A reliability analysis method for the void length of mortar filling layer in an in-service bridge-ballastless track system

Abstract

The present invention discloses a reliability analysis method for the de-gap length of the mortar filling layer of an in-service bridge-ballastless track system, respectively establishing a train sub-model and a track-bridge sub-model considering the de-gap of the mortar filling layer, assembling them into a train-track-bridge coupling dynamics model through the wheel-rail contact relationship and verifying them; then, the coupling dynamics model calculation is carried out based on the Design-Expert software and the Box-Behnken method, and then a nonlinear mapping model of the wheel-rail system is established based on the support vector regression principle, and learning, prediction and verification are carried out; finally, based on the established nonlinear mapping model of the wheel-rail system and the Latin hypercube sampling method, the reliable probability of the distribution of the train and structural response index amplification coefficient in different ranges is obtained, and the limit value of the de-gap length of the mortar filling layer is obtained. The vehicle-track-bridge coupling dynamics model established by the present invention is accurate and reliable, the nonlinear mapping model of the wheel-rail system has high fitting accuracy, significant calculation efficiency, and good applicability and application value.

Description

Technical Field

[0001] The invention relates to a study on track diseases of a high-speed railway track system, and in particular to a reliability analysis method for the void length of a mortar filling layer of an in-service bridge-ballastless track system. Background Art

[0002] Under the general background of "bridges replacing roads" in high-speed railways, bridges on lines under special geological and extreme climatic conditions will inevitably produce pier settlement, which will cause additional deformation of the bridges; and during the long-term service of the line, the track structure on the bridge will also produce random track diseases, such as interlayer gaps, voids and arching. Both additional deformation of the bridge and track diseases will cause changes in the track bearing mode and the force transmission mechanism of interlayer components. When the train passes, these changes will cause the driving quality to deteriorate, and in severe cases, they will even endanger driving safety and cause immeasurable consequences. Therefore, in order to minimize the risk of unacceptable failure of the structure, it is necessary to consider the randomness of damage forms and mechanical parameters when determining the damage limit.

[0003] In recent years, there have been many studies on the effects of pier settlement and interlayer damage on the train-track-bridge system. These studies can be summarized into two forms: one is to determine the damage limit based on the vehicle-bridge coupled vibration, and the other is to obtain the damage limit based on reliability theory analysis. Generally speaking, compared with the limit determined directly based on the vehicle-bridge coupled vibration, the limit based on reliability theory analysis is more reasonable. It takes the uncertainty of the structural resistance and load into the scope of research and consideration, thereby calculating a dynamic index with time-varying characteristics, namely the reliability index. However, considering randomness requires tens of thousands of calculations, which is huge and arduous. In addition, the current research on the effects of pier settlement and interlayer damage on the train-track-bridge system still has the following two problems: 1) Current research rarely considers the effects of pier settlement, track diseases and random changes in interlayer component stiffness, which makes the analysis of the dynamic response of the train-track-bridge system not comprehensive enough; 2) Most existing studies use the train-track-bridge system dynamics model. The formula established under this model is time-consuming and inefficient to solve, which is not conducive to research progress. Summary of the invention

[0004] In view of the above-mentioned problems, the present invention provides a reliability analysis method for the de-spacing length of the mortar filling layer of an in-service bridge-ballastless track system. The train-CRTSⅡ type slab ballastless track-bridge is taken as the research object, and a train-track-bridge system dynamic model including pier settlement and mortar de-spacing is established. The fastener stiffness, mortar elastic modulus, mortar de-spacing length and randomness of pier settlement are considered, and the support vector regression (SVR) theory is introduced to establish a mapping relationship between the mortar de-spacing length and the dynamic response of the high-speed train-track-bridge system; finally, based on the reliability theory, a control standard for the limit value of the mortar filling layer length is proposed. The specific technical scheme is as follows:

[0005] A reliability analysis method for the void length of a mortar filling layer of an in-service bridge-ballastless track system comprises the following steps:

[0006] S1: Establish a train-track-bridge coupled dynamics model: Establish a train sub-model based on multi-body dynamics theory; establish a ballastless track-bridge sub-model based on finite element theory; and assemble the train sub-model and the ballastless track-bridge sub-model based on the wheel-rail contact relationship to obtain a train-track-bridge coupled dynamics model;

[0007] S2: Model verification: verify the correctness of the established train-track-bridge coupling dynamic model;

[0008] S3: Obtain samples: Select fastener stiffness, mortar elastic modulus, mortar void length and fastener stiffness as random variables; adopt the Box-Behnken test design method and obtain SVR test point samples based on Design-Expert software;

[0009] S4: Establishing a wheel-rail dynamic system mapping model: Based on the SVR principle, using the SVR test point samples obtained in step S3, a dynamic nonlinear mapping model of the train-track-bridge system, i.e., a wheel-rail dynamic system mapping model, is established, and the model is trained and verified to ensure the reliability of the model;

[0010] S5: Parameter sensitivity analysis: define the sensitivity coefficients of random variables to the vertical acceleration of the vehicle body, vertical wheel-rail force, wheel-load reduction rate, vertical displacement of the rail and vertical displacement of the track plate; analyze the sensitivity of the vertical acceleration of the vehicle body, vertical wheel-rail force, wheel-load reduction rate, vertical displacement of the rail and vertical displacement of the track plate to the mortar void length; determine the research object for analyzing the reliability of the mortar void length;

[0011] S6: Control standard limits for mortar void length at different levels: Based on the reliability theory, the reliability probability when the dynamic response amplification factor is greater than a certain value is used as the basis for dividing the control standard for mortar void length, and the mortar void length value corresponding to the amplification factor is used as the control limit; then, the wheel-rail dynamic system mapping model is used to calculate the mortar void length limit under different levels of control standards.

