Railway bridge post-earthquake traffic safety probability evaluation method and device

Abstract

The invention relates to a railway bridge post-earthquake traffic safety probability evaluation method and device, which are applied to the technical field of traffic safety, and the method comprises the steps: obtaining an earthquake-induced damage value set of each component through a probability distribution function of different material parameters of a railway track-bridge system; the method comprises the following steps: acquiring a mapping relation between the earthquake-induced damage of a key component and track irregularity through a balance differential equation of a bridge and railway track structural mechanical model, and acquiring earthquake-induced track random irregularity samples of different components based on an earthquake-induced damage value set of each component and the mapping relation between the earthquake-induced damage of the key component and track irregularity; constructing a power spectrum of the track irregularity caused by vibration of different components; establishing a rapid prediction model of the driving performance indexes on the axle after the earthquake through the earthquake-induced track irregularity sample and the coupling dynamic response result; through a Monte Carlo method, based on the earthquake-induced track irregularity power spectrum and the rapid prediction model, the overrun probability and the confidence interval of the driving safety on the axle after the earthquake are rapidly and accurately obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of traffic safety, and in particular to a method and device for evaluating the probability of driving safety after an earthquake on a railway bridge. Background Art

[0002] In recent years, my country's high-speed railway has achieved remarkable rapid development. Among the railway lines, the proportion of bridge structure mileage to the total railway mileage is very high. With the continuous expansion of railway construction, some bridges will inevitably pass through seismically active areas, which will inevitably cause earthquake-induced damage to the bridges. This damage is then reflected to the track surface through the interlayer interaction between structural components, resulting in the deterioration of the track smoothness, and finally a serious threat to driving safety.

[0003] Current research on bridge vehicle performance under earthquakes primarily focuses on deterministic analysis of performance limit values. However, research on uncertainty analysis of the probability of exceeding performance limits, which comprehensively considers the randomness of both seismic motion and structural parameters, is relatively scarce. This is due to insufficient information, engineering construction errors, and the influence of accidental factors. Seismic motion and structural parameter information are both difficult to clearly determine and exhibit strong random characteristics.

[0004] However, accounting for randomness requires tens of thousands of calculations, which makes the computational analysis method based on the dynamic model of the train-track-bridge system unfavorable for research progress; and current research on the performance of vehicles on bridges under earthquakes rarely considers the impact of random changes in earthquake-induced damage to key components of the railway track-bridge system. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide a method and device for evaluating the probability of driving safety after an earthquake on a railway bridge, so as to solve the problems in the prior art of the lack of uncertainty analysis research on the probability of exceeding the limit of driving performance indicators considering the randomness of seismic motion and structural parameters, and the lack of research on the impact of random changes in earthquake-induced damage to key components of the railway track-bridge system.

[0006] According to a first aspect of an embodiment of the present invention, a method for evaluating the probability of driving safety on a railway bridge after an earthquake is provided, the method comprising:

[0007] A train model is established using multi-rigid body dynamics theory, and a railway track-bridge model is established using finite element theory; a train-track-bridge coupling system calculation model is established using the train model and the railway track-bridge model;

[0008] Obtaining probability distribution functions of different material parameters of the railway track-bridge system, establishing a random time history analysis sample sequence for the railway track-bridge model based on the probability distribution function, and performing nonlinear time history calculations on the random time history analysis sample sequence to obtain a set of earthquake-induced damage values ​​for each component of the railway track-bridge system;

[0009] The basic assumptions of the railway track-bridge structure theoretical model are set, and the equilibrium differential equations of the bridge and railway track structure mechanical models are established based on the mechanical properties of the railway track-bridge structure. Based on the equilibrium differential equations, the mapping relationship between seismic damage to key railway track-bridge components and track irregularities is obtained;

[0010] Obtaining initial track irregularity samples, obtaining additional track irregularity samples caused by earthquake-induced damage to different components of the railway track-bridge system based on a set of earthquake-induced damage values ​​for each component of the railway track-bridge system and a mapping relationship between earthquake-induced damage to key components of the railway track-bridge system and track irregularity, and superimposing the initial track irregularity samples with the additional track irregularity samples to obtain earthquake-induced random track irregularity samples of different components;

[0011] Using a spectrum estimation method, the seismic-induced track irregularity power spectrum density curves of different components are generated by using seismic-induced track random irregularity samples of different components; and the seismic-induced track irregularity power spectrum of different components is obtained according to the seismic-induced track irregularity power spectrum density curves.

[0012] Randomly generating a plurality of seismic-induced track irregularity samples based on the seismic-induced track irregularity power spectra of the different components, inputting the seismic-induced track irregularity samples into the train-track-bridge coupling system calculation model, and obtaining train-track-bridge coupling dynamic response results;

[0013] The earthquake-induced track irregularity sample is used as a first parameter, and the train-track-bridge coupled dynamic response result is used as a second parameter. The pre-built model architecture is trained using the first and second parameters to obtain a rapid prediction model for the vehicle performance index on the bridge after the earthquake;

[0014] Based on the power spectrum of the earthquake-induced track irregularities of the different components and the rapid prediction model of the driving performance index on the bridge after the earthquake, multiple Monte Carlo simulation calculations were performed to obtain the exceeding probability and confidence interval of the driving safety on the bridge after the earthquake.

[0015] Preferably,

[0016] The train model is established by adopting multi-rigid body dynamics theory, and the railway track-bridge model is established by adopting finite element theory; and the train-track-bridge coupling system calculation model is established by using the train model and the railway track-bridge model, including:

[0017] The train model is obtained by using a rigid body to simulate the train body, front and rear bogies and four wheel sets, and using a spring-damper to simulate the primary and secondary suspension systems of the train.

[0018] The track base plate and track plate are simulated using spatial beam elements or plate elements, the track rails, bridge foundations, abutments, piers and main beams are simulated using spatial beam elements, and the track interlayer connection components and bridge supports are simulated using spring-damping elements to obtain a railway track-bridge model.

[0019] A coupling relationship between the train model and the railway track-bridge model is established through the wheel-rail interaction between the train and the track-bridge system, thereby establishing a calculation model of the train-track-bridge coupling system;

[0020] The wheel-rail interaction includes: normal action and tangential action between the wheelset and the rail;

[0021] The normal action is obtained by adopting the nonlinear Hertz contact theory, and the tangential action is obtained by adopting the Kaller theory.

[0022] Preferably,

[0023] The method for obtaining the probability distribution functions of different material parameters of the railway track-bridge system includes:

[0024] Obtain the logarithmic normal distribution function of concrete parameters, steel parameters and support friction coefficient, and obtain the Gaussian distribution function of the damping ratio of the reinforced concrete structure;

[0025] The random time history analysis sample sequence for establishing the railway track-bridge model based on the probability distribution function includes:

[0026] Based on the probability distribution functions of different material parameters of the railway track-bridge system, a hypercube Latin sampling method is used to perform N stratified sampling on each structural material parameter to obtain N groups of different structural parameter samples, and N railway track-bridge numerical models are randomly generated based on the N groups of different structural parameter samples;

[0027] Generate N random seismic motions that take site characteristics into consideration by adopting the method of artificially synthesizing seismic waves or selecting natural seismic waves;

[0028] Randomly combining the N railway track-bridge numerical models with N random earthquake motions to generate N groups of time history analysis samples of the earthquake motion-railway-bridge integrated numerical model;

[0029] Based on the time history analysis samples of the N groups of seismic motion-line-bridge integrated numerical models, N groups of nonlinear finite element models of railway track-bridge systems are established. Considering the M seismic motion peaks of the N groups of nonlinear finite element models of railway track-bridge systems, random time history analysis sample sequences of MN groups of railway track-bridge models are generated.

