Method for calculating post-earthquake response and traffic capacity of rail bridge system, medium and equipment

Abstract

The invention relates to the technical field of rail bridge post-earthquake traffic, in particular to a method, medium and equipment for calculating post-earthquake response and traffic capacity of a rail bridge system. The method comprises the following steps: establishing a nonlinear simulation model of a high-speed railway system; the post-earthquake track residual irregularity is calculated, a post-earthquake track residual irregularity characteristic curve is constructed, and fast calculation of post-earthquake response is achieved; establishing a wheel-rail power system nonlinear mapping model based on the convolutional neural network; and performing Monte Carlo simulation on the track residual irregularity quantitative index, inputting the track residual irregularity quantitative index into a wheel-rail power system nonlinear mapping model, and calculating a train power response index to obtain the post-earthquake traffic capacity of the train. A reasonable calculation model is established according to the structural characteristics of the track system, and the time and economic cost is reduced; post-earthquake dynamic response is calculated through a wheel-rail power system nonlinear mapping model, the relation between post-earthquake track residual deformation and train dynamic response is established, and the post-earthquake traffic capacity of the track bridge system under different safety levels is obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of post-earthquake passage of track bridges, and particularly relates to a calculation method, medium and device for post-earthquake response and passage capacity of a track 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 a ballastless track-bridge system built using a test model filled the gap 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 refined finite element models often face significant time and economic cost challenges. Therefore, it is particularly important to reduce the calculation time and economic cost through methods such as simplified modeling, parameter optimization, and scaled experiments.

[0003] During the post-earthquake rescue and reconstruction process, ensuring the normal operation of high-speed railway trains after an earthquake is of crucial significance. According to 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 through methods such as peak deduction method, track quality index method, and power spectral density analysis method, or target earthquake-induced track irregularities can be proposed for specific structural systems, sites, etc., to evaluate the track state from a statistical perspective. However, the above research mainly focuses on CRTS I and CRTS II type ballastless tracks, and mostly focuses on the analysis at the track system level, ignoring the comprehensive consideration of trains, tracks, and bridges as a whole, and failing to fully explore the mutual relationship between track smoothness and train dynamic response, making it difficult to provide reasonable and accurate guidance for safe driving after an earthquake.

[0004] Therefore, to evaluate the post-earthquake passage capacity of the CRTS III type ballastless track-bridge system, the following key problems must be solved: (1) According to the structural characteristics of the track system, propose a reasonable calculation model to reduce time and economic costs; (2) According to the post-earthquake dynamic response of the track system, clarify the distribution law of post-earthquake residual deformation of the track; (3) Establish a mapping relationship between post-earthquake residual deformation of the track and train dynamic response. Therefore, to solve the above key problems, an evaluation method is needed that can systematically evaluate the track smoothness state and post-earthquake passage capacity of the CRTS III type slab ballastless track-bridge system. Summary of the Invention

[0005] The object of the present invention is to provide a method for systematically evaluating the track smoothness state and post-earthquake traffic capacity of the CRTS III slab ballastless track-bridge system. The specific technical solution is as follows: A method for calculating the post-earthquake response and traffic capacity of a track-bridge system, comprising the following steps: S1: Establish a non-linear simulation model of the high-speed railway system, which includes a simplified model of the track-bridge system and a coupled model of the train-track-bridge system; S2: Calculate the post-earthquake track residual irregularity through the simplified model of the track-bridge system, construct the post-earthquake track residual irregularity characteristic curve by using the residual irregularity database, and perform a rapid prediction of the post-earthquake response of the track-bridge system through the post-earthquake track residual irregularity characteristic curve; S4: Propose a quantitative index for track residual irregularity and determine its distribution; S5: Establish a non-linear mapping model of the wheel-rail dynamic system based on a convolutional neural network, with the quantitative index of track residual irregularity and train speed as inputs and the post-earthquake train dynamic response index as the output; 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 Monte Carlo simulation into the non-linear mapping model of the wheel-rail dynamic system, calculate the train dynamic response index, divide the train safety level, and obtain the post-earthquake traffic capacity of the train under different levels.

