CN115577635A - Method for analyzing reliability of void length of mortar filling layer of in-service bridge-ballastless track system - Google Patents

Method for analyzing reliability of void length of mortar filling layer of in-service bridge-ballastless track system Download PDF

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CN115577635A
CN115577635A CN202211310864.4A CN202211310864A CN115577635A CN 115577635 A CN115577635 A CN 115577635A CN 202211310864 A CN202211310864 A CN 202211310864A CN 115577635 A CN115577635 A CN 115577635A
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mortar
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何彬彬
文胜
冯玉林
蒋丽忠
周旺保
柴喜林
侯宇
李金平
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Central South University
East China Jiaotong University
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Abstract

The invention discloses a method for analyzing the reliability of the void length of a mortar filling layer of an in-service bridge-ballastless track system, which comprises the steps of respectively establishing a train sub-model and a track-bridge sub-model considering the void of the mortar filling layer, assembling the train sub-model and the track-bridge sub-model into a train-track-bridge coupling dynamic model through a wheel-track contact relation, and verifying the train-track-bridge coupling dynamic model; then, developing the calculation of a coupling dynamics model based on Design-Expert software and a Box-Behnken method, establishing a wheel-rail system nonlinear mapping model based on a support vector regression principle, and performing learning, prediction and verification; and finally, based on the established wheel-rail system nonlinear mapping model and the Latin hypercube sampling method, obtaining the reliable probability of the amplification coefficient distribution of the train and structural response indexes in different ranges, and obtaining the void length limit value of the mortar filling layer. The train rail bridge coupling dynamic model established by the invention is accurate and reliable, the fitting precision of the nonlinear mapping model of the wheel rail system is high, the calculation efficiency is obvious, and the method has good applicability and application value.

Description

Method for analyzing reliability of void length of mortar filling layer of in-service bridge-ballastless track system
Technical Field
The invention relates to a research on track diseases of a high-speed rail system, in particular to a method for analyzing the reliability of a void length of a mortar filling layer of an in-service bridge-ballastless track system.
Background
Under the large background of 'replacing roads with bridges' of a high-speed railway, the bridge inevitably generates pier settlement under the conditions of special geology and extreme climate, so that additional deformation of the bridge is caused; and in the long-term service process of the line, the on-bridge track structure can also generate random track diseases, such as interlayer crack separation, void, upwarp and the like. The additional deformation of the bridge and the damage of the rail can cause the change of a rail bearing mode and an interlayer component force transmission mechanism, when a train passes through, the changes can cause the deterioration of the driving quality, and in the serious condition, the driving safety can be endangered, and the inestimable result can be caused. Therefore, in order to minimize the risk of unacceptable failure of the structure, it is necessary to take into account the randomness of the damage pattern and the mechanical parameters when determining the damage limits.
In recent years, many studies on a train-track-bridge system are conducted on bridge pier settlement and interlayer damage, and the studies can be summarized into two forms, namely, determining the limit value of the damage based on axle coupling vibration, and obtaining the limit value of the damage based on reliability theoretical analysis. Generally speaking, compared with the limit determined directly based on axle coupling vibration, the limit is more reasonable based on the theoretical analysis of the reliability, and the uncertainty of the resistance and the load of the structure is taken into the research and consideration scope, so that a dynamic index with time-varying characteristics, namely the reliability index, is obtained through calculation. However, considering randomness, tens of thousands of calculations are required, and the calculation amount is huge, and the work is difficult. In addition, the following two problems still exist in the current research on the influence of bridge pier settlement and interlayer damage on a train-track-bridge system: 1) The current research rarely considers the influence of pier settlement, track diseases and the randomness of the rigidity change of an interlayer member, so that the dynamic response of a train-track-bridge system is not comprehensive; 2) Most of the existing researches adopt a train-track-bridge system dynamic model, and the formula established under the model is long in time consumption and low in efficiency, so that the research progress is not facilitated.
