Method for calculating post-earthquake running speed threshold value of high-speed railway bridge, medium and equipment

Abstract

The invention relates to the technical field of bridge post-earthquake driving safety, in particular to a high-speed railway bridge post-earthquake driving speed threshold calculation method, a medium and equipment. The method comprises the following steps: establishing a track-bridge system model and a train-track-bridge coupling system model; a post-earthquake track irregularity quantitative index is put forward, the relation between the post-earthquake track irregularity quantitative index and a post-earthquake driving performance index is established, and the fitting parameter relation between the driving speed and the mapping relation is established; and the driving performance index limit value and the post-earthquake driving speed threshold value of the safety margin are quantified and guaranteed. According to the method, the post-earthquake track irregularity quantitative index TICrms suitable for the two track types is provided, and the index has good applicability in high-speed railway bridge tracks; a train running speed threshold calculation formula meeting the post-earthquake traffic safety requirement is provided, so that the post-earthquake traffic capacity calculation of the high-speed railway bridge is simple, the speed threshold calculation result has reasonable safety margin, and a basis is provided for post-earthquake safe operation and maintenance of the high-speed railway bridge.

Description

Technical Field

[0001] The present invention relates to the technical field of post-earthquake driving safety of bridges, and particularly to a method, medium and device for calculating the driving speed threshold of high-speed railway bridges after an earthquake. Background Art

[0002] Under the action of an earthquake, the high-speed railway track-bridge system will inevitably generate residual deformation, which seriously threatens the safety of trains running on the bridge after the earthquake. Effectively evaluating the track smoothness and traffic capacity of high-speed railway bridges after an earthquake has important engineering practical value. With the construction of the high-speed railway network developing towards mountainous areas with frequent seismic activities and high-intensity seismic areas along the coast, the concept of "replacing roads with bridges" is usually adopted to ensure the stability of the line. However, under the action of an earthquake, the acceleration response of the bridge is usually greater than that of the ground, and the driving safety on the bridge after the earthquake faces a huge safety threat. At present, there have been extensive studies on the impact of earthquake action on the driving safety of trains on high-speed railway bridges. The results show that earthquake excitation has a significant impact on the safe operation of trains, far greater than other loads. However, the above studies are mainly based on complex dynamic coupling models and scaled tests, which are difficult to complete the evaluation of driving performance after an earthquake in a short time and cannot meet the demand for rapid traffic after an earthquake.

[0003] As the carrier of train operation, the smoothness of the track directly affects the safety and comfort of train operation. Therefore, many scholars have tried to carry out research on driving safety on the bridge from the perspective of the smooth state of the track, and timely repair the track that does not meet the standards to ensure the operation safety of trains. However, the strong destructiveness and high randomness of earthquakes determine that the above research is difficult to be popularized and applied in the evaluation of driving performance after an earthquake. To solve this problem, although the prior art can achieve a rapid evaluation of driving performance after an earthquake, there are still the following defects in this research: (1) The research object is single, only targeting the CRTS III slab ballastless track, which will affect the popularization and application of quantitative indicators. (2) The influence of driving speed on the driving performance index after an earthquake is not correctly revealed, resulting in the proposed prediction formula being too conservative. (3) The coefficient of determination R2 is relatively low during fitting, resulting in insufficient accuracy of the prediction formula.

[0004] In view of the above problems, there is an urgent need for a method for calculating the train operation speed threshold that can accurately calculate the driving safety requirements after an earthquake for high-speed railway CRTS II and CRTS III slab ballastless tracks. Summary of the Invention

[0005] The purpose of the present invention is to provide a method that can accurately calculate the driving speed threshold of trains on bridges after an earthquake and meet the demand for rapid traffic after an earthquake. The specific technical solution is as follows:

[0006] A method for calculating the driving speed threshold of high-speed railway bridges after an earthquake includes the following steps:

[0007] S1: Establish a three-dimensional non-linear dynamic simulation model TBSSM of the high-speed railway track-bridge system and a high-speed railway train-track-bridge coupling system model TTBCSM;

[0008] S2: Propose a post-earthquake track irregularity quantification index applicable to CRTS II and CRTS III track types;

[0009] S3: Establish a mapping relationship between the post-earthquake track irregularity quantification index and the post-earthquake train operation performance index, and fit the relationship between the expression parameters of this mapping relationship and the train operation speed;

[0010] S4: Quantify the train operation performance index limit to ensure a safety margin, and obtain the post-earthquake train operation speed threshold to ensure a safety margin.

[0011] Preferably, the S2 includes:

[0012] Taking CRTS II and CRTS III slab ballastless tracks as the objects, use TBSSM to calculate the post-earthquake track irregularity under seismic ground motion;

[0013] Ignore the post-earthquake gauge, alignment and level irregularities and use the post-earthquake track irregularity to replace the alignment irregularity;

[0014] Propose a track irregularity root mean square change rate index TIC rms as the post-earthquake track irregularity quantification index, and take the train operation speed into account in TIC rms and the fitting function parameters of the train operation performance index;

[0015] Let the post-earthquake track irregularity be A(x), where x represents the track line mileage range, and calculate the post-earthquake track irregularity quantification index TIC rms , and the calculation method is as follows:

[0016]

[0017] In the formula, l represents the total mileage of the rail.