[0030] Preferably,

[0031] The method of establishing a balanced differential equation of the mechanical model of the bridge and railway track structure based on the mechanical characteristics of the railway track-bridge structure and obtaining a mapping relationship between earthquake-induced damage to key components of the railway track-bridge and track irregularity based on the balanced differential equation includes:

[0032] Establishing deformation expressions of the rails, track plates, and base plates according to the railway track structural mechanics model, and obtaining matrix expressions of rail deformation, track plate deformation, and base plate deformation according to the deformation expressions of the rails, track plates, and base plates;

[0033] Establishing a deformation expression of the bridge girder according to the bridge structure mechanics model;

[0034] Obtaining spring force expressions for components between different layers of the track structure under horizontal deformation, substituting the matrix expressions for rail deformation, track plate deformation, base plate deformation, and bridge girder deformation into the spring force expressions for components between different layers of the track structure under horizontal deformation to obtain a fastener spring force matrix under horizontal deformation;

[0035] The fastener spring force matrix under horizontal action is substituted into the matrix expression of the rail deformation to obtain the mapping relationship between the earthquake-induced damage to the key components of the railway track-bridge and the track irregularity.

[0036] Preferably,

[0037] The obtaining of the initial track irregularity sample comprises:

[0038] Acquiring an initial track irregularity power spectrum, and generating the initial track irregularity samples by a numerical method based on the initial track irregularity power spectrum;

[0039] The additional track irregularity samples caused by the earthquake-induced damage of different components of the railway track-bridge system are obtained by using the earthquake-induced damage value set of each component of the railway track-bridge system and the mapping relationship between the earthquake-induced damage of key components of the railway track-bridge and track irregularity, including:

[0040] The numerical value set of earthquake-induced damage of each component of the railway track-bridge system is input into the mapping relationship between earthquake-induced damage of key components of the railway track-bridge and track irregularity, so as to obtain additional track irregularity samples caused by earthquake-induced damage of different components of the railway track-bridge system.

[0041] Preferably,

[0042] The spectrum estimation method is used to generate the power spectrum density curves of the seismic track irregularity of different components by using the seismic track random irregularity samples of different components, including:

[0043] Performing fast Fourier transform on the vibration-induced track irregularity samples of the different components, and generating power spectral density curves of the vibration-induced track irregularity of the different components based on the windowed modified Welch periodogram method;

[0044] The step of obtaining the vibration-induced track irregularity power spectrum of different components according to the vibration-induced track irregularity power spectrum density curve includes:

[0045] The seismic-induced track irregularity power of multiple groups of components is obtained according to the seismic-induced track irregularity power spectrum density curve, the corresponding track irregularity limit spectra are obtained through the seismic-induced track irregularity power of the multiple groups of components, and the corresponding track irregularity limit spectra are fitted in sections to obtain the seismic-induced track irregularity power spectra of the different components.

[0046] Preferably,

[0047] The randomly generating a plurality of vibration-induced track irregularity samples by using the vibration-induced track irregularity power spectra of the different components comprises:

[0048] Based on the power spectra of the vibration-induced track irregularity of the different components, a plurality of vibration-induced track irregularity samples are randomly generated by a trigonometric series superposition method or a fast Fourier transform method.

[0049] Preferably,

[0050] The pre-built model architecture is trained by using the first parameter and the second parameter to obtain a rapid prediction model for the driving performance index on the bridge after the earthquake, including:

[0051] Preprocessing the first parameter and the second parameter, and selecting a deep learning model based on the data characteristics and types of the first parameter and the second parameter;

[0052] A training data set is constructed using the first and second parameters, a selected deep learning model is trained using the training data set, and the trained deep learning model is used as a rapid prediction model for post-earthquake bridge driving performance indicators.

[0053] Preferably,

[0054] The power spectrum of the earthquake-induced track irregularity of the different components and the rapid prediction model of the driving performance index on the bridge after the earthquake are used to perform multiple Monte Carlo simulation calculations to obtain the exceeding probability and confidence interval of the driving safety on the bridge after the earthquake, including:

[0055] Randomly generating multiple groups of earthquake-induced track irregularity samples based on the earthquake-induced track irregularity power spectra of the different components, inputting the multiple groups of earthquake-induced track irregularity samples into the rapid prediction model for post-earthquake on-bridge vehicle performance indicators, and obtaining multiple groups of train-track-bridge system dynamic response results;

[0056] For each set of train-track-bridge system dynamic response results, determine whether an over-limit event occurs. If so, obtain the over-limit probability through multiple Monte Carlo simulations; and obtain the confidence interval of the over-limit probability through binomial distribution or normal approximation.

[0057] According to a second aspect of an embodiment of the present invention, a device for evaluating the probability of driving safety on a railway bridge after an earthquake is provided, the device comprising:

[0058] Model building module: used to build a train model using multi-rigid body dynamics theory and a railway track-bridge model using finite element theory; and to build a train-track-bridge coupling system calculation model using the train model and the railway track-bridge model;

[0059] Damage value acquisition module: used to obtain the probability distribution function of different material parameters of the railway track-bridge system, establish a random time history analysis sample sequence of the railway track-bridge model based on the probability distribution function, and perform nonlinear time history calculation on the random time history analysis sample sequence to obtain a set of earthquake-induced damage values ​​for each component of the railway track-bridge system;

[0060] Mapping relationship acquisition module: used to set the basic assumptions of the railway track-bridge structure theoretical model, establish the equilibrium differential equations of the bridge and railway track structure mechanical models based on the mechanical characteristics of the railway track-bridge structure, and obtain the mapping relationship between seismic damage to key railway track-bridge components and track irregularities based on the equilibrium differential equations;

[0061] Sample acquisition module: used to obtain initial track irregularity samples, obtain additional track irregularity samples caused by earthquake-induced damage to different components of the railway track-bridge system through the set of earthquake-induced damage values ​​of each component of the railway track-bridge system and the mapping relationship between earthquake-induced damage to key components of the railway track-bridge and track irregularity, and superimpose the initial track irregularity samples with the additional track irregularity samples to obtain earthquake-induced random track irregularity samples of different components;

[0062] Power spectrum acquisition module: used to generate the power spectrum density curves of seismic track irregularities of different components through the seismic track random irregularity samples of different components by using the spectrum estimation method; and obtain the power spectrum of seismic track irregularities of different components according to the seismic track irregularity power spectrum density curves;

[0063] A response acquisition module is configured to randomly generate a plurality of vibration-induced track irregularity samples based on the vibration-induced track irregularity power spectra of the different components, input the vibration-induced track irregularity samples into the train-track-bridge coupling system calculation model, and obtain the train-track-bridge coupling dynamic response results;

[0064] Model training module: used to train a pre-built model architecture using the earthquake-induced track irregularity sample as a first parameter and the train-track-bridge coupled dynamic response result as a second parameter to obtain a rapid prediction model for post-earthquake bridge driving performance indicators;

[0065] Safety probability acquisition module: used to perform multiple Monte Carlo simulation calculations based on the power spectrum of the earthquake-induced track irregularities of the different components and the rapid prediction model of the driving performance index on the bridge after the earthquake, so as to obtain the exceeding probability and confidence interval of the driving safety on the bridge after the earthquake.