[0012] As a preferred technical solution, in step S1, the train sub-model is established in MATLAB, which consists of a car body, 2 bogies and 4 wheel pairs; the suspension system between the car body, bogies and wheelsets is simulated by spring-damper units; the car body and two bogies consider 5 degrees of freedom: lateral movement, heave, roll, nod and shake of the head, and each wheelset considers 4 degrees of freedom: lateral movement, heave, roll and shake of the head, and it is assumed that the car body, frame and wheelset are rigid bodies.

[0013] As a preferred technical solution, in step S1, the ballastless track-bridge sub-model is established in ANSYS; wherein the ballastless track is mainly composed of rails, fasteners, track plates, CA mortar layers, base plates and "two cloths and one membrane" sliding layers; the rails, track plates, base plates and bridges are all simulated by beam units; the fasteners and CA mortar layers are simulated by spring-damping units; and the sliding layer is simulated by a unidirectional compression spring.

[0014] As a preferred technical solution, in step S1, the specific steps of assembling the train sub-model and the ballastless track-bridge sub-model based on the wheel-rail contact relationship to obtain the train-track-bridge coupled dynamics model are as follows:

[0015] S1-1: Perform modal analysis on the ballastless track-bridge sub-model and obtain the .full binary file containing the overall mass, stiffness and damping matrix of the sub-model;

[0016] S1-2: Use HBMAT command to convert the binary file into Harwell-Boeing file, and convert it into sparse matrix form through Python; use HBMAT to extract the locations of mass, stiffness and damping matrix nodes in the binary file and generate .Mapping file;

[0017] S1-3: Using the wheel-rail contact relationship, the .Mapping file and sparse matrix of the ballastless track-bridge sub-model are linked with the train sub-model to establish the train-track-bridge coupled dynamic model.

[0018] Further preferably, in the established train-track-bridge coupling dynamic model, the wheel-rail normal force is simulated by Hertz contact, and the wheel-rail lateral force takes creep force into consideration.

[0019] As a preferred technical solution, in step S2, the model verification requires that the calculation results of the constructed model are compared with the calculation results of the comparison model, and the vertical displacement change trends of the rails at the beam ends and mid-span are basically consistent, and the maximum amplitude error does not exceed 5%.

[0020] As a preferred technical solution, in step S3, the random variables, among which: the pier settlement is 2 to 10 m and is uniformly distributed; the mortar void length is 3 to 5 m and is uniformly distributed; the fastener stiffness is subject to a truncated normal distribution, with a mean of 30 and a standard deviation of 23.33; the mortar elastic modulus is subject to a normal distribution, with a mean of 8500 and a standard deviation of 500.

[0021] As a preferred technical solution, in step S4, the wheel-rail dynamic system mapping model uses random variables fastener stiffness, mortar elastic modulus, mortar void length and fastener stiffness as input samples, and wheel-rail dynamic response as output samples; the input and output samples are normalized; a part of the SVR test point samples are used as sample data for modeling, and the remaining SVR test point samples are used to verify the established wheel-rail dynamic system mapping model.

[0022] As a preferred technical solution, in step S5, in the parameter sensitivity analysis, when calculating the sensitivity coefficient of a certain random variable, the remaining random variables are taken as initial values; the initial values ​​of fastener stiffness, mortar elastic modulus, mortar void length and pier settlement are taken as 20mm, 7000MPa, 3m and 2mm respectively.

[0023] As a preferred technical solution, in step S6, the different levels of control standard limits for the mortar void length are: the state when the reliable probability that the dynamic response amplification factor of the wheel-rail system is greater than a certain value is 50%, 30% and 10% is evaluated as level I, level II and level III mortar void length control standards.

[0024] The beneficial effects of the present invention are as follows:

[0025] 1) The wheel-rail system dynamic response mapping model established by the present invention using the support vector regression (SVR) principle has high fitting accuracy. The SVR nonlinear mapping model established by the present invention has high fitting accuracy, reaching 0.993; compared with the existing analysis method, the calculation speed of the wheel-rail system dynamic response prediction method is increased by 99.86%, and the calculation efficiency is significant.

[0026] 2) The present invention takes into account the pier settlement, track disease (the length of the mortar filling layer voids) and the randomness of the interlayer component stiffness changes, studies the impact of pier settlement and interlayer damage on the train-track-bridge system, and further comprehensively analyzes the dynamic response of the train-track-bridge system to ensure train driving safety.