[0018] Preferably, the steps of establishing the mapping relationship between the post-earthquake track irregularity quantification index and the post-earthquake train operation performance index in the S3 are as follows:

[0019] Input the post-earthquake track irregularity into TTBCSM to calculate the post-earthquake train operation performance index at different train speeds; conduct a correlation analysis between TIC rms and the train operation performance index at different train speeds, and obtain the Pearson correlation coefficient r rms between TIC p and different train operation performance indexes and the Spearman rank correlation coefficient ρs ; Both r p and ρ s with a driving performance index above 0.95 are expressed using a linear model with respect to TIC rms . For a driving performance index where r p is less than 0.8 but ρ s is greater than 0.95, a non - linear model with respect to TIC rms is used for expression;

[0020] At different vehicle speeds, regression analysis is separately performed on TIC rms and each driving performance index to obtain the mapping relationship between TIC rms and each post - earthquake driving performance index, which is expressed as follows:

[0021]

[0022] In the formula, i represents the type of ballastless track, i = II, III; DPI i represents the driving performance index matrix; a i represents the fitting curve coefficient matrix; b i represents the fitting curve power matrix; c i represents the fitting curve intercept matrix; ⊙ represents the Hadamard product;

[0023] The matrix composition form is as follows:

[0024]

[0025] In the formula, a y represents the lateral acceleration of the car body; ΔPP represents the wheel load reduction rate; QP represents the derailment coefficient; SP y represents the lateral Sperling; Q y represents the lateral wheel - rail force; a1, a2…a5 represent the coefficients corresponding to each post - earthquake driving performance index, and c1, c2…c5 represent the intercepts corresponding to each post - earthquake driving performance index; b4 represents the power of the lateral Sperling index.

[0026] Preferably, the regression analysis includes:

[0027] Simple linear regression analysis simulates the relationship between two variables by fitting a linear equation of the data, and is expressed by the following formula:

[0028] Y = β0 + β1X+ε, ε~N(0,σ 2 )3);

[0029] In the formula, Y is the response variable; X is the predictor variable; β0 and β1 are the regression parameter and regression coefficient respectively; ε is the random error, representing the difference between the predicted data and the real data; ε~N(0,σ 2)It is indicated that the error term follows a normal distribution with a mean of 0 and a variance of σ 2 ;

[0030] The predicted value of Equation (3) is in the form shown in Equation (4):

[0031]

[0032] wherein, is the predicted value of the response variable; and are the estimated values of the regression parameter and the regression coefficient respectively, which are estimated by the maximum likelihood estimation method, as shown in Equation (5):

[0033]

[0034] wherein, n represents the sample size; represents the sample mean of the dependent variable; represents the sample mean of the independent variable; X i represents the value of the independent variable at the i-th observation point; Y i represents the value of the dependent variable at the i-th observation point;

[0035] Univariate non-linear regression analysis also uses a function to describe the relationship between the response variable and the predictor variable, and the form of the function is expressed by Equation (6):

[0036] Y = f(X,β)+ε, ε~N(0,σ 2 )(6);

[0037] wherein, f(X,β) is the mean function; β=(β1,…,β k ) represents the regression coefficient with k unknown parameters;

[0038] For a set of observed data (x1,y1),…,(x n ,y n ), Equation (6) is applicable to the ideal situation where there is no error in the response variable, and Equation (6) is represented by the mean function shown in Equation (7):

[0039]

[0040] wherein, is the estimated value of the regression coefficient;

[0041] Non-linear regression analysis should define the function based on the scatter distribution of the data or use a known model;

[0042] For a given set of data, the fitting quality of the regression model is judged by the coefficient of determination R 2 and is calculated by Equation (8):

[0043]

[0044] In the formula, is the correlation coefficient; represents the sum of squared residuals; represents the total sum of squared deviations;

[0045] The coefficient of determination R 2 has a value between 0 and 1. The closer it is to 1, the better the explanatory power of the predictor variable for the response variable in the regression analysis. R 2 = 0.9 means that 90% of the total variability of the response variable is caused by the predictor variable.

[0046] Preferably, the relationship between the expression parameters of the mapping relationship in S3 and the driving speed V is as follows:

[0047]

[0048] In the formula, ξ i , θ i , μ i represent the quadratic coefficient matrix, λ i , η i , ν i represent the linear coefficient matrix; δ i , ω i represent the constant term matrix.