[0066] The technical solutions provided by the embodiments of the present invention may have the following beneficial effects:

[0067] The present application obtains a numerical set of earthquake-induced damage of various components of the railway track-bridge system through the probability distribution function of different material parameters of the railway track-bridge system; obtains the mapping relationship between earthquake-induced damage of key components of the railway track-bridge and track unevenness through the equilibrium differential equation of the structural mechanics model of the bridge and the railway track, and obtains additional track unevenness samples; obtains initial track unevenness samples, and obtains earthquake-induced random track unevenness samples of different components based on the additional track unevenness samples and the initial track unevenness samples; constructs earthquake-induced track unevenness power spectra of different components based on the earthquake-induced random track unevenness samples of different components; establishes a rapid prediction model for post-earthquake bridge driving performance indicators through the earthquake-induced track unevenness samples and the train-track-bridge coupled dynamic response results; and through the Monte Carlo method, based on the earthquake-induced track unevenness power spectrum and the rapid prediction model for post-earthquake bridge driving performance indicators, quickly and accurately obtains the over-limit probability and confidence interval of post-earthquake bridge driving safety.

[0068] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0070] Figure 1 This is a flow chart showing a method for evaluating the probability of driving safety on a railway bridge after an earthquake according to an exemplary embodiment;

[0071] Figure 2 is a schematic diagram of a train calculation model according to another exemplary embodiment;

[0072] Figure 3 is a schematic diagram of a railway track-bridge calculation model according to another exemplary embodiment;

[0073] Figure 4 is a flow chart illustrating obtaining random earthquake-induced damage to key components of a railway track-bridge system according to another exemplary embodiment;

[0074] Figure 5 is a flowchart illustrating a mapping relationship calculation between earthquake-induced damage to railway track-bridge key components and track irregularity according to another exemplary embodiment;

[0075] Figure 6 is a schematic diagram showing a sample of track irregularity caused by vibration of a bridge component according to another exemplary embodiment;

[0076] Figure 7 is a schematic diagram of a power spectrum fitting curve of track irregularity caused by earthquake-induced damage to bridge components according to another exemplary embodiment;

[0077] Figure 8 is a schematic diagram of a deep learning analysis process according to another exemplary embodiment;

[0078] Figure 9 is a flow chart showing the calculation of the probability of exceeding the limit and the confidence interval for driving safety on a bridge after an earthquake according to another exemplary embodiment;

[0079] Figure 10 is a system schematic diagram of a device for evaluating the probability of driving safety after an earthquake on a railway bridge according to another exemplary embodiment;

[0080] In the attached figure: 1-model building module, 2-damage value acquisition module, 3-mapping relationship acquisition module, 4-sample acquisition module, 5-power spectrum acquisition module, 6-response acquisition module, 7-model training module, 8-safety probability acquisition module. DETAILED DESCRIPTION

[0081] Exemplary embodiments will be described in detail herein, examples of which are illustrated in the accompanying drawings. In the following description, when referring to the drawings, like numbers in different figures represent like or similar elements unless otherwise indicated. The embodiments described in the following exemplary embodiments are not intended to represent all possible embodiments consistent with the present invention. Rather, they are merely examples of apparatus and methods consistent with certain aspects of the present invention, as detailed in the appended claims.

[0082] Example 1

[0083] Figure 1 FIG. 1 is a flow chart showing a method for evaluating the probability of driving safety of a railway bridge after an earthquake according to an exemplary embodiment. Figure 1 As shown, the method includes:

[0084] S1, establishing a train model using multi-rigid body dynamics theory and a railway track-bridge model using finite element theory; and establishing a train-track-bridge coupling system calculation model using the train model and the railway track-bridge model;

[0085] S2, obtaining probability distribution functions of different material parameters of the railway track-bridge system, establishing a random time history analysis sample sequence of the railway track-bridge model based on the probability distribution function, and performing nonlinear time history calculation on the random time history analysis sample sequence to obtain a set of earthquake-induced damage values ​​for each component of the railway track-bridge system;

[0086] S3. Setting basic assumptions for the theoretical model of the railway track-bridge structure, and establishing equilibrium differential equations for the mechanical models of the bridge and railway track structure based on the mechanical properties of the railway track-bridge structure. Based on the equilibrium differential equations, the mapping relationship between seismic damage to key railway track-bridge components and track irregularities is obtained.

[0087] S4, obtaining initial track irregularity samples, obtaining additional track irregularity samples caused by the earthquake-induced damage to different components of the railway track-bridge system based on a set of earthquake-induced damage values ​​for each component of the railway track-bridge system and a mapping relationship between earthquake-induced damage to key components of the railway track-bridge system and track irregularity, and superimposing the initial track irregularity samples with the additional track irregularity samples to obtain earthquake-induced random track irregularity samples of different components;

[0088] S5, using a spectrum estimation method, generating seismic track irregularity power spectrum density curves of different components based on seismic track random irregularity samples of different components; obtaining seismic track irregularity power spectra of different components based on the seismic track irregularity power spectrum density curves;

[0089] S6, randomly generating a plurality of seismic track irregularity samples based on the seismic track irregularity power spectra of the different components, inputting the seismic track irregularity samples into the train-track-bridge coupling system calculation model, and obtaining a train-track-bridge coupling dynamic response result;

[0090] S7, using the earthquake-induced track irregularity sample as a first parameter and the train-track-bridge coupled dynamic response result as a second parameter, training a pre-built model architecture using the first and second parameters to obtain a rapid prediction model for post-earthquake on-bridge vehicle performance indicators;

[0091] S8, performing multiple Monte Carlo simulations based on the power spectra of the earthquake-induced track irregularities of the different components and the rapid prediction model for the performance index of driving on the bridge after the earthquake, to obtain the probability of exceeding the limit and the confidence interval of driving safety on the bridge after the earthquake;

[0092] It is understood that the train model includes a car body, two bogies and four wheel sets, wherein a single bogie is composed of four wheel sets, a primary suspension and a secondary suspension; the train body, bogie and wheel sets are all simulated by rigid bodies, and the primary and secondary suspension systems are simulated by spring-damper; each rigid body has five degrees of freedom: lateral movement, sinking and floating, rolling, nodding and shaking, for a total of 35 degrees of freedom, as shown in the attached figure. Figure 2 As shown in the figure, the train dynamics model is established using the MATLAB platform. Without considering the longitudinal interaction between vehicles, the motion equation of the single train subsystem is:

[0093]

[0094] Where M v 、C v , K v with U v are the mass matrix, damping matrix, stiffness matrix and displacement vector of the train subsystem respectively; F v With F w are the train's own weight vector and the wheel-rail force vector respectively;

[0095] The railway track-bridge model includes a track numerical model and a bridge numerical model, as shown in the attached Figure 3The figure shows a CRTSⅠ double-block ballastless track-simply supported beam bridge. The bridge consists of piers, supports and main beams from bottom to top, and the track consists of base plate, isolation layer and limit grooves, track plate, fastener layer and rails. The railway track-bridge model can be established using OpenSees finite element software, in which the main beam, base plate, track plate and rails are simulated using elastic beam-column elements; supports, fasteners, geotextile layers and limit grooves are simulated using zero-length elements; bridge piers are simulated using nonlinear fiber section beam-column elements; pile-soil interaction is simulated using six springs at the pier bottom, and the spring stiffness is calculated using the m-method.