[0006] Preferably, S1 further includes simplifying the simplified model of the track-bridge system, and the method is as follows: Adopt the composite beam theory and the Euler-Bernoulli beam equation theory, and calculate the equivalent elastic modulus of the track slab-self-compacting composite slab and the base slab-box girder composite beam based on the weighted average method and the position of the equivalent neutral axis , and the calculation formulas are as follows: ; ; In the formula, , and respectively represent the elastic modulus, cross-sectional area and neutral axis position of the upper track structure; , and respectively represent the elastic modulus, cross-sectional area and neutral axis position of the lower track structure.

[0007] Preferably, when modeling the train in S1, the following assumptions are made: Only consider the rigid body motion of the car body, bogie and wheelset, and ignore the elastic deformation of these components; 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 conditions, and the influence of the power system is ignored.

[0008] Preferably, the post-earthquake track residual unevenness characteristic curve is constructed by the following method: Record the randomly selected post-earthquake track residual unevenness in the residual unevenness database as the signal , and for After windowing, perform discrete Fourier transform DFT to obtain the space-frequency complex matrix The expression of is as follows: ; In the formula, , represents the number of the post-earthquake track residual unevenness signal; , represents the number of signal data points; Represents the spatial frequency; Represents the serial number of the window function; Represents the overlap rate of the window function; Is the window function, and the expression is as follows: ; In the formula, Is the length of the window function; Adopt the spatial coordinate Instead of , and introduce the evolutionary power spectral density Represents the magnitude of the signal energy within different frequencies , and is represented by the following formula And The relationship between them: ; In the formula, Represents the interval between analysis points; Perform logarithmic transformation on the evolutionary power spectral density With non-stationary characteristics to construct a logarithmic set ; Use the JB statistic to perform a statistical distribution test on , and define the JB statistic as: ; In the formula, Represents the sample size; And Respectively represent the skewness coefficient and kurtosis coefficient of the sample, and are calculated by the following formula: ; ; In the formula, 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; Define the function , when , the evolutionary power spectral density follows a normal distribution with mean and variance being and respectively. At this time, there is: ; In the formula, represents the significance level; is the critical value of the chi-square test at the significance level ; Solve for the upper bound of the confidence interval of the track residual irregularity characteristic curve. The expression is as follows: ; ; In the formula, represents the track irregularity sample mean, represents the quantile of the standard normal distribution, represents the track irregularity sample standard deviation; Take the significance level to be 0.05, and reconstruct the post-earthquake track residual irregularity characteristic curve with a 95% probability guarantee rate through the inverse discrete Fourier transform.

[0009] Preferably, the calculation formula of the track residual irregularity quantization index is as follows: ; In the formula, represents the post-earthquake track residual irregularity, represents the total rail mileage.

[0010] Preferably, the non-linear mapping model of the wheel-rail dynamic system based on the convolutional neural network is specifically: The input layer of the convolutional neural network is used to receive two parameters, namely the train speed and the track residual irregularity quantization index, and the output layer is used to provide the predicted value of the post-earthquake train dynamic response index obtained by training the non-linear mapping model of the wheel-rail dynamic system; Input the post-earthquake track residual irregularity samples into the train-track-bridge system coupling model. Take 80% of the total samples as training samples and the remaining 20% as test samples; Conduct independent standardization and scaling processing for each type of sample; The feature extraction process gradually refines the data features through a combination of a series of convolutional layers and pooling layers; After multiple convolutional and pooling operations, the high-dimensional features are converted into one-dimensional vectors by the flatten layer, and then passed through the dense layer. Finally, the prediction output is performed by a single neuron in the output layer; Precisely minimize the loss function through the RAdam algorithm; Measure the error between the predicted value and the actual value through the mean squared error loss function; Select the advanced non-linear activation function PReLU as the activation function.