Disclosure of Invention
Aiming at the existing problems, the invention provides a reliability analysis method for the void length of a mortar filling layer of an in-service bridge-ballastless track system, which takes a train-CRTS II type slab ballastless track-bridge as a research object, establishes a train-track-bridge system dynamic model containing pier settlement and mortar void, introduces a Support Vector Regression (SVR) theory by considering the rigidity of a fastener, the elastic modulus of mortar, the void length of mortar and the randomness of pier settlement, and establishes a mapping relation between the mortar void length and the dynamic response of a high-speed train-track-bridge system; and finally, based on the reliability theory, providing a control standard of the length limit value of the mortar filling layer. The specific technical scheme is as follows:
a method for analyzing the reliability of the void length of a mortar filling layer of an in-service bridge-ballastless track system comprises the following steps:
s1: establishing a train-track-bridge coupling dynamic model: establishing a train sub-model based on a multi-body dynamics theory; establishing a ballastless track-bridge sub-model based on a finite element theory; assembling the train sub-model and the ballastless track-bridge sub-model based on the wheel-track contact relationship to obtain a train-track-bridge coupling dynamic model;
s2: and (3) model verification: verifying the correctness of the established train-track-bridge coupling dynamic model;
s3: obtaining a sample: selecting the rigidity of the fastener, the elastic modulus of mortar, the void length of the mortar and the rigidity of the fastener as random variables; obtaining an SVR test point sample based on Design-Expert software by adopting a Box-Behnken test Design method;
s4: establishing a wheel-rail power system mapping model: based on the SVR principle, establishing a dynamic nonlinear mapping model of the train-track-bridge system, namely a wheel-track power system mapping model, by adopting the SVR test point sample obtained in the step S3, and training and verifying the model to ensure the reliability of the model;
s5: and (3) analyzing parameter sensitivity: respectively defining the sensitivity coefficients of the random variables to the vertical acceleration of a vehicle body, the vertical wheeltrack force, the wheelload shedding rate, the vertical displacement of a steel rail and the vertical displacement of a track plate; analyzing the sensitivity of the vertical acceleration of the vehicle body, the vertical wheel-rail force, the wheel weight load shedding rate, the vertical displacement of the steel rail and the vertical displacement of the rail plate to the mortar void length; determining a research object for analyzing the reliability of the mortar void length;
s6: controlling standard limit values of different grades of the mortar void length: based on a reliability theory, taking the reliability probability when the power response amplification factor is greater than a certain value as a division basis of a mortar void length control standard, and taking a mortar void length value corresponding to the amplification factor as a control limit value; and then calculating the mortar void length limit value under the control standards of different grades through a wheel-rail power system mapping model.
As a preferred technical solution, in step S1, the train sub-model is established in MATLAB, and is composed of 1 train body, 2 bogies, and 4 wheel pairs; a suspension system among the vehicle body, the bogie and the wheel set is simulated by adopting a spring-damping unit; the car body and the two bogies consider 5 degrees of freedom of transverse movement, sinking and floating, side rolling, nodding and shaking, each wheel pair considers 4 degrees of freedom of transverse movement, sinking and floating, side rolling and shaking, and the car body, the framework and the wheel pair are assumed to be rigid bodies.
In a preferable technical scheme, in the step S1, the ballastless track-bridge sub-model is established in ANSYS; the ballastless track mainly comprises steel rails, fasteners, track plates, a CA mortar layer, a base plate and a 'two-cloth-one-film' sliding layer; the steel rail, the track plate, the base plate and the bridge are all simulated by adopting a beam unit; the fastener and the CA mortar layer are simulated by a spring-damping unit; the sliding layer is simulated by adopting a one-way compression spring.
As a preferred technical scheme, in the step S1, the step 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 coupling dynamic model specifically includes the following steps:
s1-1: performing modal analysis on the ballastless track-bridge submodel to obtain a full binary file storing the overall mass, rigidity and damping matrix of the submodel;
s1-2: converting the binary file into a Harwell-Boeing file by adopting an HBMAT command, and converting the Harwell-Boeing file into a sparse matrix form by Python; extracting the positions of the quality, rigidity and damping matrix nodes in the binary file by utilizing HBMAT, and generating a Mapping file;
s1-3: and (3) associating the Mapping file and the sparse matrix of the ballastless track-bridge sub-model with the train sub-model by adopting a wheel-rail contact relation, and establishing a train-track-bridge coupling dynamic model.
Further preferably, the wheel-rail-bridge coupling dynamic model is established by adopting Hertz contact simulation for wheel-rail normal force, and the wheel-rail transverse force takes the creep force into consideration.
As a preferable technical solution, in the step S2, the model verification requires that the calculation result of the established model is substantially consistent with the calculation result of the comparison model in the vertical displacement variation trend of the beam end and the mid-span steel rail, and the maximum amplitude error does not exceed 5%.