[0096] The equation of motion for the track and bridge system is:

[0097]

[0098] Where M tb 、C tb , K tb with U tb are the mass matrix, damping matrix, stiffness matrix and displacement vector of the track-bridge system respectively; F w is the wheel-rail force vector;

[0099] The train-track-bridge coupling system calculation model is formed by coupling the train model and the track-bridge model based on the wheel-rail interaction between the train and track-bridge models. The wheel-rail interaction is divided into normal action and tangential action between the wheelset and the rail. The wheel-rail normal action is calculated using the nonlinear Hertz contact theory, and the wheel-rail tangential creep action is calculated using the Kaller theory.

[0100] The computational model of the train-track-bridge coupling system is established through the following steps;

[0101] ① Modal analysis and vibration mode acquisition of the track-bridge structure: Calculate the natural frequencies and vibration modes of the track-bridge. Generally, if only the overall vibration characteristics of the bridge are of concern, low-order vibration modes are sufficient to meet the analysis requirements. However, if the vibration of local bridge members needs to be considered, more high-order vibration modes need to be selected.

[0102] ② Decoupling of the track-bridge motion equations: After obtaining the vibration modes of the track-bridge model, the orthogonality of the vibration modes is utilized to decouple the coupled nodal motion equations in the track-bridge using the generalized coordinate method. This converts the originally complex coupled equations into a set of independent modal equations, significantly reducing the system's degrees of freedom and making subsequent dynamic analysis more efficient.

[0103] ③ Generating the load vector and system matrix: In the vehicle-bridge coupling calculation model, the vehicle load vector is derived from the forces acting on each wheelset, which change dynamically with the wheelset position and vehicle-bridge interaction. The track-bridge load vector, on the other hand, is composed of the loads generated by the interaction between the vehicle and the track. The system matrix includes the vehicle matrix (representing the dynamic characteristics of the vehicle, such as mass, stiffness, and damping); the track-bridge matrix (representing the dynamic characteristics of the track-bridge, such as mass, stiffness, and damping); and the vehicle-track interaction matrix (representing the stiffness and damping of the interaction between the vehicle and the track-bridge).

[0104] ④ Establishing the interaction between the vehicle and the track-bridge: The vehicle's equations of motion are combined with the bridge's generalized coordinate equations to establish a complete vibration model of the vehicle-bridge coupling system. In this process, the interaction forces between the vehicle and the track-bridge are converted into generalized forces, and the vibration response of the track-bridge is calculated using the modal superposition method.

[0105] 5. Calculation of the train-track-bridge coupled system response: Use appropriate numerical methods (such as the Newmark method or other step-by-step integration methods) to solve the dynamic equations and ultimately obtain the dynamic response results of the vehicle and bridge at different time points;

[0106] Obtaining random earthquake-induced damage to each component of the railway track-bridge system includes: establishing a random time history analysis sample sequence of the railway track-bridge numerical model based on the probability distribution function of different material parameters of the railway track-bridge system, and then obtaining a numerical set of earthquake-induced damage to each component of the railway track-bridge system through nonlinear time history calculation, as shown in the attached figure. Figure 4 As shown;

[0107] The probability distribution functions of different material parameters of the railway track-bridge system include: concrete material parameters, steel material parameters, logarithmic normal distribution function of bearing friction, and normal distribution function of reinforced concrete structure damping ratio. The specific values ​​are shown in Table 1:

[0108] Table 1

[0109]

[0110] The establishing of the random time history analysis sample sequence of the railway track-bridge numerical model based on the probability distribution function of different material parameters of the railway track-bridge system includes:

[0111] First, based on the probability distribution function of the railway track-bridge structural parameters, the hypercube Latin sampling method was used to perform 50 stratified samplings on the structural material parameters to obtain 50 groups of different structural parameter samples, and 50 track-bridge numerical models were randomly generated.

[0112] Then, 50 earthquake motion records with a high degree of match with the design response spectrum of the bridge site were selected from the PEER earthquake motion database. By randomly combining 50 railway track-bridge numerical models with the 50 selected earthquake motions, 50 sets of earthquake motion-line-bridge integrated numerical model time-history analysis samples were generated.

[0113] Finally, based on 50 established nonlinear finite element models of high-speed railway bridge-track systems, and considering three types of earthquakes, namely, octave design, frequent, and rare, in Category II sites, 150 sets of ground motion-line-bridge integrated finite element model time-history analysis samples were generated. Nonlinear time-history analysis was then performed accordingly, and the random seismic damage values ​​of various components in the railway track-bridge system were calculated.

[0114] The mapping relationship between earthquake-induced damage to key railway track-bridge components and track irregularities is obtained by:

[0115] First, the basic assumptions of the theoretical model of the railway track-bridge structure are determined. Then, the equilibrium differential equations of the mechanical models of the bridge and track structures are constructed. The deformation of each component is solved, and the deformation equations of the track and bridge components are linked through the forces acting on the system's interlayer components. Finally, the mapping relationship between the earthquake-induced damage deformation of different interlayer components and the rail deformation is solved.

[0116] The basic assumptions of the track-bridge structure theoretical model mainly include:

[0117] ① Ignore the impact of track on bridge deformation;

[0118] ② The inter-layer components of the track, such as the fastener system, are assumed to be springs uniformly distributed along the centerline of the rail;

[0119] ③ Consider that the track in the roadbed section has sufficient track extension sections, and assume that the track boundary of the extension section is simply supported;

[0120] ④ It is considered that the deformation of the base plate is consistent with that of the bridge;

[0121] According to the track structure mechanics model, the mechanical equilibrium differential equation of the rail is established, and the expression (3) of the rail deformation is obtained by solving it, as shown below:

[0122]

[0123] Where Y ri is the deformation at the rail fastener position; E r I r is the bending stiffness of the rail; l MNK+1 is the total length of the rail; F j is the fastener spring force, l iis the distance from the rail end point to the i-th fastener force; M is the number of bridge spans; N is the number of main beam track plates per span; K is the number of fasteners per track plate.