[0011] Preferably, S6 includes the following steps: Input the multiple track residual irregularity quantization indexes obtained after Monte Carlo simulation into the non-linear mapping model of the wheel-rail dynamic system, calculate the train dynamic response indexes at different train speeds, and obtain the probability distribution diagram and cumulative probability curve of these train dynamic response indexes; Divide the train safety levels according to the cumulative probability threshold to obtain the post-earthquake passing capacity of the train at different levels.

[0012] The present invention also provides a readable storage medium, on which computer program instructions are stored. When the computer program instructions are executed by a processor, the post-earthquake response and passing capacity calculation method of the above-mentioned track-bridge system is realized.

[0013] The present invention also provides 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 post-earthquake response and passing capacity calculation method of the above-mentioned track-bridge system is realized.

[0014] Applying the technical solution of the present invention has the following beneficial effects: A calculation method for the post-earthquake response and traffic capacity of an orbital bridge system, comprising: S1: establishing a non-linear simulation model of a high-speed railway system, which includes a simplified model of an orbit-bridge system and a coupled model of a train-orbit-bridge system; S2: calculating the post-earthquake residual track irregularity through the simplified model of the orbit-bridge system to obtain a residual irregularity database; constructing a post-earthquake residual track irregularity characteristic curve by using the residual irregularity database, and quickly predicting the post-earthquake response of the orbit-bridge system through the post-earthquake residual track irregularity characteristic curve; S3: inputting the random post-earthquake residual track irregularity in the residual irregularity database and the train speed into the coupled model of the train-orbit-bridge system to obtain the post-earthquake train dynamic response index; S4: proposing a quantization index for the residual track irregularity and determining its distribution; S5: taking the quantization index of the residual track irregularity and the train speed as inputs and the post-earthquake train dynamic response index as the output, establishing a non-linear mapping model of the wheel-rail dynamic system based on a convolutional neural network; S6: performing Monte Carlo simulation on the quantization index of the residual track irregularity according to the distribution of the quantization index of the residual track irregularity; S7: inputting the quantization index of the residual track irregularity obtained after Monte Carlo simulation into the non-linear mapping model of the wheel-rail dynamic system, calculating the train dynamic response index, dividing the train safety level, and obtaining the post-earthquake traffic capacity of the train under different levels. This method establishes a reasonable calculation model according to the structural characteristics of the track system, reducing time and economic costs; calculating the post-earthquake dynamic response of the track system through the non-linear mapping model of the wheel-rail dynamic system, establishing the mapping relationship between the post-earthquake residual deformation of the track and the train dynamic response, and obtaining the post-earthquake traffic capacity of the orbital bridge system after the design earthquake and the rare earthquake under different safety levels.

[0015] In addition to the purposes, features and advantages described above, the present invention has other purposes, features and advantages. The following will refer to the drawings to further elaborate on the present invention in detail. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The drawings forming a part of this application are used to provide a further understanding of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation to the present invention. In the drawings: Figure 1 It is a schematic flow chart of the calculation method for the post-earthquake response and traffic capacity of the orbital bridge system according to the embodiment of the present invention; Figure 2 It is a probability distribution diagram of the lateral acceleration in this embodiment; Figure 3 It is a cumulative probability curve of the lateral acceleration in this embodiment; Figure 4 It is the maximum cumulative probability of the safe operation of the train at different vehicle speeds after the design earthquake in this embodiment; Figure 5The maximum cumulative probability of the safe operation of the train at different vehicle speeds after a rare earthquake in this embodiment. Detailed implementation manners

[0017] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings. However, the present invention can be implemented in many different ways defined and covered by the claims.

[0018] In one embodiment, referring to Figure 1 , a method for calculating the post-earthquake response and traffic capacity of an orbital bridge system includes the following steps: S1: Establish a non-linear simulation model of the high-speed railway system, which includes a simplified model of the track-bridge system and a coupled model of the train-track-bridge system; The simplified model of the track-bridge system is simplified as follows: Adopt the composite beam theory and the Euler-Bernoulli beam equation theory, and calculate the equivalent elastic modulus of the track slab-self-compacting composite slab and the base slab-box girder composite beam based on the weighted average method and the position of the equivalent neutral axis , and the calculation formulas are as follows: ; ; In the formula, , and respectively represent the elastic modulus, cross-sectional area and neutral axis position of the upper track structure; , and respectively represent the elastic modulus, cross-sectional area and neutral axis position of the lower track structure.