As a preferred technical solution, in step S3, the random variable includes: the settlement value of the bridge pier is 2-10 m and is subject to uniform distribution; the void length of the mortar is 3-5 m and is subject to uniform distribution; the rigidity of the fastener follows the truncation normal distribution, the mean value is 30, and the standard deviation is 23.33; the elastic modulus of the mortar follows normal distribution, the mean value is 8500, and the standard deviation is 500.
In a preferred technical scheme, in step S4, the wheel-rail dynamic system mapping model takes random variables of fastener stiffness, mortar elastic modulus, mortar void length and fastener stiffness as input samples, and takes wheel-rail dynamic response as an output sample; normalizing the input and output samples; and modeling by taking a part of SVR test point samples as sample data, and verifying the established wheel-rail power system mapping model by using the rest of SVR test point samples.
As a preferred technical solution, in step S5, in the parameter sensitivity analysis, when a sensitivity coefficient of a certain random variable is calculated, the other random variables are all taken as initial values; initial values of the rigidity of the fastener, the elastic modulus of the mortar, the void length of the mortar and the settlement of the pier are respectively 20mm, 7000MPa, 3m and 2mm.
In a preferable technical solution, in step S6, the control standard limit values of different levels of the mortar void length are: and evaluating the states of the wheel-rail system when the reliable probability of the dynamic response amplification coefficient of the wheel-rail system being greater than a certain value is 50%, 30% and 10% as I-grade, II-grade and III-grade mortar void length control standards.
The invention has the following beneficial effects:
1) The wheel-rail system dynamic response mapping model established by the Support Vector Regression (SVR) principle has high fitting precision, and the SVR nonlinear mapping model established by the invention has high fitting precision which reaches 0.993; compared with the existing analysis method, the method is used for predicting the dynamic response of the wheel-rail system, the calculation speed is increased by 99.86%, and the calculation efficiency is obvious.
2) The method takes pier settlement, track damage (mortar filling layer void length) and rigidity change randomness of the interlayer member into consideration, researches the influence of the pier settlement and interlayer damage on the train-track-bridge system, further comprehensively analyzes the dynamic response of the train-track-bridge system, and ensures the driving safety of the train.
3) The analysis method provided by the invention verifies that the influence of pier settlement on the vertical acceleration of the vehicle body is most obvious, and the sensitivity of the mortar void length on the vertical force of the wheel rail, the wheel weight load shedding rate, the vertical displacement of the steel rail and the vertical displacement of the track plate is obviously greater than that of other influence factors, so that a foundation is laid for further research.
4) By the analysis of the method, the I, II and III grade limit values of the mortar void length are 3.932, 4.337 and 4.766mm respectively in the train running speed interval with the train speed of 250-350 km/h respectively; the method provides a more exact and safe limit threshold value for the reliability of the void length of the mortar filling layer of the in-service bridge-ballastless track system.
5) The train-track-bridge coupling dynamic model established by the invention is not only suitable for the reliability analysis of the void length of the mortar filling layer, but also can be properly improved and used aiming at other track diseases, and has good applicability and popularization value.
Drawings
FIG. 1 is a schematic structural diagram of a high-speed train-track-bridge coupling dynamic model considering pier settlement and mortar emptying;
FIG. 2 is a comparison of the validation results of the model of the present invention and the literature model;
wherein: (a) The model beam end steel rail vertical displacement of the invention, (b) the model span steel rail vertical displacement of the invention; (c) The vertical displacement of the steel rail at the beam end of the document model, and (d) the vertical displacement of the steel rail across the center of the document model;
FIG. 3 is a graph showing the amplification results of the maximum dynamic response of the wheel and rail system of the present invention;
wherein: (a) is a vehicle system dynamic response; (b) is a rail system dynamic response;
FIG. 4 is a diagram of a linear regression function, a loss function and a network structure of the support vector machine of the present invention;
wherein: (a) is a linear regression function of a support vector machine; (b) is a support vector machine penalty function; (c) is a structure diagram of a support vector machine network;
FIG. 5 is a SVR parameter selection result of the present invention;
wherein: (a) is a vehicle contour map; (b) is a three-dimensional spatial distribution map;
FIG. 6 is a graph of SVR prediction results according to the present invention;
FIG. 7 is a diagram of SVR prediction error in accordance with the present invention
FIG. 8 is a graph showing how sensitive the random variable of the present invention is to the dynamic response of the wheel rail;
FIG. 9 is a graph of the power response probability density of the wheel and rail system of the present invention;
wherein: the method comprises the following steps of (a) obtaining vertical acceleration of a vehicle body, (b) obtaining vertical force of a wheel rail, (c) obtaining wheel weight load reduction rate, (d) obtaining vertical displacement of a steel rail, and (e) obtaining vertical displacement of a rail plate;
FIG. 10 is a graph of the cumulative probability of the dynamic response of the wheel and rail system of the present invention;
wherein: the method comprises the following steps of (a) obtaining vertical acceleration of a vehicle body, (b) obtaining vertical force of a wheel rail, (c) obtaining wheel weight load reduction rate, (d) obtaining vertical displacement of a steel rail, and (e) obtaining vertical displacement of a rail plate;
FIG. 11 is a standard division of mortar void length control according to the present invention.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the embodiments and the accompanying drawings, and it is to be understood that the described embodiments are merely preferred embodiments of the present invention, rather than all embodiments, and are not intended to limit the present invention in other forms, and that any person skilled in the art may make changes or modifications using the technical contents disclosed. However, any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention are within the protection scope of the technical solution of the present invention.