[0124] From formula (3), the matrix expression of rail deformation can be obtained as follows:

[0125] [Y r ]=[R][F](4)where [Y r ] is the rail deformation matrix; [R] is the rail fastener spring force coefficient matrix; [F] is the fastener spring force matrix;

[0126] According to the track structure mechanics model, the mechanical equilibrium differential equation of the track plate is established, and the expression (5) of the deformation of a single track plate is obtained by solving it, as shown below:

[0127]

[0128] Where Y smi is the deformation of the mth track plate at the fastener position; F mj is the spring force of the fastener at the jth fastener position of the mth track plate; Y bm (x) is the displacement of the main beam at the position of the mth track plate; l mi is the distance from the track plate end point to the i-th fastener force; d m1 with d m2 are the distances between the end point of the limiting groove and the left end point of the track plate; k d is the stiffness of the isolation layer; k g is the stiffness of the elastic pad; A m1 , A m2 With A m3 is a constant;

[0129] Given the deformation of each position of the mth track plate, the deformation of the M×N track plates on the M-span main beam can be organized into the following matrix form:

[0130] [Y s ]=[S][F]+[C](6)

[0131] In the formula, [Y s ] is the deformation matrix of M×N track plates; [S] is the fastener spring force coefficient matrix of the track plate; [F] is the fastener spring force matrix of the track plate; [C] is the influence matrix of the main beam deformation on the track plate deformation;

[0132] The displacement expression of the bridge girder is as follows:

[0133]

[0134] Where Y bi is the displacement of any position of the main beam of span i; hi1 is the residual displacement of the left end support of the main beam of span i; is the main beam deflection angle; L b is the total length of a single span of a simply supported beam bridge; L b0 is the distance from the support to the beam end; d is the distance between the expansion joints of the simply supported beams; X i is the distance from the point on the main beam of span i to the coordinate origin;

[0135] Under the action of horizontal deformation, the fastener force and the internal force of the isolation layer can be expressed as:

[0136] [F f ]=k r ([Y s ]-[Y r ]-[Y f ])(8)

[0137] [R d ]=k d ([Y s ]-[Y b ]-[Y d ])(9)

[0138] Where k r is the fastener stiffness; [Y f ] is the residual deformation of the fastener layer, [Y d ] is the residual deformation of the isolation layer;

[0139] Substituting equations (4), (6) and (7) into equation (8), we can obtain:

[0140] [F f ]=([I]-k r [S]+k r [R]) -1 k r ([C]-[Y f ])(10)

[0141] Substituting formula (10) into formula (4), we can obtain the rail mapping deformation expression:

[0142] [Y r ]=[R]([I]-k r [S]+k r [R]) -1 k r ([C]-[Y f ])(11)

[0143] Since the mapping model between bridge structure deformation and track surface geometry has many nodes and heavy computational workload, the track deformation can be solved using MATLAB. The solution process is as follows: Figure 5 As shown;

[0144] The acquisition of earthquake-induced random track irregularity samples of different components of the railway track-bridge system includes:

[0145] First, the initial track irregularity is randomly generated based on the initial track irregularity power spectrum. This embodiment takes the ballastless track irregularity spectrum of China's high-speed railway as an example and generates the initial track random irregularity samples by the trigonometric series superposition method. The ballastless track irregularity spectrum of China's high-speed railway is represented by a piecewise power function:

[0146] S(f)=Af -k (12)

[0147] Where, f is the spatial frequency (1 / m); A is the fitting coefficient;

[0148] Secondly, the random seismic damage values ​​of each component of the railway track-bridge system obtained in step S2 are substituted into the mapping relationship between seismic damage of key railway track-bridge components and track irregularity established in step S3 to obtain component-added track random irregularity samples.

[0149] Finally, the initial track random irregularity samples obtained are superimposed with the component additional track random irregularity samples to obtain the component vibration-induced track random irregularity samples. In this embodiment, the vibration-induced track random samples caused by the vibration-induced damage of the main beam are taken as an example. The generated vibration-induced track irregularity samples are as follows: Figure 6 As shown;

[0150] The fitting formulas for obtaining the power spectrum of track irregularities caused by component vibration include:

[0151] Firstly, the sample sequence of component vibration-induced track irregularity is Fourier transformed. Then, the corresponding power spectrum density function of vibration-induced track irregularity is generated based on the spectrum estimation method. Finally, the fitting formula of the component vibration-induced track irregularity spectrum is obtained by the least squares method.

[0152] The spectrum estimation method can adopt the windowed modified Welch periodogram method, and the specific steps are as follows:

[0153] Let x(n), (n=0,1,…,M-1), be the sample sequence of track irregularities caused by the bridge components after the earthquake. By performing Fourier transform on this sequence, we can obtain:

[0154]

[0155] The corresponding PSD estimate can be expressed as:

[0156]

[0157] To ensure that Equation (14) satisfies the consistent estimation condition, the averaging method is generally used to improve it. First, the component vibration-induced track irregularity data samples are divided into several segments. Then, the periodogram of each segment is calculated separately. Finally, the average periodogram of each segment is taken to estimate the power spectrum of the initial vibration-induced track irregularity data.

[0158] The initial generated earthquake-induced track irregularity sample sequence is denoted as x(n), which is then divided into x1(n), x2(n), ...x k (n), the length of each segment of track irregularity caused by earthquake is recorded as L, in which adjacent data segments will have overlapping parts, that is, the length of each segment of track irregularity caused by earthquake is recorded as L, in which adjacent data segments will have overlapping parts, that is,

[0159] x k (n) = x M (n+(K-1)D),0 <n≤L-1(15)

[0160] Where M = (K-1)D + L, and LD represents the number of overlapping adjacent seismic track irregularity data. Therefore, the power spectrum estimate S(w) of the initial seismic track irregularity data sequence can be expressed as:

[0161]

[0162]

[0163] h(n) represents the window function applied to the truncated data. The main purpose of a window function is to ensure a narrow main lobe of the signal spectrum, resulting in smooth signal near both ends. Commonly used window functions include rectangular, triangular, Hanning, Hamming, Blackman, and cosine rectangular windows.

[0164] This embodiment takes the power spectrum of track irregularity induced by main beam vibration as an example, and uses the above method to obtain multiple groups of power spectra of track irregularity induced by vibration, such as Figure 7 As shown; then, in order to make the most unfavorable estimate of the power spectrum of earthquake-induced track irregularity, the maximum envelope curve of the power spectrum of track irregularity after earthquake is selected as the spectrum estimate of the earthquake-induced track irregularity caused by earthquake-induced damage to the railway bridge main beam after the earthquake; finally, the fitting formula for the earthquake-induced track irregularity spectrum caused by earthquake-induced damage to the main beam under different earthquake levels is obtained through fitting as follows:

[0165] The fitting formulas for track irregularity spectra caused by main beam earthquake damage under frequent, design, and rare earthquakes are:

[0166]

[0167] The train-track-bridge coupled dynamic response results include:

[0168] First, a large number of seismic-induced track irregularity samples are randomly generated using the trigonometric series superposition method, using the power spectrum fitting formula for component seismic-induced track irregularity. These seismic-induced track irregularity samples can include frequency components not covered by existing samples and can more comprehensively reflect the random characteristics of irregularity. These seismic-induced track irregularity samples are then input into the train-track-bridge coupled system calculation model, and finally the train-track-bridge coupled dynamic response results are calculated.

[0169] The construction of a rapid prediction model for post-earthquake bridge driving performance indicators includes:

[0170] First, the seismic-induced random track irregularities of the railway track-bridge system components obtained above are used as the first parameter. Second, the train-track-bridge coupled dynamic response results are used as the second parameter. Finally, the pre-built model architecture is trained using the first and second parameters, and deep learning, an important implementation method in artificial neural networks, is used to establish a rapid prediction model for post-earthquake bridge driving performance indicators. The seismic-induced random track irregularity samples take into account the randomness of seismic motion and structural parameters. Finally, the train driving safety and stability indicators are obtained based on the established rapid prediction model.