[0019] Based on the multi-body dynamics and the theory of train-track-bridge interaction, a system dynamic response calculation program is established for the coupled model of the train-track-bridge system using the numerical programming software MATLAB. When modeling the train, the following assumptions are made: Only consider the rigid body motion of the car body, bogie and wheel set, and ignore the elastic deformation of these components; The car body, bogie and wheel set have three-axis symmetry in the inertial principal axis coordinate system; The speed of the train is determined by the speed constraint conditions, and the influence of the power system is ignored.

[0020] S2: Calculate the post-earthquake track residual irregularity through the simplified model of the track-bridge system, construct the post-earthquake track residual irregularity characteristic curve using the residual irregularity database, and perform a rapid prediction of the post-earthquake response of the track-bridge system through the post-earthquake track residual irregularity characteristic curve; The post-earthquake track residual irregularity characteristic curve is constructed by the following method: Denote the random post-earthquake track residual irregularity as a signal , and perform discrete Fourier transform DFT on it after windowing to obtain the space-frequency complex matrix . The expression of is as follows: ; In the formula, represents the number of the post-earthquake track residual irregularity signal; represents the number of signal data points; represents the spatial frequency; represents the serial number of the window function; represents the overlapping rate of the window function; is the window function, and the expression is as follows: ; In the formula, is the length of the window function; Use the spatial coordinate to replace , and introduce the evolutionary power spectral density to represent the magnitude of the signal energy within different frequencies . The relationship between and is expressed by the following formula: ; In the formula, represents the interval between analysis points; Perform logarithmic transformation on the evolutionary power spectral density with non-stationary characteristics to construct a logarithmic set ; Use the JB statistic to test the statistical distribution of . Define the JB statistic as: ; In the formula, represents the sample size; and represent the skewness coefficient and kurtosis coefficient of the sample respectively, and are calculated by the following formula: ; ; In the formula, 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, denotes the sample mean; Define the function such that when the evolutionary power spectral density follows a normal distribution with mean and variance and respectively, and at this time there is: ; In the formula, denotes the significance level; is the critical value of the chi-square test at the significance level ; Solve for the upper bound of the confidence interval of the track residual irregularity characteristic curve, and the expression is as follows: ; ; In the formula, denotes the track irregularity sample mean, denotes the quantile of the standard normal distribution, denotes the track irregularity sample standard deviation; Take the significance level to be 0.05, and reconstruct the post-earthquake track residual irregularity characteristic curve based on a 95% probability guarantee rate through the inverse discrete Fourier transform .

[0021] The track residual irregularity usually presents as a curve varying with mileage and cannot be directly used for sensitivity coefficient calculation.

[0022] S3: Input the randomly selected post-earthquake track residual irregularity and train speed in the residual irregularity database into the train-track-bridge system coupling model to obtain the post-earthquake train dynamic response index; S4: Propose a track residual irregularity quantification index, the track residual irregularity quantification index shown below , which is used to quantify the track smoothness state. According to the post-earthquake residual irregularity, set the distribution characteristic of the track residual irregularity quantification index to a lognormal distribution.

[0023] The above-mentioned track residual irregularity quantification index is calculated as follows: ; In the formula, denotes the post-earthquake track residual irregularity, denotes the total rail mileage.

[0024] S5: Using the track residual irregularity quantification index and train speed as inputs and the post-earthquake train dynamic response index as the output, establish a non-linear mapping model of the wheel-rail dynamic system based on a convolutional neural network; A typical CNN structure includes an input, an output, and multiple hidden layers; The input layer of the convolutional neural network is used to receive two parameters, the train speed and the track residual irregularity quantification index, and the output layer is used to provide the predicted value of the post-earthquake train dynamic response index obtained from the training of the non-linear 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.