Example 1
The embodiment is a method for analyzing the reliability of the void length of a mortar filling layer of an in-service bridge-ballastless track system, which comprises the following steps:
s1: establishing a train-track-bridge coupling dynamic model: establishing a train sub-model based on a multi-body dynamics theory; establishing a ballastless track-bridge sub-model based on a finite element theory; and assembling the train submodel and the ballastless track-bridge submodel based on the wheel-rail contact relation to obtain a train-track-bridge coupling dynamic model. Wherein:
the train submodel is established in MATLAB and consists of 1 train body, 2 bogies and 4 wheel pairs; a suspension system among the vehicle body, the bogie and the wheel set is simulated by a spring-damping unit; the car body and the two bogies consider 5 degrees of freedom of transverse movement, sinking and floating, side rolling, nodding and shaking, each wheel pair considers 4 degrees of freedom of transverse movement, sinking and floating, side rolling and shaking, and the car body, the framework and the wheel pair are assumed to be rigid bodies.
The ballastless track-bridge sub-model is established in ANSYS; the ballastless track mainly comprises steel rails, fasteners, a track plate, a CA mortar layer, a base plate and a 'two-cloth-one-film' sliding layer; the steel rail, the track plate, the base plate and the bridge are all simulated by adopting a beam unit; the fastener and the CA mortar layer are simulated by a spring-damping unit; the sliding layer is simulated by adopting a one-way compression spring.
Assembling the train sub-model and the ballastless track-bridge sub-model based on the wheel-track contact relationship to obtain a train-track-bridge coupling dynamic model, wherein the wheel-track normal force is subjected to Hertz contact simulation, and the wheel-track transverse force takes the creep force into consideration; the method comprises the following specific steps:
s1-1: performing modal analysis on the ballastless track-bridge submodel to obtain a full binary file storing the overall mass, rigidity and damping matrix of the submodel;
s1-2: converting the binary file into a Harwell-Boeing file by adopting an HBMAT command, and converting the Harwell-Boeing file into a sparse matrix form by Python; extracting the positions of the quality, rigidity and damping matrix nodes in the binary file by utilizing HBMAT, and generating a Mapping file;
s1-3: and (3) associating the Mapping file and the sparse matrix of the ballastless track-bridge sub-model with the train sub-model by adopting a wheel-rail contact relation, and establishing a train-track-bridge coupling dynamic model.
S2: and (3) model verification: verifying the correctness of the established train-track-bridge coupling dynamic model; compared with the calculation results of comparison models published by the existing documents, the calculation results of the established models are required to have the beam ends and the midspan steel rail with basically consistent vertical displacement variation trends and the maximum amplitude error not exceeding 5 percent.
S3: obtaining a sample: selecting the rigidity of the fastener, the elastic modulus of mortar, the void length of the mortar and the rigidity of the fastener as random variables; wherein: the settlement value of the bridge piers is 2-10 m and is subject to uniform distribution; the void length of the mortar is 3-5 m and is subject to uniform distribution; the rigidity of the fastener follows the truncation normal distribution, the mean value is 30, and the standard deviation is 23.33; the elastic modulus of the mortar follows normal distribution, the mean value is 8500, and the standard deviation is 500. Then, a Box-Behnken test Design method is adopted, and SVR test point samples are obtained based on Design-Expert software.