[0171] Specifically, the analysis process of deep learning is as follows: Figure 8 As shown, the basic steps are as follows:

[0172] (1) Data acquisition and preprocessing:

[0173] A data set is constructed using the first and second parameters, and the data set is cleaned and denoised to ensure that the component seismic-induced track irregularity data and the train-track-bridge coupled dynamic response data are completely caused by the earthquake, including extremely small deformation data generated by the track-bridge system under its own weight. The data is also preprocessed to improve data quality and usability. The data is divided into a training set, a validation set, and a test set, with the general division ratio being: 60%-70% for the training set, 15%-20% for the validation set, and 15%-20% for the test set.

[0174] (2) Design model architecture:

[0175] Based on the characteristics and type of data, an appropriate deep learning model architecture is selected. The basic LSTM framework includes memory cells and three gating mechanisms. These gating mechanisms control the flow and update of information, enabling LSTM to effectively capture long-term dependencies. Therefore, this embodiment selects the LSTM model architecture and designs the LSTM structure, including the number of layers, number of cells, and input sequence length. Specifically, the LSTM is configured with five hidden layers, initially designed with 32 nodes, and continuously adjusted to determine the LSTM input sequence length. Padding can be used to align the lengths of all input sequences.

[0176] (3) Model training and application:

[0177] First, the designed deep learning model is trained using the training dataset, and the model parameters are continuously adjusted through the back-propagation algorithm to minimize the loss function. Second, in order to improve the training efficiency and performance of the deep learning model, the Adam optimization algorithm can be used in combination with momentum and adaptive learning rate to dynamically adjust the learning rate. Then, at the end of each training cycle, the loss value and accuracy of the training set and validation set are recorded, and the performance changes of the model are visually observed by drawing the loss curve and accuracy curve. The model parameters are adjusted and optimized according to the performance evaluation results of the model. Finally, the final tuned model is tested using the test set, the final test results are analyzed, and the trained model is saved as a program for predicting train driving safety and stability indicators.

[0178] Obtaining the exceedance probability and confidence interval for driving safety on the bridge after the earthquake includes:

[0179] Based on the power spectrum of the earthquake-induced track irregularity and the rapid prediction model of the vehicle driving performance index on the bridge after the earthquake, multiple Monte Carlo simulations were performed to calculate the probability of exceeding the limit and the confidence interval of vehicle driving safety on the bridge after the earthquake:

[0180] Specifically, the process of obtaining the exceeding probability and confidence interval of driving safety on the bridge after the earthquake is as shown in the attached figure. Figure 9 As shown, the basic steps are as follows:

[0181] (1) Based on the power spectrum of track irregularity induced by component vibration, the trigonometric series superposition method is used to generate track irregularity samples induced by component vibration. Multiple irregularity samples are generated to cover the random characteristics of track irregularity.

[0182] (2) Input the track irregularity samples caused by the component earthquake into the established rapid prediction model of vehicle performance indicators on the bridge after the earthquake, and run the model to obtain vehicle safety indicators and stability indicators, such as derailment coefficient and vehicle acceleration.

[0183] (3) According to the "Specifications for Evaluation and Experimental Appraisal of Locomotive and Train Dynamic Performance" and the "High-Speed ​​Railway Design Specifications", the limits of train driving safety and stability indicators can be determined as shown in Table 2 below:

[0184] Table 2

[0185]

[0186] In Table 1, Q is the lateral horizontal force of the wheelset; P is the dynamic wheel weight; ΔP is the vehicle axle weight reduction; P0 is the static axle weight; a z is the vertical vibration acceleration of the vehicle body; a y is the lateral vibration acceleration of the vehicle body; g is the acceleration due to gravity, which is generally taken as 9.8m / s 2 .

[0187] Assume that N Monte Carlo simulations are performed and determine whether the result of each simulation is greater than the driving performance limit; the number of times the limit is exceeded is N L , then the probability of exceeding the limit is:

[0188]

[0189] (4) Since the results of the Monte Carlo method have statistical errors, confidence intervals need to be used to quantify them.

[0190] The probability of exceeding the limit is considered to be a binomial distribution, that is:

[0191]

[0192] When N is large, it can be approximated as a normal distribution:

[0193]

[0194] According to the normal distribution, the confidence interval is: [P L -z α / 2 σ,P L +z α / 2 σ], where z α / 2 is the quantile of the standard normal distribution;

[0195] Finally, based on programming tools (such as MATLAB and Python), the probability of exceeding the limit and the confidence interval of the driving performance indicators are obtained.

[0196] Based on the above method, this example statistically analyzes the exceeding of travel parameters on bridges after earthquakes of varying magnitudes. The results show that track irregularities caused by girder damage under frequent earthquakes have minimal impact on post-earthquake travel, and train safety and stability indicators remain within safety thresholds, with no exceeding of limits occurring. When the local vibration level is the design earthquake level, the probability of exceeding the safety travel parameters after the earthquake is 8.16%, with a 95% confidence interval of (0.50% to 15.83%). The probability of exceeding the lateral acceleration after the earthquake is 46.94%, with a confidence interval of (32.97% to 60.90%). When the local vibration level is the rare earthquake level, the probability of exceeding the derailment coefficient after the earthquake is as high as 38.89%, with a confidence interval of (22.96% to 54.81%), indicating an extremely high probability of train derailment. Analysis of the post-earthquake train stability indicators indicates that all lateral accelerations have exceeded their limits.

[0197] Example 2:

[0198] Figure 10 2 is a system schematic diagram of a device for evaluating the probability of driving safety after an earthquake on a railway bridge according to another exemplary embodiment, the device comprising:

[0199] Model building module 1: used to establish a train model using multi-rigid body dynamics theory and a railway track-bridge model using finite element theory; and to establish a train-track-bridge coupling system calculation model using the train model and the railway track-bridge model;

[0200] Damage Value Acquisition Module 2: Used to obtain the probability distribution function of different material parameters of the railway track-bridge system, establish a random time history analysis sample sequence for the railway track-bridge model based on the probability distribution function, and perform nonlinear time history calculation on the random time history analysis sample sequence to obtain a set of earthquake-induced damage values ​​for each component of the railway track-bridge system;

[0201] Mapping relationship acquisition module 3: used to set the basic assumptions of the railway track-bridge structure theoretical model, establish the equilibrium differential equations of the bridge and railway track structure mechanical models based on the mechanical properties of the railway track-bridge structure, and obtain the mapping relationship between seismic damage to key railway track-bridge components and track irregularities based on the equilibrium differential equations;

[0202] Sample acquisition module 4 is used to obtain initial track irregularity samples. Additional track irregularity samples caused by earthquake-induced damage to different components of the railway track-bridge system are obtained by using the earthquake-induced damage value set of each component of the railway track-bridge system and the mapping relationship between earthquake-induced damage to key components of the railway track-bridge system and track irregularity. The initial track irregularity samples and the additional track irregularity samples are superimposed to obtain earthquake-induced random track irregularity samples of different components.