[0025] In this embodiment, 320 post-earthquake track residual irregularity samples are input into the train-track-bridge system coupling model established in this embodiment. The train speed range is set from 100 km / h to 350 km / h, increasing at intervals of 10 km / h. A total of 9920 samples are obtained. 80% of the total samples are taken as training samples, and the remaining 20% are test samples. Independent standardization and scaling processes are performed for each type of sample to optimize the data distribution and enhance the training efficiency of the network, effectively suppressing the occurrence of overfitting.

[0026] 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 convolutional kernels are used. Since the convolutional and pooling operations extract and compress feature information layer by layer, the size of the feature map in subsequent layers is halved. In addition, considering the lack of significant physical association between two input features, this embodiment selects smaller convolutional and pooling kernels (2×1) and sets the stride to 1 for fine feature extraction in a small range. After multiple convolutional 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 output by a single neuron in the output layer.

[0027] In addition, RAdam (Rectified Adam) is an advanced algorithm designed for optimizing deep learning models, and its main goal is to accurately minimize the loss function. The algorithm significantly improves the fluctuations and instability problems that the standard Adam algorithm may encounter in the initial stage of training by introducing an adaptive warm-up phase. The mean squared error MSE is widely used as the loss function for measuring the error between the predicted value and the actual value. In the selection of the activation function, the advanced non-linear activation function PReLU (Parametric ReLU) is adopted to replace the traditional ReLU function. Combining the above parameter settings, a non-linear mapping model of the wheel-rail dynamic system is established.

[0028] Train speed and the track residual irregularity quantification index It has a significant impact on the dynamic service performance of high-speed railways. Therefore, to ensure the long-term operational safety of high-speed railways, it is necessary to conduct a feasibility study on post-earthquake train operation for these two sensitive parameters.

[0029] As a random variable that significantly affects the train dynamic response, the quantification index of track residual irregularity should first determine its distribution characteristics. Calculate the post-earthquake track residual irregularity under the design earthquake (0.3g) and the rare earthquake (0.6g), and draw the distribution histogram after logarithmic transformation. The distribution characteristics of the quantification index of track residual irregularity under the design earthquake and the rare earthquake show a log-normal distribution. In addition, further statistical tests on the normality of the quantification index of track residual irregularity show that the results are all 0, determining that the sample of the quantification index of track residual irregularity conforms to the normal distribution characteristics.

[0030] Based on the above analysis, set the distribution characteristics of the quantification index of track residual irregularity as a log-normal distribution.

[0031] S6: According to the distribution of the quantification index of track residual irregularity, conduct Monte Carlo simulation on the quantification index of track residual irregularity; In this embodiment, conduct 10,000 Monte Carlo simulations on the quantification index of track residual irregularity, and set the train speed range from 50 km / h to 350 km / h, increasing at intervals of 10 km / h. Substitute the obtained sample data of random variables into the non-linear mapping model of the wheel-rail dynamic system, calculate the train dynamic response index, and obtain the probability distribution diagram and cumulative probability curve of different dynamic response indexes. Taking the lateral acceleration as an example of a dynamic response index, Figure 2 This is the probability distribution diagram of the lateral acceleration under the design earthquake (0.3g) and the vehicle speed of 350 km / h in this embodiment; Figure 3 This is the cumulative probability curve of the lateral acceleration under the design earthquake (0.3g) and the vehicle speed of 350 km / h.

[0032] S7: Input the quantification index of track residual irregularity obtained after Monte Carlo simulation into the non-linear mapping model of the wheel-rail dynamic system, calculate the train dynamic response index, divide the train safety level, and obtain the post-earthquake passing capacity of the train under different levels. The specific content of S5 is: On the premise of the safe operation of the train, extract the maximum cumulative probability of each dynamic response index at different vehicle speeds. Based on the reliability theory, in this embodiment, the train operation safety level is divided into two levels: level I and level II with cumulative probability thresholds of 0.90 and 0.95, as shown in Figure 4 and Figure 5As shown, 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 all the train safety dynamic response indicators at the current vehicle speed do not exceed their safety limits, and the higher the running safety of the train in this state. From Figure 4 it can be seen that after the design earthquake, under the condition of the first-level safety level, it is recommended to control the train speed within 306 km / h. Under the condition of the second-level safety level, the train can run normally. From Figure 5 it can be seen that after the rare earthquake, under the condition of the first-level safety level, it is recommended to control the train speed within 187 km / h. Under the condition of the second-level safety level, the train speed should be maintained between 187 and 256 km / h.

