a quantitative index of residual track irregularity. The output layer provides predicted values of the post-earthquake train dynamic response index obtained by training the nonlinear mapping model of the wheel-rail dynamic system. The hidden layer is relatively complex, including 10 convolutional layers, 5 pooling layers, 1 flatten layer, and 1 dense layer.

[0120] This example inputs 320 samples of residual track irregularities after an earthquake into the train-track-bridge system coupling model established in this example. The train speed range is set to 100 km / h to 350 km / h, increasing in 10 km / h increments. A total of 9,920 samples are obtained, 80% of which are used as training samples, and the remaining 20% are used as testing samples. Each sample type is independently normalized and scaled to optimize data distribution, enhance network training efficiency, and effectively prevent overfitting.

[0121] The feature extraction process gradually refines data features through a combination of a series of convolutional layers and pooling layers. Each operation includes two convolutional layers and one pooling layer. In the first feature extraction, 256 convolution kernels were used. Because the convolution and pooling operations extract and compress feature information layer by layer, the size of the feature map of the subsequent layers will be halved. In addition, given the lack of significant physical correlation between the two input features, this embodiment uses smaller convolution and pooling kernels (2×1) and sets the stride to 1 to enable fine feature extraction within a small range. After multiple layers of convolution and pooling operations, the high-dimensional features are converted into one-dimensional vectors by the flatten layer, then pass through the dense layer, and are finally predicted and output by a single neuron in the output layer.

[0122] Furthermore, RAdam (Rectified Adam) is an advanced algorithm designed for deep learning model optimization, with the primary goal of accurately minimizing the loss function. By introducing an adaptive warm-up phase, this algorithm significantly improves the fluctuations and instabilities that can occur in the standard Adam algorithm during early training. Mean squared error (MSE) is a widely used loss function to measure the error between predicted and actual values. In terms of activation function, the advanced nonlinear activation function PReLU (Parametric ReLU) replaces the traditional ReLU function. Combining these parameter settings, a nonlinear mapping model of the wheel-rail dynamics system is established.

[0123] Train speed and quantitative index of track residual irregularity The impact of these two parameters on the dynamic service performance of high-speed railways is significant. Therefore, in order to ensure the long-term operational safety of high-speed railways, it is necessary to conduct a feasibility study on post-earthquake operation based on these two sensitive parameters.

[0124] As a random variable that significantly affects the dynamic response of trains, the quantitative index of track residual irregularity must first be determined for its distribution characteristics. The post-earthquake track residual irregularity for a design earthquake (0.3g) and a rare earthquake (0.6g) was calculated and histograms of the logarithmic distributions were plotted. The distribution characteristics of the quantitative index of track residual irregularity for both the design earthquake and the rare earthquake exhibited a log-normal distribution. Furthermore, further statistical tests of the normality of the quantitative index of track residual irregularity revealed that the results were all zero, confirming that the sample of the quantitative index of track residual irregularity conforms to the normal distribution characteristics.

[0125] Based on the above analysis, the distribution characteristics of the track residual irregularity quantitative index are set to log-normal distribution.

[0126] S6: performing a Monte Carlo simulation on the quantitative index of track residual irregularity according to the distribution of the quantitative index of track residual irregularity;

[0127] In this example, 10,000 Monte Carlo simulations were performed on the quantitative index of residual track irregularity, and the train speed range was set to 50 km / h to 350 km / h, increasing in intervals of 10 km / h. The obtained random variable sample data was introduced into the nonlinear mapping model of the wheel-rail dynamic system to calculate the train dynamic response index. The probability distribution diagram and cumulative probability curve of different dynamic response indicators were obtained. Taking the dynamic response indicator of lateral acceleration as an example, Figure 2 This is the probability distribution diagram of the lateral acceleration in this embodiment under the design earthquake (0.3g) and the vehicle speed of 350km / h; Figure 3 It is the cumulative probability curve of lateral acceleration under the design earthquake (0.3g) and vehicle speed of 350km / h.

[0128] S7: Input the quantitative index of track residual irregularity obtained after Monte Carlo simulation into the nonlinear mapping model of the wheel-rail dynamic system, calculate the train dynamic response index, divide the train safety level, and obtain the post-earthquake train capacity under different levels.