S4: establishing a wheel-rail power system mapping model: based on the SVR principle, random variable fastener rigidity, mortar elastic modulus, mortar void length and fastener rigidity are used as input samples, and wheel-rail dynamic response is used as an output sample; normalizing the input and output samples; modeling by taking a part of the obtained SVR test point samples as sample data to obtain a dynamic nonlinear mapping model of the train-track-bridge system, namely a wheel-track power system mapping model; and then verifying the built model by using the rest part of SVR test point samples to ensure the reliability of the model.
S5: and (3) analyzing parameter sensitivity: respectively defining the sensitivity coefficients of random variables to the vertical acceleration of a vehicle body, the vertical wheel-rail force, the wheel load shedding rate, the vertical displacement of a steel rail and the vertical displacement of a track plate; analyzing the sensitivity of the vertical acceleration of the vehicle body, the vertical wheel-rail force, the wheel weight load shedding rate, the vertical displacement of the steel rail and the vertical displacement of the rail plate to the mortar void length; when the sensitivity coefficient of a certain random variable is calculated, the other random variables are all taken as initial values; initial values of the rigidity of the fastener, the elastic modulus of the mortar, the void length of the mortar and the settlement of the pier are respectively 20mm, 7000MPa, 3m and 2mm. And determining the vertical force of the wheel rail, the wheel weight load shedding rate, the vertical displacement of the steel rail and the vertical displacement of the track plate as research objects through calculation.
S6: controlling standard limit values of different grades of the mortar void length: based on a reliability theory, taking the reliability probability when the power response amplification factor is greater than a certain value as a division basis of a mortar void length control standard, and taking a mortar void length value corresponding to the amplification factor as a control limit value; and then calculating the mortar void length limit value under the control standards of different grades through a wheel-rail power system mapping model.
Next, the above analysis method explained in detail is exemplified:
1. establishing a train-track-bridge system dynamic model considering pier settlement and interlayer damage
Establishing a train-track-bridge coupling dynamic model considering pier settlement and track diseases (taking mortar void as an example), wherein as shown in figure 1, the modeling process is as follows:
1.1 model building
1.1.1 train submodel
In MATLAB, based on the quality of many dynamic theories equipment train, damping and rigidity matrix, the train submodel comprises 1 automobile body, 2 bogies and 4 wheel pairs. A suspension system among a vehicle body, bogies and wheel pairs is simulated by adopting a spring-damping unit, the vehicle body and the two bogies consider 5 degrees of freedom of transverse movement, sinking and floating, side rolling, nodding and shaking, each wheel pair considers 4 degrees of freedom of transverse movement, sinking and floating, side rolling and shaking, and the vehicle body, a framework and the wheel pairs are assumed to be rigid bodies. The motion equation of the train submodel is
Figure BDA0003907998750000081
In the formula: m v 、C v 、K v And U v Respectively a mass matrix, a damping matrix, a rigidity matrix and a displacement vector of the train sub-model; f g And F w Respectively the self weight vector and the wheel track force vector of the train.
1.1.2 ballastless track-bridge submodel
In ANSYS, a ballastless track-bridge sub-model is established based on a finite element theory. The ballastless track mainly comprises steel rails, fasteners, track plates, a CA mortar layer, a base plate and a 'two-cloth-one-film' sliding layer, wherein the steel rails, the track plates, the base plate and a bridge are simulated by beam units, the fasteners and the CA mortar layer are simulated by spring-damping units, the sliding layer is simulated by unidirectional compression springs, and the ballastless track-bridge submodel equation of motion is
Figure BDA0003907998750000082
In the formula: m tb 、C tb 、K tb And U tb Respectively a mass matrix, a damping matrix, a rigidity matrix and a displacement vector of the track-bridge submodel.
1.1.3 wheel-track contact relation Assembly
And assembling a train-track-bridge coupling dynamic model based on the wheel-track contact relation. The method comprises the following specific steps: firstly, carrying out modal analysis on a ballastless track-bridge submodel to obtain a full binary file storing the overall mass, rigidity and damping matrix of the submodel; then, converting the binary file into a Harwell-Boeing file by adopting an HBMAT command, and converting the Harwell-Boeing file into a sparse matrix form by Python; meanwhile, HBMAT is utilized to extract the positions of the quality, rigidity and damping matrix nodes in the binary file, and a Mapping file is generated; further, mapping files and sparse matrixes of the ballastless track-bridge submodel are linked with the train submodel by adopting a wheel-rail contact relation, a train-track-bridge coupling dynamic model is established, wheel-rail normal force is subjected to Hertz contact simulation, and wheel-rail transverse force is considered in creep force.