[0049] Preferably, the steps of quantifying the limit value of the driving performance index to ensure the safety margin include:

[0050] Let x0 be a specified value of the predictor variable x, and use the regression model to calculate the value of the empirical regression function corresponding to x0 From the sum of squared residuals Qe and being independent of each other, we get

[0051]

[0052] In the formula, Y0 represents the true value; represents the residual standard deviation; the sum of squares of the independent variable

[0053] For a given confidence level 1 - α, there is

[0054]

[0055] In the formula, P represents the probability of the occurrence of the entire event; σ represents the standard deviation of the regression model error; t α / 2 represents the critical value of the t - distribution;

[0056] From Equation 11), we get The prediction interval of is:

[0057]

[0058] When the sample size n > 30 and x0 is close to At this time, Equation (12) is simplified to:

[0059]

[0060] In the formula, z α / 2 represents the standard normal distribution;

[0061] Combining Equation (2) and Equation (13), the calculation formula for the limit value of the post-earthquake driving index to ensure the safety margin is as follows:

[0062]

[0063] In the formula, represents the residual standard deviation;

[0064] The limit values of various driving performance indexes in CRTS II and CRTS III slab ballastless tracks are calculated by Equation (14).

[0065] Preferably, the steps for calculating the post-earthquake driving speed threshold to ensure the safety margin include:

[0066] Taking the derailment coefficient, wheel load reduction rate, and lateral wheel-rail force as the safety indexes for train operation, and taking the lateral car body acceleration and Sperling as the comfort indexes for train operation,

[0067] Based on the limit requirements of vehicle driving performance indexes and Equation (14), the solution formula for the post-earthquake driving speed threshold on the bridge is proposed as follows:

[0068]

[0069] Solving Equation (15), the speed threshold expression based on the post-earthquake driving safety performance indexes is obtained as follows:

[0070]

[0071] In the formula, V II_1 represents the post-earthquake driving speed threshold of the II-type slab ballastless track based on the driving safety indexes, and V III_1 represents the post-earthquake driving speed threshold of the III-type slab ballastless track based on the driving safety indexes;

[0072] Using a quadratic power function to fit the solution result, the speed threshold expression based on the post-earthquake driving smoothness performance indexes is obtained as follows:

[0073]

[0074] In the formula, VII_2 denotes the post - earthquake train running speed threshold of the type - II slab ballastless track based on the train running smoothness index; V III_2 denotes the post - earthquake train running speed threshold of the type - III slab ballastless track based on the train running smoothness index.

[0075] 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 method for calculating the post - earthquake train running speed threshold of a high - speed railway bridge as described above is implemented.

[0076] 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 method for calculating the post - earthquake train running speed threshold of a high - speed railway bridge as described above is implemented.

[0077] Applying the technical solution of the present invention has the following beneficial effects:

[0078] A method for calculating the post - earthquake train running speed threshold of a high - speed railway bridge includes: establishing a three - dimensional non - linear dynamic simulation model TBSSM of a high - speed railway track - bridge system and a train - track - bridge coupling system model TTBCSM of a high - speed railway train; proposing a post - earthquake track irregularity quantification index applicable to CRTS II and CRTS III track types; establishing a mapping relationship between the post - earthquake track irregularity quantification index and the post - earthquake train running performance index, and fitting the relationship between the expression parameters of the mapping relationship and the train running speed; quantifying the train running performance index limit that guarantees a safety margin to obtain the post - earthquake train running speed threshold that guarantees a safety margin. Through the method for calculating the post - earthquake train running speed threshold of a high - speed railway bridge proposed by the present invention, a simulation model of the track - bridge system and a train - track - bridge coupling system is respectively established, and a post - earthquake track irregularity quantification index TICrms applicable to two track types is proposed. This index and the train running speed index have a significant impact on the post - earthquake train running performance index, and it has good applicability in both CRTS II and CRTS III type tracks of high - speed railway bridges; by establishing a mapping relationship between the post - earthquake track irregularity quantification index and the post - earthquake train running performance index, the quantitative influence law of the train speed on the post - earthquake train running performance index is revealed, and a calculation formula for the train running speed threshold that meets the post - earthquake train running safety requirements is proposed, making the calculation of the post - earthquake passing capacity of a high - speed railway bridge simple, and the calculation result of the speed threshold has a reasonable safety margin, providing a basis for the post - earthquake safety operation and maintenance of high - speed railway bridges.

[0079] 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

[0080] The accompanying drawings, which form 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:

[0081] Figure 1 It is a schematic flow chart of a method for calculating the post-earthquake driving speed threshold of a high-speed railway bridge according to an embodiment of the present invention;

[0082] Figure 2 It is a curve graph of the post-earthquake driving speed threshold of the CRTS II type slab ballastless track system;

[0083] Figure 3 It is a curve graph of the post-earthquake driving speed threshold of the CRTS III type slab ballastless track system. Detailed Embodiment

[0084] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings, but the present invention can be implemented in many different ways defined and covered by the claims.