[0203] Power spectrum acquisition module 5: used to generate the power spectrum density curves of the seismic track irregularity of different components by using the seismic track random irregularity samples of different components using a spectrum estimation method; and obtain the power spectrum of the seismic track irregularity of different components according to the seismic track irregularity power spectrum density curves;

[0204] Response acquisition module 6: configured to randomly generate a plurality of vibration-induced track irregularity samples based on the vibration-induced track irregularity power spectra of the different components, input the vibration-induced track irregularity samples into the train-track-bridge coupling system calculation model, and obtain the train-track-bridge coupling dynamic response results;

[0205] Model training module 7: used to train a pre-built model architecture using the earthquake-induced track irregularity sample as a first parameter and the train-track-bridge coupled dynamic response result as a second parameter to obtain a rapid prediction model for post-earthquake bridge driving performance indicators;

[0206] Safety probability acquisition module 8: is used to perform multiple Monte Carlo simulation calculations based on the power spectrum of the earthquake-induced track irregularities of the different components and the rapid prediction model of the driving performance index on the bridge after the earthquake, so as to obtain the exceeding probability and confidence interval of the driving safety on the bridge after the earthquake.

[0207] It can be understood that the same or similar parts of the above embodiments can be referenced to each other, and the contents not described in detail in some embodiments can refer to the same or similar contents in other embodiments.

[0208] It should be noted that, in the description of the present invention, the terms "first," "second," etc. are used for descriptive purposes only and should not be understood as indicating or implying relative importance. In addition, in the description of the present invention, unless otherwise specified, "a small number of sparsely distributed" means at least two.

[0209] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, segment or portion of code comprising one or less sparsely distributed executable instructions for implementing the steps of a specific logical function or process, and the scope of the preferred embodiments of the present invention includes alternative implementations in which functions may be performed out of the order shown or discussed, including performing functions in a substantially simultaneous manner or in the reverse order depending on the functions involved, which should be understood by those skilled in the art to which the embodiments of the present invention pertain.

[0210] It should be understood that various parts of the present invention can be implemented using hardware, software, firmware, or a combination thereof. In the above-described embodiment, a small number of sparsely distributed steps or methods can be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented using hardware, as in another embodiment, any one of the following technologies known in the art or a combination thereof can be used to implement it: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application-specific integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0211] Those skilled in the art will understand that all or part of the steps in the method of the above embodiment can be completed by instructing related hardware through a program, and the program can be stored in a computer-readable storage medium. When the program is executed, it includes one or a combination of the steps of the method embodiment.

[0212] In addition, the functional units in the various embodiments of the present invention may be integrated into a single processing module, or each unit may exist physically separately, or two or more units may be integrated into a single module. The aforementioned integrated modules may be implemented in the form of hardware or in the form of software functional modules. If the integrated modules are implemented in the form of software functional modules and sold or used as independent products, they may also be stored in a computer-readable storage medium.

[0213] The storage medium mentioned above can be a read-only memory, a magnetic disk or an optical disk, etc.

[0214] Throughout this specification, references to terms such as "one embodiment," "some embodiments," "examples," "specific examples," or "some examples" indicate that the specific features, structures, materials, or characteristics described in conjunction with that embodiment or example are included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or a small number of sparsely distributed embodiments or examples.

[0215] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention.

Claims

1. A method for evaluating the probability of driving safety on railway bridges after an earthquake, characterized in that: The method comprises: A train model is established using multi-rigid body dynamics theory, and a railway track-bridge model is established using finite element theory; a train-track-bridge coupling system calculation model is established using the train model and the railway track-bridge model; Obtaining probability distribution functions of different material parameters of the railway track-bridge system, establishing a random time history analysis sample sequence for the railway track-bridge model based on the probability distribution function, and performing nonlinear time history calculations on the random time history analysis sample sequence to obtain a set of earthquake-induced damage values ​​for each component of the railway track-bridge system; The basic assumptions of the railway track-bridge structure theoretical model are set, and the equilibrium differential equations of the bridge and railway track structure mechanical models are established based on the mechanical properties of the railway track-bridge structure. Based on the equilibrium differential equations, the mapping relationship between seismic damage to key railway track-bridge components and track irregularities is obtained; Obtaining initial track irregularity samples, obtaining additional track irregularity samples caused by earthquake-induced damage to different components of the railway track-bridge system based on a set of earthquake-induced damage values ​​for each component of the railway track-bridge system and a mapping relationship between earthquake-induced damage to key components of the railway track-bridge system and track irregularity, and superimposing the initial track irregularity samples with the additional track irregularity samples to obtain earthquake-induced random track irregularity samples of different components; Using a spectrum estimation method, the seismic-induced track irregularity power spectrum density curves of different components are generated by using seismic-induced track random irregularity samples of different components; and the seismic-induced track irregularity power spectrum of different components is obtained according to the seismic-induced track irregularity power spectrum density curves. Randomly generating a plurality of seismic-induced track irregularity samples based on the seismic-induced track irregularity power spectra of the different components, inputting the seismic-induced track irregularity samples into the train-track-bridge coupling system calculation model, and obtaining train-track-bridge coupling dynamic response results; The earthquake-induced track irregularity sample is used as a first parameter, and the train-track-bridge coupled dynamic response result is used as a second parameter. The pre-built model architecture is trained using the first and second parameters to obtain a rapid prediction model for the vehicle performance index on the bridge after the earthquake; Based on the power spectrum of the earthquake-induced track irregularities of the different components and the rapid prediction model of the driving performance index on the bridge after the earthquake, multiple Monte Carlo simulation calculations were performed to obtain the exceeding probability and confidence interval of the driving safety on the bridge after the earthquake.

2. The method according to claim 1, characterized in that The train model is established by adopting multi-rigid body dynamics theory, and the railway track-bridge model is established by adopting finite element theory; and the train-track-bridge coupling system calculation model is established by using the train model and the railway track-bridge model, including: The train model is obtained by using a rigid body to simulate the train body, front and rear bogies and four wheel sets, and using a spring-damper to simulate the primary and secondary suspension systems of the train. The track base plate and track plate are simulated using spatial beam elements or plate elements, the track rails, bridge foundations, abutments, piers and main beams are simulated using spatial beam elements, and the track interlayer connection components and bridge supports are simulated using spring-damping elements to obtain a railway track-bridge model. Establishing a coupling relationship between the train model and the railway track-bridge model through the wheel-rail interaction between the train and the track-bridge system, thereby obtaining a train-track-bridge coupling system calculation model; The wheel-rail interaction includes: normal action and tangential action between the wheelset and the rail; The normal action is obtained by adopting the nonlinear Hertz contact theory, and the tangential action is obtained by adopting the Kaller theory.

3. The method according to claim 2, characterized in that The method for obtaining the probability distribution functions of different material parameters of the railway track-bridge system includes: Obtain the logarithmic normal distribution function of concrete parameters, steel parameters and support friction coefficient, and obtain the Gaussian distribution function of the damping ratio of the reinforced concrete structure; The random time history analysis sample sequence for establishing the railway track-bridge model based on the probability distribution function includes: Based on the probability distribution functions of different material parameters of the railway track-bridge system, a hypercube Latin sampling method is used to perform N stratified sampling on each structural material parameter to obtain N groups of different structural parameter samples, and N railway track-bridge numerical models are randomly generated based on the N groups of different structural parameter samples; Generate N random seismic motions that take site characteristics into consideration by adopting the method of artificially synthesizing seismic waves or selecting natural seismic waves; Randomly combining the N railway track-bridge numerical models with N random earthquake motions to generate N groups of time history analysis samples of the earthquake motion-railway-bridge integrated numerical model; Based on the time history analysis samples of the N groups of seismic motion-line-bridge integrated numerical models, N groups of nonlinear finite element models of railway track-bridge systems are established. Considering the M seismic motion peaks of the N groups of nonlinear finite element models of railway track-bridge systems, random time history analysis sample sequences of MN groups of railway track-bridge models are generated.