[0027] 3) The analysis method of the present invention verifies that the pier settlement has the most significant impact on the vertical acceleration of the vehicle body, while the sensitivity of the mortar void length to the wheel-rail vertical force, wheel weight reduction rate, rail vertical displacement and track plate vertical displacement is significantly greater than other influencing factors, laying a foundation for further research.

[0028] 4) According to the analysis of the method of the present invention, when the train speed is in the range of 250-350 km / h, the limit values ​​of level I, II and III of the mortar void length are 3.932, 4.337 and 4.766 mm respectively, which effectively provides a more accurate and safe limit threshold for the reliability of the void length of the mortar filling layer of the in-service bridge-ballastless track system.

[0029] 5) The train-track-bridge coupling dynamic model established in the present invention is not only suitable for the reliability analysis of the void length of the mortar filling layer, but can also be appropriately improved and used for other track diseases, and has good applicability and promotion value. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is a schematic diagram of the structure of the high-speed train-track-bridge coupling dynamic model considering the pier settlement and mortar degassing of the present invention;

[0031] Figure 2 The comparison and verification results of the model of the present invention and the model in the literature;

[0032] Wherein: (a) is the vertical displacement of the rail at the end of the beam of the model of the present invention, (b) is the vertical displacement of the rail at the mid-span of the model of the present invention; (c) is the vertical displacement of the rail at the end of the beam of the model of the literature, (d) is the vertical displacement of the rail at the mid-span of the model of the literature;

[0033] Figure 3 is the amplification factor result of the maximum value of the dynamic response of the wheel-rail system of the present invention;

[0034] Among them: (a) is the dynamic response of the vehicle system; (b) is the dynamic response of the track system;

[0035] Figure 4 The linear regression function, loss function and network structure diagram of the support vector machine of the present invention;

[0036] Among them: (a) is the linear regression function of the support vector machine; (b) is the loss function of the support vector machine; (c) is the network structure diagram of the support vector machine;

[0037] Figure 5 It is the SVR parameter selection result of the present invention;

[0038] Among them: (a) is the vehicle contour map; (b) is the three-dimensional spatial distribution map;

[0039] Figure 6 is the SVR prediction result of the present invention;

[0040] Figure 7 is the SVR prediction error of the present invention

[0041] Figure 8 is the sensitivity of the random variable of the present invention to the wheel-rail dynamic response;

[0042] Fig. 9 is a probability density distribution diagram of the dynamic response of the wheel-rail system of the present invention;

[0043] Where: (a) is the vertical acceleration of the vehicle body, (b) is the vertical force of the wheel-rail, (c) is the wheel load reduction rate, (d) is the vertical displacement of the rail, and (e) is the vertical displacement of the track plate;

[0044] Fig.10 is the cumulative probability of the dynamic response of the wheel-rail system of the present invention;

[0045] Where: (a) is the vertical acceleration of the vehicle body, (b) is the vertical force of the wheel-rail, (c) is the wheel load reduction rate, (d) is the vertical displacement of the rail, and (e) is the vertical displacement of the track plate;

[0046] Fig.11 This is the classification of the mortar void length control standard of the present invention. DETAILED DESCRIPTION

[0047] The following will be combined with the embodiments and drawings to clearly and completely describe the technical solution of the present invention. Obviously, the described embodiments are only preferred embodiments of the present invention, not all embodiments, and are not intended to limit the present invention in other forms. Any technician familiar with the profession may use the disclosed technical content to make changes or modifications. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.

[0048] Example 1

[0049] This embodiment is a reliability analysis method for the void length of the mortar filling layer of an in-service bridge-ballastless track system, comprising the following steps:

[0050] S1: Establish a train-track-bridge coupled dynamics model: Establish a train sub-model based on multi-body dynamics theory; establish a ballastless track-bridge sub-model based on finite element theory; and assemble the train sub-model and the ballastless track-bridge sub-model based on the wheel-rail contact relationship to obtain a train-track-bridge coupled dynamics model. Among them:

[0051] The train sub-model is established in MATLAB, which consists of a car body, two bogies and four wheel sets; the suspension system between the car body, bogies and wheelsets is simulated by spring-damper units; the car body and two bogies consider five degrees of freedom: lateral movement, heave, roll, nod and shake, and each wheelset considers four degrees of freedom: lateral movement, heave, roll and shake, and it is assumed that the car body, frame and wheelsets are all rigid bodies.

[0052] The ballastless track-bridge sub-model is established in ANSYS; the ballastless track is mainly composed of rails, fasteners, track plates, CA mortar layers, base plates and "two cloths and one membrane" sliding layers; the rails, track plates, base plates and bridges are all simulated by beam units; the fasteners and CA mortar layers are simulated by spring-damper units; the sliding layer is simulated by a unidirectional compression spring.