[0085] In one embodiment, referring to Figure 1 , a method for calculating the post-earthquake driving speed threshold of a high-speed railway bridge includes the following steps:

[0086] A method for calculating the post-earthquake driving speed threshold of a high-speed railway bridge includes the following steps:

[0087] S1: Establish a three-dimensional non-linear dynamic simulation model TBSSM of the high-speed railway track-bridge system and a train-track-bridge coupling system model TTBCSM of the high-speed railway;

[0088] In this embodiment, the bridge type is a 5-span 32.5m simply supported beam bridge for high-speed railways, the track types are CRTS II and CRTS III type slab ballastless tracks, the abutment type is a straight abutment with a longitudinal length of 7.8m, the pier type is a high circular-ended solid pier with a pier height of 14m, and the bearing type is a 5000kN pot rubber bearing. The CRTS II type slab ballastless track system is composed of components such as rails, fasteners, track slabs, CA mortar layers, base slabs, sliding layers, shear tooth grooves, shear steel bars and lateral retaining blocks, and the CRTS III type slab ballastless track system is composed of components such as rails, fasteners, track slabs, self-compacting concrete layers, isolation layer geotextiles and base slabs.

[0089] To consider the randomness and universality of ground motions, the "M-R method" is adopted in this embodiment to select ground motions with magnitudes ranging from 5 to 8 m and epicentral distances from 0 to 60 km. Forty-eight uniformly distributed ground motions are screened from the PEER strong motion database, and seismic excitations are applied to the high-speed railway track-bridge system model. Under frequently-occurring earthquakes, the rails basically remain in their initial straight state, having little impact on post-earthquake train operation. Therefore, in this embodiment, only two PGA levels, 0.38 g (design earthquake) and 0.6 g (rare earthquake), are considered, and different PGA levels are achieved by adjusting the peak values of the seismic waves.

[0090] Based on the theory of multi-body dynamics and train-track-bridge interaction, a high-speed railway train-track-bridge coupling system model (TTBCSM) is established in MATLAB software. The model includes a train sub-model and a ballastless track-bridge sub-model, and the two sub-models are coupled through the wheel-rail relationship. The train sub-model consists of one car body, two bogies, and four wheel sets, with a total of 31 degrees of freedom. The ballastless track-bridge sub-model includes structures such as rails, fasteners, track slabs, CA mortar (CRTS II), self-compacting concrete (CRTS III), base plates, and simply supported beams.

[0091] S2: Propose post-earthquake track irregularity quantification indices applicable to CRTS II and CRTS III track types, specifically including:

[0092] Taking CRTS II and CRTS III slab ballastless tracks as the research objects, use TBSSM to calculate the post-earthquake track irregularities under the first 100 ground motions;

[0093] Under lateral seismic action, the lateral residual displacements of the bearings are mapped layer by layer upwards, causing large post-earthquake track alignment irregularities in the rails. In contrast, the post-earthquake gauge, vertical, and level irregularities can be ignored. Therefore, the post-earthquake track irregularities referred to in this embodiment all represent track alignment irregularities.

[0094] Propose the root mean square change rate index TIC of track irregularities applicable to CRTS II and CRTS III slab ballastless tracks rms As the post-earthquake track irregularity quantification index, and consider the train speed into the fitting function parameters of TIC rms and the train operation performance index;

[0095] Assume the post-earthquake track irregularity is A(x), where x represents the track line mileage range, and calculate the post-earthquake track irregularity quantification index TIC rms , and the calculation method is as follows:

[0096]

[0097] In the formula, l represents the total mileage of the rails.

[0098] S3: Establish the mapping relationship between the post-earthquake track irregularity quantification index and the post-earthquake train operation performance index, and fit the relationship between the expression parameters of this mapping relationship and the train operation speed, specifically including:

[0099] To evaluate the correlation between the track smoothness quantification index TIC rms and different train operation performance indexes, taking CRTS II and CRTS III slab ballastless tracks as objects, select train speeds of 150, 200, 250, 300, and 350 km / h, and conduct a correlation analysis on TIC rms and the train operation performance indexes;

[0100] Select different train speeds to conduct a correlation analysis on TIC rms and the train operation performance indexes, and obtain the correlation between TIC rms and different train operation performance indexes; For the train operation performance indexes with both r p and ρ s reaching above 0.95, use a linear model about TIC rms to express them, and for the train operation performance indexes with r p less than 0.8 but ρ s greater than 0.95, use a non-linear model about TIC rms to express them;

[0101] For CRTS II and CRTS III slab ballastless tracks, the correlation trend between TIC rms and the train operation performance indexes is similar. Specifically, the correlation between TIC rms and the lateral car body acceleration, wheel load reduction rate, derailment coefficient, and lateral wheel-rail force is extremely strong, and both r p and ρ s reach above 0.95, which indicates that the above train operation performance indexes at different train speeds can be expressed by a linear model about TIC rms . However, the r rms between TIC p and Lateral sperling is relatively weak, especially in CRTS III slab ballastless tracks, less than 0.8, but the ρ between TIC rms and Lateral sperling at different train speeds is greater than 0.95, indicating that Lateral sperling needs to be expressed by a non-linear model about TIC rms ;

[0102] In the CRTS II and CRTS III slab ballastless track systems, with the increase of the train speed and TIC rms , each post-earthquake train operation performance index increases significantly. TIC at different train speedsrms There is a significant linear or non - linear correlation with each post - earthquake train operation performance index, and R 2 can reach 0.95 or above, which indicates that TIC rms has strong applicability in two types of slab ballastless track systems, and the influence of seismic action on post - earthquake train operation comfort and safety can be effectively evaluated by TIC rms The post - earthquake track irregularities are input into TTBCSM to calculate the post - earthquake train operation performance indexes; at different vehicle speeds, regression analysis is respectively carried out on TIC rms and each train operation performance index, and the mapping relationship between TIC rms and each post - earthquake train operation performance index is expressed as follows:

[0103]

[0104] In the formula, i represents the type of ballastless track, i = II, III; DPI i represents the matrix of train operation performance indexes; a i represents the matrix of fitting curve coefficients; b i represents the matrix of fitting curve powers; c i represents the matrix of fitting curve intercepts; ⊙ represents the Hadamard product;

[0105] The matrix composition form is as follows:

[0106]

[0107] In the formula, a y represents the lateral acceleration of the car body; ΔPP represents the wheel load reduction rate; QP represents the derailment coefficient; SP y represents the lateral Sperling; Q y represents the lateral wheel - rail force; a1, a2…a5 represent the coefficients corresponding to each post - earthquake train operation performance index, c1, c2…c5 represent the intercepts corresponding to each post - earthquake train operation performance index; b4 represents the power of the lateral Sperling index.

[0108] To establish the quantitative relationship between TIC rms and the train operation performance indexes, 100 post - earthquake track irregularities calculated previously are used to calculate the corresponding TIC rms indexes. At the same time, the post - earthquake track irregularities are input into TTBCSM to calculate the post - earthquake train operation performance indexes such as lateral car body acceleration and wheel load reduction rate. Taking vehicle speeds of 250, 300, and 350 km / h as examples, the following formula is used to carry out regression analysis on TIC rms and each train operation performance index respectively. The regression analysis includes:

[0109] Simple linear regression analysis simulates the relationship between two variables by fitting a linear equation to the data, which is expressed by the following formula:

[0110] Y = β0 + β1X + ε, ε ~ N(0, σ 2 )3);

[0111] Wherein, Y is the response variable; X is the predictor variable; β0 and β1 are the regression parameter and the regression coefficient respectively; ε is the random error, indicating the difference between the predicted data and the actual data; ε ~ N(0, σ 2 ) indicates that the error term follows a normal distribution with a mean of 0 and a variance of σ 2 ;

[0112] The predicted value of formula 3) is shown in formula 4) as follows:

[0113]

[0114] Wherein, is the predicted value of the response variable; and are the estimated values of the regression parameter and the regression coefficient respectively, which are estimated by the maximum likelihood estimation method, as shown in formula 5):

[0115]

[0116] Wherein, n represents the sample size; represents the sample mean of the dependent variable; represents the sample mean of the independent variable; X i represents the value of the independent variable at the i-th observation point; Y i represents the value of the dependent variable at the i-th observation point;

[0117] Simple non-linear regression analysis also uses a function to describe the relationship between the response variable and the predictor variable, and the form of the function is expressed by formula 6):

[0118] Y = f(X, β) + ε, ε ~ N(0, σ 2 )6);

[0119] Wherein, f(X, β) is the mean function; β = (β1,..., β k ) represents the regression coefficient with k unknown parameters;

[0120] For a set of observed data (x1, y1),...,(x n , y n ), formula 6) is applicable to the ideal situation where the response variable has no error, and formula 6) is represented by the mean function shown in formula 7):

[0121]

[0122] In the formula, is the estimated value of the regression coefficient;

[0123] Nonlinear regression analysis is based on the scatter distribution of the data to define the function or use a known model;

[0124] For a given set of data, the goodness of fit of the regression model is judged by the coefficient of determination R 2 and is calculated by Equation (8):

[0125]

[0126] In the formula, is the correlation coefficient; represents the sum of squared residuals; represents the total sum of squared deviations;

[0127] The coefficient of determination R 2 has a value between 0 and 1. The closer it is to 1, the better the prediction variable explains the response variable in the regression analysis. R 2 = 0.9 means that 90% of the total variability of the response variable is caused by the prediction variable.

[0128] There is a very significant quadratic polynomial relationship between the driving speed and the fitting parameters of the lateral acceleration, and R 2 is close to 1. Similar conclusions can be drawn for the regression functions of other post-earthquake driving performance indicators. This indicates that the driving speed is another important factor affecting the post-earthquake driving performance indicators. Considering the driving speed independently outside the track regularity quantification index is more conducive to establishing a mapping relationship with high accuracy and wide applicability between the post-earthquake irregularity and the driving performance indicators. The relationship between the expression parameters for fitting this mapping relationship and the driving speed V is expressed by the following formula:

[0129]

[0130] In the formula, ξ i , θ i , μ i represent the quadratic coefficient matrix, and λ i , η i , ν i represent the linear coefficient matrix; δ i , ω i represent the constant term matrix.