[0129] Under the premise of safe train operation, the maximum cumulative probability of each dynamic response index at different speeds is extracted. Based on the reliability theory, this embodiment divides the train operation safety level into two levels: Level I and Level II with cumulative probability thresholds of 0.90 and 0.95. Figure 4 and Figure 5 The magnitude of the cumulative probability directly reflects the safety redundancy of the train. Specifically, the higher the cumulative probability value, the greater the probability that the train safety dynamic response indicators do not exceed their safety limits at the current speed, and the higher the running safety of the train in this state. Figure 4 It can be seen that after the design earthquake, under the safety level I condition, it is recommended to control the train speed within 306km / h, and under the safety level II condition, the train can operate normally; Figure 5 It can be seen that after a rare earthquake, under the condition of Level I safety level, it is recommended to control the train speed within 187km / h, and under the condition of Level II safety level, the train speed should be maintained between 187~256km / h.

[0130] This example proposes a systematic evaluation method for the track smoothness and post-earthquake capacity of the CRTS III slab track-bridge system. A train-track-bridge system coupling model was established, and the train dynamic response sensitive parameters were analyzed. Based on the structural characteristics of the track system, a reasonable calculation model was proposed to reduce time and economic costs. On this basis, a CNN-based nonlinear mapping model of the wheel-rail dynamic system was developed. Based on the calculation results of the simplified track-bridge system model, characteristic curves of post-earthquake residual track irregularities were constructed for different pier heights. The train dynamic response sensitive parameters were analyzed, and the feasibility of post-earthquake operation was explored in conjunction with the nonlinear mapping model of the wheel-rail dynamic system. While ensuring the accuracy of the calculation results, the TBSSM improved computational efficiency by approximately 40%. Ultimately, the train speeds after design earthquakes and rare earthquakes under different safety levels were obtained, i.e., the post-earthquake capacity of the track-bridge system.

[0131] This embodiment also includes a readable storage medium having computer program instructions stored thereon. When the computer program instructions are executed by a processor, the above-mentioned method for calculating the post-seismic response and traffic capacity of the rail bridge system is implemented.

[0132] Exemplarily, the computer program can be divided into one or more modules / units, and the one or more modules / units are stored in the memory and executed by the processor to complete the present invention. The one or more modules / units can be a series of computer program instruction segments that can perform specific functions, and the instruction segments are used to describe the execution process of the computer program in the electronic device. This embodiment also includes an electronic device, including: at least one processor, at least one memory, and computer program instructions stored in the memory. When the computer program instructions are executed by the processor, the above-mentioned method for calculating the post-earthquake response and traffic capacity of the rail bridge system is performed.

[0133] The electronic device may be a computing device such as a mobile phone, desktop computer, laptop, PDA, or cloud server. The electronic device may include, but is not limited to, a processor and memory. For example, the electronic device may also include input / output devices, network access devices, buses, etc.

[0134] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A method for calculating post-seismic response and traffic capacity of a rail bridge system, characterized in that: The steps include: S1: Establish a nonlinear simulation model for the high-speed railway system, which includes a simplified track-bridge system model and a coupled train-track-bridge system model; S2: Calculate the post-earthquake track residual irregularity using the simplified track-bridge system model to obtain a residual irregularity database; construct a post-earthquake track residual irregularity characteristic curve using the residual irregularity characteristic curve, and quickly predict the post-earthquake response of the track-bridge system using the post-earthquake track residual irregularity characteristic curve; S3: The random post-earthquake track residual irregularities and train speeds in the residual irregularity database are input into the train-track-bridge system coupling model to obtain the post-earthquake train dynamic response index; S4: Propose quantitative indicators of track residual irregularity and determine their distribution; S5: Using the track residual irregularity quantification index and train speed as input and the post-earthquake train dynamic response index as output, a nonlinear mapping model of the wheel-rail dynamic system based on a convolutional neural network is established; S6: performing a Monte Carlo simulation on the quantitative index of track residual irregularity according to the distribution of the quantitative index of track residual irregularity; S7: The quantitative index of track residual irregularity obtained after Monte Carlo simulation is input into the nonlinear mapping model of the wheel-rail dynamic system to calculate the train dynamic response index, classify the train safety level, and obtain the post-earthquake traffic capacity of the train under different levels.

2. The method for calculating post-seismic response and traffic capacity of a track bridge system according to claim 1, characterized in that: The S1 further includes simplifying the simplified model of the track-bridge system in the following manner: The equivalent elastic modulus of the track slab-self-compacting composite slab and base plate-box girder composite beams is calculated based on the weighted average method using composite beam theory and the Euler-Bernoulli beam equation. and the equivalent neutral axis position , the calculation formula is as follows: ； ； Where, 、 and represent the elastic modulus, cross-sectional area and neutral axis position of the upper track structure respectively; 、 and They represent the elastic modulus, cross-sectional area and neutral axis position of the lower track structure respectively.