[0053] The train-track-bridge coupling dynamics model is obtained by assembling the train sub-model and the ballastless track-bridge sub-model based on the wheel-rail contact relationship, wherein the wheel-rail normal force is simulated by Hertz contact, and the wheel-rail lateral force takes creep force into consideration; the specific steps are as follows:

[0054] S1-1: Perform modal analysis on the ballastless track-bridge sub-model and obtain the .full binary file containing the overall mass, stiffness and damping matrix of the sub-model;

[0055] S1-2: Use HBMAT command to convert the binary file into Harwell-Boeing file, and convert it into sparse matrix form through Python; use HBMAT to extract the locations of mass, stiffness and damping matrix nodes in the binary file and generate .Mapping file;

[0056] S1-3: Using the wheel-rail contact relationship, the .Mapping file and sparse matrix of the ballastless track-bridge sub-model are linked with the train sub-model to establish the train-track-bridge coupled dynamic model.

[0057] S2: Model verification: Verify the correctness of the established train-track-bridge coupling dynamic model; the calculation results of the established model are required to be basically consistent with the calculation results of the comparative model published in the existing literature, and the vertical displacement change trends of the rails at the beam ends and mid-span are basically consistent, and the maximum amplitude error does not exceed 5%.

[0058] S3: Obtain samples: Select fastener stiffness, mortar elastic modulus, mortar void length and fastener stiffness as random variables; among them: the pier settlement is 2-10m and obeys uniform distribution; the mortar void length is 3-5m and obeys uniform distribution; the fastener stiffness obeys truncated normal distribution, with a mean of 30 and a standard deviation of 23.33; the mortar elastic modulus obeys normal distribution, with a mean of 8500 and a standard deviation of 500. Then, the Box-Behnken test design method is used to obtain SVR test point samples based on Design-Expert software.

[0059] S4: Establish a wheel-rail dynamic system mapping model: Based on the SVR principle, the random variables fastener stiffness, mortar elastic modulus, mortar void length and fastener stiffness are used as input samples, and the wheel-rail dynamic response is used as output samples; the input and output samples are normalized; a part of the SVR test point samples obtained are used as sample data for modeling to obtain the dynamic nonlinear mapping model of the train-track-bridge system, that is, the wheel-rail dynamic system mapping model; and the remaining SVR test point samples are used to verify the constructed model to ensure the reliability of the model.

[0060] S5: Parameter sensitivity analysis: define the sensitivity coefficients of random variables to the vertical acceleration of the vehicle body, vertical wheel-rail force, wheel-load reduction rate, vertical displacement of the rail and vertical displacement of the track plate respectively; analyze the sensitivity of the vertical acceleration of the vehicle body, vertical wheel-rail force, wheel-load reduction rate, vertical displacement of the rail and vertical displacement of the track plate to the mortar void length; when calculating the sensitivity coefficient of a random variable, the remaining random variables are taken as initial values; the initial values ​​of fastener stiffness, mortar elastic modulus, mortar void length and pier settlement are taken as 20mm, 7000MPa, 3m and 2mm respectively. The wheel-rail vertical force, wheel-load reduction rate, vertical displacement of the rail and vertical displacement of the track plate are determined as the research objects through calculation.

[0061] S6: Control standard limits for mortar void length at different levels: Based on the reliability theory, the reliability probability when the dynamic response amplification factor is greater than a certain value is used as the basis for dividing the control standard for mortar void length, and the mortar void length value corresponding to the amplification factor is used as the control limit; then, the wheel-rail dynamic system mapping model is used to calculate the mortar void length limit under different levels of control standards.

[0062] Next, the above analysis method is explained in detail with examples:

[0063] 1. Establish a dynamic model of the train-track-bridge system considering pier settlement and interlayer damage

[0064] A train-track-bridge coupling dynamic model considering bridge pier settlement and track damage (taking mortar degassing as an example) is established. Figure 1As shown, the modeling process is as follows:

[0065] 1.1 Model establishment

[0066] 1.1.1 Train sub-model

[0067] In MATLAB, the mass, damping and stiffness matrices of the train are assembled based on the multi-body dynamics theory. The train sub-model consists of a car body, two bogies and four wheel sets. The suspension system between the car body, bogies and wheel sets is simulated using spring-damper units. The car body and two bogies consider five degrees of freedom: lateral movement, heave, roll, nod and shake. Each wheel set considers four degrees of freedom: lateral movement, heave, roll and shake. It is assumed that the car body, frame and wheel sets are all rigid bodies. The train sub-model motion equation is:

[0068]

[0069] Where: M v , C v , K v and U v are the mass matrix, damping matrix, stiffness matrix and displacement vector of the train sub-model respectively; F g and F w are the train’s own weight vector and wheel-rail force vector respectively.

[0070] 1.1.2 Ballastless track-bridge sub-model

[0071] In ANSYS, a ballastless track-bridge sub-model is established based on finite element theory. The ballastless track is mainly composed of rails, fasteners, track plates, CA mortar layers, base plates and "two fabrics and one membrane" sliding layers. The rails, track plates, base plates and bridges are simulated by beam units, the fasteners and CA mortar layers are simulated by spring-damper units, and the sliding layer is simulated by unidirectional compression springs. The motion equation of the ballastless track-bridge sub-model is:

[0072]

[0073] Where: M tb , C tb , K tb and U tb are the mass matrix, damping matrix, stiffness matrix and displacement vector of the track-bridge sub-model respectively.