[0131] S4: Quantify the driving performance index limit that guarantees the safety margin to obtain the post-earthquake driving speed threshold that guarantees the safety margin, specifically including:

[0132] The steps to quantify the driving performance index limit that guarantees the safety margin include:

[0133] Let \(x_0\) be a specified value of the predictor variable \(x\), and use the regression model to calculate the value of the empirical regression function corresponding to \(x_0\). From the sum of squared residuals \(Q_e\) and being independent of each other, we obtain

[0134]

[0135] where \(Y_0\) represents the true value; represents the residual standard deviation; the sum of squares of the independent variables

[0136] For a given confidence level \(1 - \alpha\), we have

[0137]

[0138] where \(P\) represents the probability of the entire event occurring; \(\sigma\) represents the standard deviation of the regression model error; \(t\) α / 2 represents the critical value of the \(t\)-distribution;

[0139] From equation (11), we get The prediction interval of is:

[0140]

[0141] When the sample size \(n>30\) and \(x_0\) is close to at this time, equation (12) simplifies to:

[0142]

[0143] where \(z\) α / 2 represents the standard normal distribution;

[0144] Combining equation (2) and equation (13), the calculation formula for the limit value of the post-earthquake driving index to ensure the safety margin is as follows:

[0145]

[0146] where represents the residual standard deviation;

[0147] Use equation (14) to calculate the limit values of various driving performance indicators in CRTS II and CRTS III slab ballastless tracks.

[0148] Taking the significance level α = 0.05, with the train speeds being 100, 150, 200, 250, 300, and 350 km / h, the predicted values of the limit values of various train operation performance indicators in CRTS II and CRTS III slab ballastless tracks are calculated using Equation (14), and compared with the values of various train operation performance indicators calculated based on TTBCSM. Taking the simulation values of various train operation performance indicators as the abscissa and the predicted values as the ordinate, scatter plots of simulation values - predicted values are plotted, and it is obtained that the scatter points of various train operation performance indicators are relatively concentrated and mainly distributed in the upper part of the area close to the perfect prediction line (y = x), which indicates that the prediction model established in this embodiment can effectively predict the train operation performance indicators after an earthquake and has sufficient safety margins.

[0149] When the train runs on the bridge, the car body will vibrate under the excitation of track irregularities. When the vibration of the car body exceeds a certain limit, it will have an adverse impact on the safety and comfort of train operation. According to the relevant requirements of the "Code for Design of High-Speed Railway" (TB10621 - 2014) for vehicle-bridge coupling vibration, in this embodiment, the derailment coefficient, wheel load reduction rate, and lateral wheel-rail force are used as the safety indicators for train operation, and the lateral acceleration of the car body and Sperling are used as the comfort indicators for train operation.

[0150] The steps for calculating the post-earthquake train operation speed threshold to ensure the safety margin include:

[0151] Using the derailment coefficient, wheel load reduction rate, and lateral wheel-rail force as the safety indicators for train operation, and the lateral acceleration of the car body and Sperling as the comfort indicators for train operation,

[0152] Based on the limit requirements of vehicle operation performance indicators and Equation (14), the following formula for solving the post-earthquake train operation speed threshold on the bridge is proposed:

[0153]

[0154] Solving Equation (15), the following expression for the speed threshold based on post-earthquake train operation safety performance indicators is obtained:

[0155]

[0156] In the formula, V II_1 represents the post-earthquake train operation speed threshold of the II-type slab ballastless track based on train operation safety indicators, and V III_1 represents the post-earthquake train operation speed threshold of the III-type slab ballastless track based on train operation safety indicators;

[0157] In addition, the equations involved in the speed threshold expression based on the ride comfort index are relatively complex, and it is difficult to obtain an explicit expression. Therefore, a program is written in MATLAB for numerical solution. A quadratic power function is used to fit the solution results, and the speed threshold expression based on the post-earthquake ride comfort performance index is obtained as shown below:

[0158]

[0159] In the formula, V II_2 represents the post-earthquake driving speed threshold of the type-II slab ballastless track based on the ride comfort index; V III_2 represents the post-earthquake driving speed threshold of the type-III slab ballastless track based on the ride comfort index.

[0160] To verify the effectiveness of the research results of this embodiment, 10 earthquake records are randomly selected from the PEER strong motion database, and the post-earthquake track irregularities are utilized by TBSSM. The predicted values and simulation values of the post-earthquake driving performance indexes at different vehicle speeds are calculated by using Equation (14) and TTBCSM respectively, and the predicted value-simulation value scatter plot is drawn. The scatter points of each driving performance index are mainly concentrated on the upper side of the perfect prediction line (y = x), indicating that the prediction model can effectively predict the post-earthquake driving performance indexes, and the model has a reasonable safety margin during prediction.

[0161] In addition, the post-earthquake driving speed threshold curves are calculated by using Equation (16) and Equation (17), and the post-earthquake driving safety area and dangerous area are divided with the threshold curves as the boundary. The post-earthquake driving performance indexes are calculated based on TTBCSM, and the driving performances of 10 earthquake records at different vehicle speeds are evaluated. The calculation results are as Figure 2 and Figure 3 , where the five-pointed star symbols with × represent that the calculation results of the train-track-bridge system model exceed the limit, and the five-pointed star symbols without × represent that the results do not exceed the limit. From the calculation results, it can be seen that in the CRTS II and CRTS III type slab ballastless track systems, except for a few scattered points (five-pointed star symbols) of the post-earthquake driving performance that do not exceed the limit and are distributed in the prohibited dangerous area, the vast majority of the scattered points that exceed the limit and do not exceed the limit are respectively distributed in the safe area and the dangerous area. This indicates that the calculation method proposed in this embodiment can effectively evaluate the post-earthquake driving speed threshold and can provide a scientific basis for the post-earthquake safety operation and maintenance of high-speed railway bridges.