[0033] This embodiment proposes an evaluation method that can systematically evaluate the track smoothness state and post-earthquake passing capacity of the CRTS III slab ballastless track-bridge system. A train-track-bridge system coupling model is established, and the sensitive parameters of the train dynamic response are analyzed. A reasonable calculation model can be proposed according to the structural characteristics of the track system, reducing time and economic costs. On this basis, a non-linear mapping model of the wheel-rail dynamic system based on CNN is developed. According to the calculation results of the simplified model of the track-bridge system, the characteristic curves of the post-earthquake track residual irregularity under different pier heights are constructed, the sensitive parameters of the train dynamic response are analyzed, and the feasibility of post-earthquake train operation is explored in combination with the non-linear mapping model of the wheel-rail dynamic system. While ensuring the accuracy of the calculation results, the calculation efficiency of TBSSM is improved by about 40%. Finally, the train speeds after the design earthquake and the rare earthquake under different safety level conditions are obtained, that is, the post-earthquake passing capacity of the track-bridge system.

[0034] This embodiment also includes a readable storage medium, on which computer program instructions are stored. When the computer program instructions are executed by a processor, the above-mentioned calculation method for the post-earthquake response and passing capacity of the track-bridge system is realized.

[0035] Exemplarily, the computer program can be divided into one or more modules / units. 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 capable of performing specific functions, and these 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 calculation method for the post-earthquake response and passing capacity of the track-bridge system is realized.

[0036] The electronic device may be a computing device such as a mobile phone, a desktop computer, a notebook, a handheld computer, and a cloud server. The electronic device may include, but is not limited to, a processor and a memory. For example, the electronic device may further include input / output devices, network access devices, a bus, etc.

[0037] The foregoing are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A calculation method for the post-earthquake response and traffic capacity of an orbital bridge system, characterized in that It includes the following steps: S1: Establish a non-linear simulation model of the high-speed railway system, which includes a simplified model of the track-bridge system and a coupled model of the train-track-bridge system; S2: Calculate the post-earthquake track residual irregularity through the simplified model of the track-bridge system to obtain a residual irregularity database; construct the post-earthquake track residual irregularity characteristic curve by using the residual irregularity database, and quickly predict the post-earthquake response of the track-bridge system through the post-earthquake track residual irregularity characteristic curve; S3: Input the random post-earthquake track residual irregularity and train speed in the residual irregularity database into the coupled model of the train-track-bridge system to obtain the post-earthquake train dynamic response index; S4: Propose a quantitative index for track residual irregularity and determine its distribution; S5: Establish a non-linear mapping model of the wheel-rail dynamic system based on a convolutional neural network, with the quantitative index of track residual irregularity and train speed as the input and the post-earthquake train dynamic response index as the output; S6: Conduct Monte Carlo simulation on the quantitative index of track residual irregularity according to its distribution; S7: Input the quantitative index of track residual irregularity obtained after Monte Carlo simulation into the non-linear mapping model of the wheel-rail dynamic system, calculate the train dynamic response index, divide the train safety level, and obtain the post-earthquake passing capacity of the train at different levels.

2. The method for calculating the post-earthquake response and traffic capacity of the track bridge system according to claim 1, characterized in that, The S1 also includes simplifying the simplified model of the track-bridge system, and the method is as follows: Based on the composite beam theory and Euler-Bernoulli beam equation, the equivalent elastic modulus of the track slab-self-compacting composite slab and the base slab-box girder composite beam is calculated using the weighted average method and the position of the equivalent neutral axis , and the calculation formulas are as follows: ； ； Wherein, , and respectively represent the elastic modulus, cross-sectional area and neutral axis position of the upper track structure; , and respectively represent the elastic modulus, cross-sectional area and neutral axis position of the lower track structure.