[0074] 1.1.3 Wheel-rail contact relationship assembly

[0075] The train-track-bridge coupling dynamic model is assembled based on the wheel-rail contact relationship. The specific steps are as follows: First, perform modal analysis on the ballastless track-bridge sub-model to obtain the .full binary file containing the overall mass, stiffness and damping matrix of the sub-model; then, use the HBMAT command to convert the binary file into a Harwell-Boeing file, and convert it into a sparse matrix form through Python; at the same time, use HBMAT to extract the positions of the mass, stiffness and damping matrix nodes in the binary file, and generate a .Mapping file; further, use the wheel-rail contact relationship to link the .Mapping file and sparse matrix of the ballastless track-bridge sub-model with the train sub-model to establish the train-track-bridge coupling dynamic model, the wheel-rail normal force is simulated by Hertz contact, and the wheel-rail lateral force considers the creep force.

[0076] 1.3 Model Validation

[0077] In order to verify the correctness of the above model, the model published by Pan Peng, Lei Xiaoyan, Zhang Pengfei et al. in "Dynamic Response Analysis of Ballastless Track on Bridge under Braking Load" (Journal of Railway Science and Engineering, 2017, 14(11): 2309-2322) was used as a comparison model to verify the constructed train-track-bridge coupling dynamic model. The verification results are shown in 1 and Figure 2 .

[0078] Table 1. Comparison and verification of the model constructed in this embodiment and the comparative model

[0079]

[0080] From Table 1 and Figure 2 It can be seen that compared with the calculation results of the comparative model, the calculation results of the model established in this embodiment have basically the same trend in the vertical displacement change of the rail at the beam end and the mid-span, and the maximum amplitude error does not exceed 5%, indicating that the train-track-bridge coupling dynamic model established in this embodiment is correct; the reason for the slight difference is that the driving speed in the comparative model is uniformly decelerated from 200km / h to 0, and the braking force of the train is considered at the same time, while the train in the model established in this embodiment has been running at a uniform speed of 200km / h.

[0081] 2. Nonlinear mapping model of wheel-rail dynamic system based on SVR

[0082] 2.1 Random variables

[0083] The fastener stiffness (A), mortar elastic modulus (B), mortar void length (C) and pier settlement (D) are selected as random variables. The pier settlement is 2 to 10 m and obeys a uniform distribution; the mortar void length is 3 to 5 m and obeys a uniform distribution; the fastener stiffness obeys a truncated normal distribution with a mean of 30 and a standard deviation of 23.33; the mortar elastic modulus obeys a normal distribution with a mean of 8500 and a standard deviation of 500.

[0084] 2.2 Training Samples

[0085] The Box-Behnken experimental design method is used for experimental point design, and the number of experimental points is:

[0086] N=2k(k-1)+C0 (3)

[0087] Where: N is the number of SVR test points, k is the number of random variables, and C0 is the number of repetitions of the central test.

[0088] In this embodiment, the number of selected design variables is 4 (fastener stiffness (A), mortar elastic modulus (B), mortar void length (C) and pier settlement (D)), the number of central test repetitions is 1, so the number of test points is 25. The test data designed based on Design-Expert software is shown in Table 2.

[0089] Table 2. Box-Behnken test protocol

[0090]

[0091] Based on the above test data, the train-track-bridge system dynamics calculations were carried out at speeds of 250, 300 and 350 km / h. The ratio of the maximum system dynamic response when there is pier settlement and mortar degassing to the maximum system dynamic response when there is no pier settlement and mortar degassing is defined as the dynamic response amplification factor. The results are as follows: Figure 3 shown.

[0092] analyze Figure 3 It can be seen that the order of the system dynamic response amplification coefficient is: vertical displacement of track plate > vertical displacement of rail > vertical acceleration of vehicle body > wheel load reduction rate > wheel-rail vertical force.

[0093] 2.3 Basic Principles of SVR

[0094] like Figure 4 As shown, the basic principle of ε-SVR is: given n data samples {y i ,x i}, i = 1, 2…n. Among them, x i and iare input samples and output samples respectively. A nonlinear relationship is used to map the input sample x in the original space to a high-dimensional feature space φ(x)=(φ1(x),φ2(x),…φ n (x)), and establish a linear model in the high-dimensional feature space to estimate the regression function as follows:

[0095] f(x)=w·φ(x)+b (4)

[0096] Where: w is the weight vector, b is the threshold. After the input sample is transformed by φ, the linear regression problem can be solved in the high-dimensional space to solve the nonlinear regression problem in the original space. The insensitive damage function ε is defined as:

[0097]

[0098] The key to the SVR problem is to find a suitable function f(x) to fit the input sample so that the observed value y i And the function prediction value f(x i ) is the smallest, and its error can be expressed by the insensitive damage function ε. When the training point is within the ε band, the error of the training point is considered to be 0.