4. The method according to claim 3, characterized in that The method of establishing a balanced differential equation of the mechanical model of the bridge and railway track structure based on the mechanical characteristics of the railway track-bridge structure and obtaining a mapping relationship between earthquake-induced damage to key components of the railway track-bridge and track irregularity based on the balanced differential equation includes: Establishing deformation expressions of the rails, track plates, and base plates according to the railway track structural mechanics model, and obtaining matrix expressions of rail deformation, track plate deformation, and base plate deformation according to the deformation expressions of the rails, track plates, and base plates; Establishing a deformation expression of the bridge girder according to the bridge structure mechanics model; Obtaining spring force expressions for components between different layers of the track structure under horizontal deformation, substituting the matrix expressions for rail deformation, track plate deformation, base plate deformation, and bridge girder deformation into the spring force expressions for components between different layers of the track structure under horizontal deformation to obtain a fastener spring force matrix under horizontal deformation; The fastener spring force matrix under horizontal action is substituted into the matrix expression of the rail deformation to obtain the mapping relationship between the earthquake-induced damage to the key components of the railway track-bridge and the track irregularity.

5. The method according to claim 4, characterized in that The obtaining of the initial track irregularity sample comprises: Acquiring an initial track irregularity power spectrum, and generating the initial track irregularity samples by a numerical method based on the initial track irregularity power spectrum; The additional track irregularity samples caused by the earthquake-induced damage of different components of the railway track-bridge system are obtained by using the earthquake-induced damage value set of each component of the railway track-bridge system and the mapping relationship between the earthquake-induced damage of key components of the railway track-bridge and track irregularity, including: The numerical value set of earthquake-induced damage of each component of the railway track-bridge system is input into the mapping relationship between earthquake-induced damage of key components of the railway track-bridge and track irregularity, so as to obtain additional track irregularity samples caused by earthquake-induced damage of different components of the railway track-bridge system.

6. The method according to claim 5, characterized in that The spectrum estimation method is used to generate the power spectrum density curves of the seismic track irregularity of different components by using the seismic track random irregularity samples of different components, including: Performing fast Fourier transform on the vibration-induced track irregularity samples of the different components, and generating power spectral density curves of the vibration-induced track irregularity of the different components based on the windowed modified Welch periodogram method; The step of obtaining the vibration-induced track irregularity power spectrum of different components according to the vibration-induced track irregularity power spectrum density curve includes: The seismic-induced track irregularity power of multiple groups of components is obtained according to the seismic-induced track irregularity power spectrum density curve, the corresponding track irregularity limit spectra are obtained through the seismic-induced track irregularity power of the multiple groups of components, and the corresponding track irregularity limit spectra are fitted in sections to obtain the seismic-induced track irregularity power spectra of the different components.

7. The method according to claim 6, characterized in that The randomly generating a plurality of vibration-induced track irregularity samples by using the vibration-induced track irregularity power spectra of the different components comprises: Based on the power spectra of the vibration-induced track irregularity of the different components, a plurality of vibration-induced track irregularity samples are randomly generated by a trigonometric series superposition method or a fast Fourier transform method.

8. The method according to claim 7, characterized in that The pre-built model architecture is trained by using the first parameter and the second parameter to obtain a rapid prediction model for the driving performance index on the bridge after the earthquake, including: Preprocessing the first parameter and the second parameter, and selecting a deep learning model based on the data characteristics and types of the first parameter and the second parameter; A training data set is constructed using the first and second parameters, a selected deep learning model is trained using the training data set, and the trained deep learning model is used as a rapid prediction model for post-earthquake bridge driving performance indicators.

9. The method according to claim 8, characterized in that The power spectrum of the earthquake-induced track irregularity of the different components and the rapid prediction model of the driving performance index on the bridge after the earthquake are used to perform multiple Monte Carlo simulation calculations to obtain the exceeding probability and confidence interval of the driving safety on the bridge after the earthquake, including: Randomly generating multiple groups of earthquake-induced track irregularity samples based on the earthquake-induced track irregularity power spectra of the different components, inputting the multiple groups of earthquake-induced track irregularity samples into the rapid prediction model for post-earthquake on-bridge vehicle performance indicators, and obtaining multiple groups of train-track-bridge system dynamic response results; For each set of train-track-bridge system dynamic response results, determine whether an over-limit event occurs. If so, obtain the over-limit probability through multiple Monte Carlo simulations; and obtain the confidence interval of the over-limit probability through binomial distribution or normal approximation.

10. A device for evaluating the probability of driving safety on a railway bridge after an earthquake, characterized in that: The device comprises: Model building module: used to build a train model using multi-rigid body dynamics theory and a railway track-bridge model using finite element theory; and to build a train-track-bridge coupling system calculation model using the train model and the railway track-bridge model; Damage value acquisition module: used to obtain the probability distribution function of different material parameters of the railway track-bridge system, establish a random time history analysis sample sequence of the railway track-bridge model based on the probability distribution function, and perform nonlinear time history calculation on the random time history analysis sample sequence to obtain a set of earthquake-induced damage values ​​for each component of the railway track-bridge system; Mapping relationship acquisition module: used to set the basic assumptions of the railway track-bridge structure theoretical model, establish the equilibrium differential equations of the bridge and railway track structure mechanical models based on the mechanical characteristics of the railway track-bridge structure, and obtain the mapping relationship between seismic damage to key railway track-bridge components and track irregularities based on the equilibrium differential equations; Sample acquisition module: used to obtain initial track irregularity samples, obtain additional track irregularity samples caused by earthquake-induced damage to different components of the railway track-bridge system through the set of earthquake-induced damage values ​​of each component of the railway track-bridge system and the mapping relationship between earthquake-induced damage to key components of the railway track-bridge and track irregularity, and superimpose the initial track irregularity samples with the additional track irregularity samples to obtain earthquake-induced random track irregularity samples of different components; Power spectrum acquisition module: used to generate the power spectrum density curves of seismic track irregularities of different components through the seismic track random irregularity samples of different components by using the spectrum estimation method; and obtain the power spectrum of seismic track irregularities of different components according to the seismic track irregularity power spectrum density curves; A response acquisition module is configured to randomly generate a plurality of vibration-induced track irregularity samples based on the vibration-induced track irregularity power spectra of the different components, input the vibration-induced track irregularity samples into the train-track-bridge coupling system calculation model, and obtain the train-track-bridge coupling dynamic response results; Model training module: used to train a pre-built model architecture using the earthquake-induced track irregularity sample as a first parameter and the train-track-bridge coupled dynamic response result as a second parameter to obtain a rapid prediction model for post-earthquake bridge driving performance indicators; Safety probability acquisition module: used to perform multiple Monte Carlo simulation calculations based on the power spectrum of the earthquake-induced track irregularities of the different components and the rapid prediction model of the driving performance index on the bridge after the earthquake, so as to obtain the exceeding probability and confidence interval of the driving safety on the bridge after the earthquake.

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