[0162] 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 driving speed threshold of a high-speed railway bridge is implemented.

[0163] Exemplarily, the computer program may be divided into one or more modules / units, and the one or more modules / units are stored in the memory and executed by the processor to implement the present invention. The one or more modules / units may 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.

[0164] This embodiment further includes an electronic device, comprising: at least one processor, at least one memory, and computer program instructions stored in the memory, where when the computer program instructions are executed by the processor, the above-mentioned method for calculating the post-earthquake driving speed threshold of a high-speed railway bridge is implemented.

[0165] The electronic device may be a computing device such as a mobile phone, a desktop computer, a notebook, a palm 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.

[0166] The foregoing are only the 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 method for calculating the driving speed threshold of a high-speed railway bridge after an earthquake, characterized in that, It includes the following steps: S1: Establish a three-dimensional non-linear dynamic simulation model TBSSM of the high-speed railway track-bridge system and a train-track-bridge coupling system model TTBCSM of the high-speed railway; S2: Propose a quantification index for post-earthquake track irregularity applicable to CRTS II and CRTS III track types; S3: Establish a mapping relationship between the quantification index of post-earthquake track irregularity and the post-earthquake train operation performance index, and fit the relationship between the expression parameters of this mapping relationship and the train operation speed; S4: Quantify the limit value of the train operation performance index to ensure a safety margin, and obtain the post-earthquake train operation speed threshold to ensure a safety margin.

2. The method for calculating the post-earthquake train running speed threshold of a high-speed railway bridge according to claim 1, wherein The said S2 includes: Taking CRTS II and CRTS III slab ballastless tracks as objects, use TBSSM to calculate the post-earthquake track irregularity under earthquake ground motion; Ignore the post-earthquake gauge, alignment, and cross-level irregularities and use the post-earthquake track irregularity to replace the alignment irregularity; Propose the track irregularity root mean square change rate index TIC applicable to CRTS II and CRTS III slab track rms As the post-earthquake track irregularity quantification index, and consider the train speed into the fitting function parameters of TIC rms and the train operation performance index; Let the post-earthquake track irregularity be A(x), where x represents the track mileage range, and the post-earthquake track irregularity quantization index TIC is calculated rms , and the calculation method is as follows: In the formula, l represents the total mileage of the rail.

3. The method for calculating the post-earthquake train running speed threshold of a high-speed railway bridge according to claim 2, characterized in that, The steps for establishing the mapping relationship between the quantification index of post-earthquake track irregularity and the post-earthquake train operation performance index in the said S3 are as follows: Input the post-earthquake track irregularity into TTBCSM to calculate the post-earthquake train operation performance indicators at different vehicle speeds; conduct a correlation analysis between TIC rms and the train operation performance indicators at different vehicle speeds to obtain the Pearson correlation coefficient r rms between TIC p and different train operation performance indicators, and the Spearman rank correlation coefficient ρ s ; for the train operation performance indicators where both r p and ρ s can reach above 0.95, use a linear model regarding TIC rms to express them. For the train operation performance indicators where r p is less than 0.8 but ρ s is greater than 0.95, use a non-linear model regarding TIC rms to express them; The TIC is respectively subjected to regression analysis with various driving performance indicators at different vehicle speeds rms and the mapping relationships between the TIC rms and each post-earthquake driving performance indicator are expressed as follows: In the formula, i represents the type of ballastless track, i = II, III; DPI i represents the train operation performance index matrix; a i represents the fitting curve coefficient matrix; b i represents the fitting curve power matrix; c i represents the fitting curve intercept matrix; ⊙ represents the Hadamard product; The matrix composition form is as shown below: where a y represents the lateral acceleration of the car body; ΔPP represents the wheel load reduction rate; QP represents the derailment coefficient; SP y represents the lateral Sperling; Q y represents the lateral wheel-rail force; a1, a2…a5 represent the coefficients corresponding to the post-earthquake train operation performance indicators, c1, c2…c5 represent the intercepts of the post-earthquake train operation performance indicators; b4 represents the power of the lateral Sperling index.