[0099] The objective functions of the SVR model for minimizing empirical risk and structural risk are:

[0100]

[0101] Introducing the slack variable ξ i and The optimization problem can be transformed into:

[0102]

[0103]

[0104] Where: c is the penalty factor, which is used to balance the maximum classification interval and prediction error.

[0105] The Lagrangian function is used to optimize equation (7), and by solving the dual problem, the solution of equation (4) can be obtained:

[0106]

[0107] Where: N sv is the number of support vectors; and α i is the Lagrange multiplier; K(x i ,x) is the kernel function.

[0108] In order to eliminate the impact of the imbalance of the numerical values ​​of parameters of different dimensions on the prediction results, the maximum and minimum method is used to normalize the original data. The calculation formula is:

[0109]

[0110] Where: x min is the minimum value in the data series; x max Is the maximum value in the data series.

[0111] The four random variables in Section 2.1 are used as input samples, and the wheel-rail dynamic response is used as the output sample. Taking the vertical acceleration of the vehicle body as an example, the first 20 groups of training samples in the results calculated in Section 2.2 are used as sample data for the support vector machine regression model to build a model, and then 5 groups of test data are used to verify the model to ensure the reliability of the model. Before calculation, the input and output samples are normalized, and the normalization formula is shown in Equation (9). The results of parameter selection for the kernel function parameter g and the penalty factor c are shown in Figure 5 .

[0112] analyze Figure 5 It can be seen that the optimal kernel function parameter g and penalty factor c are 0.125 and 2.828 respectively. Substituting the optimal values ​​of parameters c and g into the SVR model, the actual value and predicted value of the vehicle vertical acceleration are as follows: Figure 6 As shown, the error between the true value and the predicted value is Figure 7 shown.

[0113] Depend on Figure 6 and Figure 7 It can be seen that the change law of the vehicle body vertical acceleration predicted by SVR is basically the same as the actual vehicle body vertical acceleration, the correlation coefficient between the two is 0.993, and the mean square error is 0.004, which shows that the wheel-rail dynamic system mapping model established based on SVR in this embodiment has a high degree of fit and accuracy.

[0114] 2.4 Parameter sensitivity analysis

[0115] In order to study the influence of the above four random variables on the dynamic response of the wheel-rail system, it is necessary to define the sensitivity coefficient of each random variable to the dynamic response of the wheel-rail system, so as to quantitatively analyze the influence of each random variable. Assuming that when the random variable changes from S1 to S2, the dynamic response of the wheel-rail system changes from M1 to M2, then the sensitivity coefficient of the random variable is defined as:

[0116]

[0117] Where: γ1, γ2, γ3, γ4 and γ5 are the sensitivity coefficients of random variables to the vertical acceleration of the vehicle body, the vertical wheel-rail force, the wheel load reduction rate, the vertical displacement of the rail and the vertical displacement of the track plate, respectively.

[0118] When calculating the sensitivity coefficient of a random variable, the other random variables are taken as initial values. The initial values ​​of fastener stiffness, mortar elastic modulus, mortar void length and pier settlement are taken as 20 mm, 7000 MPa, 3 m and 2 mm respectively. The calculation results are shown in Table 3 and Figure 8 shown.

[0119] Table 3. Sensitivity coefficients of random variables to the dynamic response of the wheel-rail system

[0120]

[0121] By analyzing Table 3 and Figure 8 It can be seen that the influence of pier settlement on the vertical acceleration of the vehicle body is the most significant, while the wheel-rail vertical force, wheel weight reduction rate, rail vertical displacement and track plate vertical displacement are more sensitive to the mortar void length. Therefore, the wheel-rail vertical force, wheel weight reduction rate, rail vertical displacement and track plate vertical displacement are selected as the research objects when evaluating the influence of mortar void on the long-term service performance of the wheel-rail system.

[0122] Table 4. Comparison of solution time of two models

[0123]

[0124] From the data in Table 4, it can be seen that the time taken by the train-track-bridge dynamics model to solve once is 738.41 times that of the SVR mapping model, and the computational efficiency of the SVR nonlinear mapping model is improved by 99.86%; the time taken by the SVR nonlinear mapping model to solve 1 million times is only 13.85s, and the train-track-bridge dynamics model cannot be completed. It can be seen that the SVR nonlinear mapping model has the advantages of high efficiency and is suitable for large sample calculations.

[0125] 3. Reliability of void length of mortar filling layer based on SVR nonlinear mapping model

[0126] 3.1 Random Sampling

[0127] The Latin hypercube sampling method is used to randomly sample the four random variables 1 million times. The generated random variable samples are substituted into the SVR nonlinear mapping model established in Section 2.3 for calculation. The probability density distribution diagrams and cumulative probability curves of the vehicle body vertical acceleration, wheel-rail vertical force, wheel load reduction rate, rail vertical displacement and track plate vertical displacement can be obtained, as shown in the figure below: Fig. 9 and Fig.10 shown.

[0128] 3.2 Control standard limits of mortar void length at different levels

[0129] Based on the reliability theory, the reliability probability when the dynamic response amplification factor is greater than a certain value is used as the basis for the division of the mortar void length control standard, and the mortar void length value corresponding to the amplification factor is used as the control limit; the state when the reliability probability of the wheel-rail system dynamic response amplification factor greater than a certain value is 50%, 30% and 10% is respectively evaluated as level I, level II and level III mortar void length control standards. The division results of the mortar void length control standard are as follows: Fig.11 shown.