3. The method for calculating post-seismic response and traffic capacity of a track bridge system according to claim 2, characterized in that: When modeling the train, S1 makes the following assumptions: Only the rigid body motion of the car body, bogie and wheelset is considered, and the elastic deformation of these components is ignored; The car body, bogie and wheelset have three-axis symmetry in the inertial principal axis coordinate system; The speed of the train is determined by the speed constraint, ignoring the influence of the power system.

4. The method for calculating post-seismic response and traffic capacity of a rail bridge system according to claim 3 is characterized in that: The post-earthquake track residual irregularity characteristic curve is constructed by the following method: The random post-earthquake track residual irregularities in the residual irregularity database are recorded as signals ,right After windowing, discrete Fourier transform DFT is performed to obtain the space-frequency complex matrix The expression is as follows: ； Where, , represents the number of the residual track irregularity signal after the earthquake; , represents the number of the signal data point; represents spatial frequency; Indicates the serial number of the window function; Indicates the overlap ratio of the window function; is the window function, and its expression is as follows: ； Where, is the length of the window function; Using spatial coordinates replace , and introduce the evolution power spectral density Indicates different frequencies The signal energy within the range is expressed as follows: and The relationship between: ； Where, Indicates the interval between analysis points; For the evolving power spectral density with non-stationary characteristics Perform logarithmic transformation and construct a logarithmic set ; Using JB statistics Perform a test of statistical distribution and define the JB statistic as: ； Where, represents the sample size; and They represent the skewness coefficient and kurtosis coefficient of the sample, respectively, and are calculated by the following formula: ； ； Where, represents the third-order central moment, represents the fourth-order central moment, represents the cube of the standard deviation, represents the fourth power of the standard deviation, represents the sample mean; Defining a function ,when When , the evolution power spectral density The mean and variance are and Normal distribution, then: ； Where, represents the significance level; is the significance level The chi-square test critical value under ; The upper bound of the confidence interval of the track residual irregularity characteristic curve is obtained by the following expression: ； ； Where, represents the sample mean of track irregularity, Represents the standard normal distribution Quantile, represents the standard deviation of track irregularity samples; Take the significance level The residual track irregularity characteristic curve after the earthquake based on the 95% probability guarantee rate was reconstructed by inverse discrete Fourier transform. .

5. The method for calculating post-seismic response and traffic capacity of a track bridge system according to claim 4, characterized in that: The track residual irregularity quantitative index The calculation formula is as follows: ； Where, It means that the track remains uneven after the earthquake. Indicates the total mileage of rails.

6. The method for calculating post-seismic response and traffic capacity of a rail bridge system according to claim 5, characterized in that: The nonlinear mapping model of the wheel-rail dynamic system based on the convolutional neural network is specifically: The input layer of the convolutional neural network receives two parameters: train speed and quantitative index of residual track irregularity. The output layer provides the predicted value of the post-earthquake train dynamic response index obtained by training the nonlinear mapping model of the wheel-rail dynamic system. The residual track irregularities after the earthquake were input into the train-track-bridge system coupling model, with 80% of the total samples used as training samples and the remaining 20% as test samples. Perform independent normalization and scaling for each type of sample; The feature extraction process gradually refines data features through a combination of a series of convolutional layers and pooling layers; After multiple layers of convolution and pooling operations, the high-dimensional features are converted into one-dimensional vectors by the flatten layer, then passed through the dense layer, and finally predicted and outputted by a single neuron in the output layer; Accurately minimize the loss function through the RAdam algorithm; The error between the predicted value and the actual value is measured by the mean square error loss function; The activation function selects the advanced nonlinear activation function PReLU.

7. The method for calculating post-seismic response and traffic capacity of a track bridge system according to claim 6, characterized in that: The S6 comprises the following steps: Multiple quantitative indicators of track residual irregularity obtained from Monte Carlo simulation are input into the nonlinear mapping model of the wheel-rail dynamic system to calculate the train dynamic response indicators at different train speeds, and obtain the probability distribution diagram and cumulative probability curve of these train dynamic response indicators; The train safety levels were divided according to the cumulative probability threshold, and the post-earthquake train capacity at different levels was obtained.

8. A readable storage medium, characterized in that: Computer program instructions are stored thereon, and when the computer program instructions are executed by a processor, the method for calculating the post-seismic response and traffic capacity of a rail bridge system according to any one of claims 1 to 7 is implemented.

9. An electronic device, characterized in that: include: At least one processor, at least one memory, and computer program instructions stored in the memory, when the computer program instructions are executed by the processor, the method for calculating the post-seismic response and traffic capacity of a rail bridge system as described in any one of claims 1 to 7.

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