4. The method for calculating the post-earthquake driving speed threshold of a high-speed railway bridge according to claim 3, wherein, The said regression analysis includes: Simple linear regression analysis simulates the relationship between two variables by fitting a linear equation of the data, which is expressed by the following formula: Y = β0 + β1X + ε, ε ~ N(0, σ 2 ) 3); Wherein, Y is the response variable; X is the predictive variable; β0 and β1 are the regression parameter and the regression coefficient respectively; ε is the random error, representing the difference between the predicted data and the true data; ε~N(0,σ 2 ) indicates that the error term follows a normal distribution with a mean of 0 and a variance of σ 2 ; The predicted value form of formula (3) is as shown in formula (4): In the formula, is the predicted value of the response variable; and are the estimated values of the regression parameter and the regression coefficient, respectively, estimated by the maximum likelihood estimation method, as shown in Equation (5): Where n represents the sample size; represents the sample mean of the dependent variable; represents the sample mean of the independent variable; X i represents the value of the independent variable at the i-th observation point; Y i represents the value of the dependent variable at the i-th observation point; Simple non-linear regression analysis also uses a function to describe the relationship between the response variable and the predictor variable, and the form of the function is expressed by formula (6): Y = f(X,β) + ε, ε ~ N(0,σ 2 ) 6); where \(f(X, eta)\) is the mean function; \(eta=(eta_1,\ldots,eta k )\) represents the regression coefficients with \(k\) unknown parameters; For a set of observed data \((x_1,y_1),\ldots,(x n ,y n ), Equation (6) applies to the ideal case where the response variable has no error, and Equation (6) is represented by the mean function shown in Equation (7): Wherein, is the estimated value of the regression coefficient; Non-linear regression analysis should define the function based on the scatter distribution of the data or use a known model; For a given set of data, the fitting quality of the regression model is judged by the coefficient of determination R 2 and is calculated by Equation (8): In the formula, is the correlation coefficient; represents the sum of squared residuals; represents the total sum of squared deviations; Coefficient of determination R 2 has a value between 0 and 1. The closer it is to 1, the better the explanatory power of the predictor variable for the response variable in the regression analysis. R 2 = 0.9 indicates that 90% of the total variability of the response variable is caused by the predictor variable.

5. The method for calculating the post-earthquake train running speed threshold of a high-speed railway bridge according to claim 4, wherein The relationship between the expression parameters of the mapping relationship in the said S3 and the train operation speed V is as follows: In the formula, ξ i , θ i , μ i represent the quadratic coefficient matrix, and λ i , η i , ν i represent the linear coefficient matrix; δ i , ω i represent the constant term matrix.

6. The method for calculating the post-earthquake train running speed threshold of a high-speed railway bridge according to claim 5, wherein, The steps for quantifying the limit value of the train operation performance index to ensure a safety margin include: Let \(x_0\) be a specified value of the predictor variable \(x\), and use the regression model to calculate the value of the empirical regression function corresponding to \(x_0\). From the sum of squared residuals \(Q_e\) and being independent of each other, we obtain In the formula, Y0 represents the true value; represents the residual standard deviation; the sum of squares of the independent variables For a given confidence level 1-α, there is Wherein, P represents the probability of the occurrence of the entire event; σ represents the standard deviation of the regression model error; t α / 2 represents the critical value of the t-distribution; Obtained from Equation (11) The prediction interval is: When the sample size n > 30 and x0 is close to , Equation (12) is simplified to: where z α / 2 represents a standard normal distribution; Combining formula (2) and formula (13), the calculation formula for the limit value of the post-earthquake train operation index to ensure a safety margin is obtained as follows: In the formula, represents the residual standard deviation; Use formula (14) to calculate the limit values of various train operation performance indexes in CRTS II and CRTS III slab ballastless tracks.

7. The method for calculating the post-earthquake train running speed threshold of a high-speed railway bridge according to claim 6, wherein The steps for calculating the post-earthquake train operation speed threshold to ensure a safety margin include: Use the derailment coefficient, wheel load reduction rate, and lateral wheel-rail force as the safety indexes for train operation, and use the lateral car body acceleration and Sperling as the comfort indexes for train operation. Based on the requirements of the limit values of vehicle operation performance indexes and formula (14), the solution formula for the post-earthquake train operation speed threshold on the bridge is proposed as follows: Solve formula (15) to obtain the speed threshold expression based on the post-earthquake train operation safety performance index as follows: In the formula, V II_1 represents the post-earthquake train running speed threshold of the type-II slab trackless ballastless track based on the train running safety index, and V III_1 represents the post-earthquake train running speed threshold of the type-III slab trackless ballastless track based on the train running safety index; Use a quadratic power function to fit the solution result to obtain the speed threshold expression based on the post-earthquake train operation smoothness performance index as follows: Where, V II_2 represents the post-earthquake train operation speed threshold of the type-II slab trackless ballastless track based on the train operation smoothness index; V III_2 represents the post-earthquake train operation speed threshold of the type-III slab trackless ballastless track based on the train operation smoothness index.

8. A readable storage medium, characterized in that, It stores computer program instructions, and when the said computer program instructions are executed by a processor, it implements the method for calculating the post-earthquake train operation speed threshold of a high-speed railway bridge as described in any one of claims 1 to 7.

9. An electronic device, characterized in that, It includes: At least one processor, at least one memory, and computer program instructions stored in the said memory, and when the said computer program instructions are executed by the processor, it implements the method for calculating the post-earthquake train operation speed threshold of a high-speed railway bridge as described in any one of claims 1 to 7.

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