[0130] The range of the dynamic response amplification factor of the wheel-rail system under different mortar void length control standard levels is shown in Table 5.

[0131] Table 5 Definition of mortar void length control standards

[0132]

[0133] After determining the control standard level of mortar void length and the corresponding wheel-rail system dynamic response amplification factor, the SVR nonlinear mapping model is used to calculate the mortar void length limit under different levels of control standards. When the fastener stiffness A = 50 kN / mm, the mortar elastic modulus B = 7000 MPa and the pier settlement D = 5 mm, the control standard limits of mortar void length under different train running speeds are shown in Table 6.

[0134] Table 6 Control standard limits of mortar void length of different grades

[0135]

[0136]

[0137] It can be seen from Table 6 that the mortar void length limit under vehicle dynamic response control first decreases and then increases with the increase of speed, while the void length limit under track dynamic response control increases with the increase of speed. This is because the track dynamic response is more sensitive to the mortar void length than the vehicle dynamic response, and when the train speed is 250-300 km / h, the influence of the train speed on the vehicle dynamic response is greater than the mortar void length. When the train speed reaches 350 km / h, the influence of the mortar void length on the vehicle dynamic response is more significant, while the track dynamic response is more sensitive to the mortar void length. When the train speed is 250, 300 and 350 km / h respectively, the level I, level II and level III control limits of the mortar void length are 3.932, 4.337 and 4.766 m; 3.948, 4.363 and 4.778 m; 3.991, 4.386 and 4.803 m.

[0138] In summary, the present invention uses MATLAB to establish a train sub-model and ANSYS to establish a track-bridge sub-model. The two sub-models are assembled into a train-track-bridge coupling system dynamics model through the wheel-rail contact relationship, and compared with the literature model for verification; then, based on the Latin hypercube sampling method, the randomness of fastener stiffness, mortar elastic modulus, mortar void length and pier settlement is considered, and the test points are designed by the Box-Behnken method to carry out coupled dynamics model calculations, and the train and structural response index values ​​are extracted. Based on support vector machine regression analysis (SVR), a nonlinear mapping model of the wheel-rail dynamic system is established and predicted, and the true value is used to compare and verify with the predicted value; finally, based on the SVR mapping model, the reliable probability of the response index amplification factor distributed in different ranges is obtained, and the reliable probability when the response index amplification factor is greater than a certain value is used as the basis for dividing the mortar filling layer void length control standard, and the mortar filling layer void length limit is obtained accordingly.

[0139] The analysis results show that: the vehicle-rail-bridge coupling dynamic model established by the present invention is accurate and reliable; the nonlinear mapping model of the wheel-rail dynamic system established by the support vector machine has high fitting accuracy and can be used to predict the dynamic response of the wheel-rail system; the pier settlement has the most significant effect on the vertical acceleration of the vehicle body, while the mortar void length has the most significant effect on the wheel-rail vertical force, wheel weight reduction rate, rail vertical displacement and track plate vertical displacement; the level I, level II and level III control limits of the mortar void length when the train speed is 250km / h, 300km / h and 350km / h respectively They are 3.932, 4.337 and 4.766m; 3.948, 4.363 and 4.778m; 3.991, 4.386 and 4.803m respectively, which effectively provide a more accurate and safe limit threshold for the reliability of the void length of the mortar filling layer of the in-service bridge-ballastless track system; and the train-track-bridge coupling dynamic model established in the present invention is not only suitable for the reliability analysis of the void length of the mortar filling layer, but also can be appropriately improved and used for other track diseases, and has good applicability and promotion value.

[0140] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other specific forms without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations that fall within the meaning and scope of the elements of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0141] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in the embodiments may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A reliability analysis method for the void length of the mortar filling layer of an in-service bridge-ballastless track system, characterized by: The steps include: S1: Establish a train-track-bridge coupled dynamics model: Establish a train sub-model based on multi-body dynamics theory; establish a ballastless track-bridge sub-model based on finite element theory; and assemble the train sub-model and the ballastless track-bridge sub-model based on the wheel-rail contact relationship to obtain a train-track-bridge coupled dynamics model; S2: Model verification: verify the correctness of the established train-track-bridge coupling dynamic model; S3: Obtain samples: Select fastener stiffness, mortar elastic modulus, mortar void length and fastener stiffness as random variables; adopt the Box-Behnken test design method and obtain SVR test point samples based on Design-Expert software; S4: Establishing a wheel-rail dynamic system mapping model: Based on the SVR principle, using the SVR test point samples obtained in step S3, a dynamic nonlinear mapping model of the train-track-bridge system, i.e., a wheel-rail dynamic system mapping model, is established, and the model is verified to ensure the reliability of the model; S5: Parameter sensitivity analysis: define the sensitivity coefficients of random variables to the vertical acceleration of the vehicle body, vertical wheel-rail force, wheel-load reduction rate, vertical displacement of the rail and vertical displacement of the track plate; analyze the sensitivity of the vertical acceleration of the vehicle body, vertical wheel-rail force, wheel-load reduction rate, vertical displacement of the rail and vertical displacement of the track plate to the mortar void length; determine the research object for analyzing the reliability of the mortar void length; S6: Control standard limits for mortar void length at different levels: Based on the reliability theory, the reliability probability when the dynamic response amplification factor is greater than a certain value is used as the basis for dividing the control standard for mortar void length, and the mortar void length value corresponding to the amplification factor is used as the control limit; then, the wheel-rail dynamic system mapping model is used to calculate the mortar void length limit under different levels of control standards.