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

4. The method for calculating the post-earthquake response and traffic capacity of the track bridge system according to claim 3, wherein The post-earthquake track residual irregularity characteristic curve is constructed by the following method: Random post-earthquake track residual irregularities in the residual irregularity database are denoted as signals , and for , after windowing, perform discrete Fourier transform DFT to obtain the space-frequency complex matrix . The expression is as follows: ； In the formula, , represents the number of the post-earthquake track residual irregularity signal; , represents the number of the signal data points; represents the spatial frequency; represents the serial number of the window function; represents the overlapping rate of the window function; is a window function, and the expression is as follows: ； In the formula, is the length of the window function; Adopt spatial coordinates instead of , and introduce the evolutionary power spectral density to represent the magnitude of the signal energy within different frequencies . It is expressed by the following formula and the relationship between them: ； In the formula, represents the interval between analysis points; For the evolving power spectral density with non-stationary characteristics perform a logarithmic transformation to construct a logarithmic set ; Use the JB statistic to perform a test of the statistical distribution, and define the JB statistic as: ； wherein, represents the sample size; and respectively represent the skewness coefficient and kurtosis coefficient of the sample, and are calculated by the following formula: ； ； In the formula, 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; Define a function , when , the evolutionary power spectral density follows a normal distribution with mean and variance being and respectively. At this time, we have: ； In the formula, represents the significance level; is the significance level and is the critical value of the chi-square test at this significance level; Solve the upper bound of the confidence interval of the track residual irregularity characteristic curve, and the expression is as follows: ； ； wherein, represents the sample mean of track irregularity, represents the quantile of the standard normal distribution, represents the sample standard deviation of track irregularity; Take the significance level as 0.05, and reconstruct the post-earthquake track residual irregularity characteristic curve based on the 95% probability guarantee rate through the inverse discrete Fourier transform .

5. The calculation method for the post-earthquake response and traffic capacity of the track bridge system according to claim 4, characterized in that The quantification index of the track residual irregularity has the following calculation formula: ； In the formula, represents the residual track irregularity after an earthquake, represents the total mileage of the rail.

6. The method for calculating the post-earthquake response and traffic capacity of the track bridge system according to claim 5, characterized in that, The non-linear mapping model of the wheel-rail dynamic system based on a convolutional neural network is specifically: The input layer of the convolutional neural network is used to receive two parameters, namely the train speed and the quantitative index of track residual irregularity, and the output layer is used to provide the predicted value of the post-earthquake train dynamic response index obtained by training the non-linear mapping model of the wheel-rail dynamic system; Input the post-earthquake track residual irregularity samples into the coupled model of the train-track-bridge system, and take 80% of the total samples as training samples and the remaining 20% as test samples; Conduct independent standardization and scaling processing for each type of sample; The feature extraction process gradually refines the data features through a combination of a series of convolutional layers and pooling layers; After multiple convolutional and pooling operations, the high-dimensional features are converted into one-dimensional vectors by the flatten layer, and then passed through the dense layer, and finally the prediction output is performed by a single neuron in the output layer; Precisely minimize the loss function through the RAdam algorithm; Measure the error between the predicted value and the actual value through the mean square error loss function; Select the advanced non-linear activation function PReLU as the activation function.

7. The method for calculating the post-earthquake response and traffic capacity of the track bridge system according to claim 6, wherein The S6 includes the following steps: Input the multiple track residual irregularity quantization indicators obtained after Monte Carlo simulation into the non-linear mapping model of the wheel-rail dynamic system, 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; Divide the train safety levels according to the cumulative probability threshold, and obtain the post-earthquake passing capacity of the train at different levels.

8. A readable storage medium, characterized in that, It stores computer program instructions, and when the computer program instructions are executed by a processor, the method for calculating the post-earthquake response and passing capacity of the track-bridge system as described in any one of claims 1 to 7 is implemented.

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

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