2. The reliability analysis method for the void length of the mortar filling layer of the in-service bridge-ballastless track system according to claim 1 is characterized by: In step S1, the train sub-model is established in MATLAB, which consists of a car body, two bogies and four wheel pairs; the suspension system between the car body, bogies and wheelsets is simulated by spring-damper units; the car body and two bogies consider five degrees of freedom: lateral movement, heave, roll, nod and shake, and each wheelset considers four degrees of freedom: lateral movement, heave, roll and shake, and it is assumed that the car body, frame and wheelsets are all rigid bodies.

3. The reliability analysis method for the void length of the mortar filling layer of the in-service bridge-ballastless track system according to claim 1 is characterized by: In step S1, the ballastless track-bridge sub-model is established in ANSYS; wherein the ballastless track is mainly composed of rails, fasteners, track plates, CA mortar layers, base plates and "two cloths and one membrane" sliding layers; the rails, track plates, base plates and bridges are all simulated by beam units; the fasteners and CA mortar layers are simulated by spring-damper units; and the sliding layer is simulated by a unidirectional compression spring.

4. The reliability analysis method for the void length of the mortar filling layer of the in-service bridge-ballastless track system according to claim 1 is characterized by: In step S1, the specific steps of assembling the train sub-model and the ballastless track-bridge sub-model based on the wheel-rail contact relationship to obtain the train-track-bridge coupled dynamics model are as follows: S1-1: Perform modal analysis on the ballastless track-bridge sub-model and obtain the .full binary file containing the overall mass, stiffness and damping matrix of the sub-model; S1-2: Use HBMAT command to convert the binary file into Harwell-Boeing file, and convert it into sparse matrix form through Python; use HBMAT to extract the locations of mass, stiffness and damping matrix nodes in the binary file and generate .Mapping file; S1-3: Using the wheel-rail contact relationship, the .Mapping file and sparse matrix of the ballastless track-bridge sub-model are linked with the train sub-model to establish the train-track-bridge coupled dynamic model.

5. The reliability analysis method for the void length of the mortar filling layer of the in-service bridge-ballastless track system according to claim 4 is characterized by: The established train-track-bridge coupled dynamic model uses Hertz contact simulation for wheel-rail normal force and creep force for wheel-rail lateral force.

6. The reliability analysis method for the void length of the mortar filling layer of the in-service bridge-ballastless track system according to claim 1 is characterized by: In step S2, the model verification requires that the calculation results of the constructed model are compared with the calculation results of the comparison model, and the vertical displacement change trends of the rails at the beam ends and mid-span are basically consistent, and the maximum amplitude error does not exceed 5%.

7. The reliability analysis method for the void length of the mortar filling layer of the in-service bridge-ballastless track system according to claim 1 is characterized by: In step S3, the random variables include: the pier settlement is 2 to 10 m and is uniformly distributed; the mortar void length is 3 to 5 m and is uniformly distributed; the fastener stiffness is truncated normal distribution, with a mean of 30 and a standard deviation of 23.33; the mortar elastic modulus is normally distributed, with a mean of 8500 and a standard deviation of 500.

8. The reliability analysis method for the void length of the mortar filling layer of the in-service bridge-ballastless track system according to claim 1 is characterized by: In step S4, the wheel-rail dynamic system mapping model uses the random variables fastener stiffness, mortar elastic modulus, mortar void length and fastener stiffness as input samples, and the wheel-rail dynamic response as output samples; the input and output samples are normalized; a part of the SVR test point samples are used as sample data for modeling, and the remaining SVR test point samples are used to verify the established wheel-rail dynamic system mapping model.

9. The reliability analysis method for the void length of the mortar filling layer of the in-service bridge-ballastless track system according to claim 1 is characterized by: In step S5, in the parameter sensitivity analysis, when calculating the sensitivity coefficient of a random variable, the remaining random variables are all taken as initial values; the initial values ​​of fastener stiffness, mortar elastic modulus, mortar void length and pier settlement are taken as 20mm, 7000MPa, 3m and 2mm respectively.

10. The reliability analysis method for the void length of the mortar filling layer of the in-service bridge-ballastless track system according to claim 1 is characterized by: In step S6, the different levels of control standard limits for the mortar void length are: the states when the reliable probability that the wheel-rail system dynamic response amplification factor is greater than a certain value is 50%, 30% and 10% are evaluated as level I, level II and level III mortar void length control standards.

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