1.3 model validation
In order to verify the correctness of the model, models published in 'ballastless track dynamic response analysis on bridge under the action of braking load' (journal of railway science and engineering, 2017,14 (11): 2309-2322.) such as Pan Peng, lei Xiaoyan and Zhang Pengfei are adopted as comparison models to verify the established train-track-bridge coupling dynamic model, and the verification results are shown in fig. 1 and fig. 2.
TABLE 1 comparative verification of the model created in this example with the comparative model
Figure BDA0003907998750000091
As can be seen from table 1 and fig. 2, compared with the calculation result of the comparison model, the calculation result of the model established in the present embodiment has the substantially same trend of vertical displacement change of the beam end and the mid-span steel rail, and the maximum amplitude error does not exceed 5%, which indicates that the train-track-bridge coupling dynamics model established in the present embodiment is correct; the reason for the slight difference is that the running speed in the comparison model is uniformly decelerated from 200km/h to 0, and the braking force of the train is considered, while the train of the model built in the embodiment always runs at a uniform speed of 200 km/h.
2. SVR-based wheel-rail power system nonlinear mapping model
2.1 random variables
Selecting the rigidity (A) of the fastener, the elastic modulus (B) of the mortar, the void length (C) of the mortar and the settlement (D) of the pier as random variables, wherein the settlement value of the pier is 2-10 m and the pier is subjected to uniform distribution; the void length of the medium mortar is 3-5 m and is subject to uniform distribution; the rigidity of the fastener follows the truncation normal distribution, the mean value is 30, and the standard deviation is 23.33; the elastic modulus of the mortar follows normal distribution, the mean value is 8500, and the standard deviation is 500.
2.2 training samples
Carrying out test point design by adopting a Box-Behnken test design method, wherein the number of the test points is as follows:
N＝2k(k-1)+C 0 (3)
wherein N is the number of SVR test points, k is the number of random variables, C 0 The number of repetitions of the central test.
In this example, the number of selected Design variables was 4 (fastener stiffness (a), mortar elastic modulus (B), mortar void length (C), and pier settlement (D)), the number of repetitions of the center test was 1, and therefore the number of test points was 25, and Design test data based on Design-Expert software is shown in table 2.
TABLE 2 Box-Behnken test protocol
Figure BDA0003907998750000101
And (4) based on the test data, respectively carrying out dynamic calculation of the train-track-bridge system at the speeds of 250km/h, 300km/h and 350 km/h. The ratio of the maximum dynamic response value of the system when bridge pier settlement and mortar emptying exist to the maximum dynamic response value of the system when bridge pier settlement and mortar emptying do not exist is defined as a dynamic response amplification coefficient, and the result is shown in figure 3.
As can be seen from fig. 3, the order of the magnitude of the power response amplification factor of the system is: the vertical displacement of the track slab, the vertical displacement of the steel rail, the vertical acceleration of the vehicle body, the wheel load reduction rate and the vertical force of the wheel rail.
2.3 SVR rationale
As shown in FIG. 4, the basic principle of ε -SVR is: given n data samples y i ,x i I =1,2 … n. Wherein x is i And y i Input samples and output samples, respectively. Mapping input sample x in original space to a high-dimensional feature space phi (x) = (phi) by adopting nonlinear relation 1 (x),φ 2 (x),…φ n (x) And a linear model is built in the high-dimensional feature space to estimate the regression function, as follows:
f(x)＝w·φ(x)+b (4)
in the formula: w is the weight vector and b is the threshold. The input samples are transformed to solve the linear regression problem in a high-dimensional space so as to solve the nonlinear regression problem in the original space, and an insensitive damage function epsilon is defined as:
Figure BDA0003907998750000111
the key to the SVR problem is to find a suitable function f (x) to fit the input samples, such that the observed value y i Sum function prediction value f (x) i ) The error between is minimal and can be expressed by an insensitive impairment function epsilon. When the training point is within epsilon band, the error of the training point is considered to be 0.
The empirical risk minimization and structural risk minimization objective function of the SVR model is:
Figure BDA0003907998750000112
introducing a relaxation variable xi i And
Figure BDA0003907998750000113
the optimization problem can be converted into:
Figure BDA0003907998750000114
Figure BDA0003907998750000115
in the formula: and c is a penalty factor used for balancing the maximum classification interval and the prediction error.
The lagrangian function is used to optimize equation (7), and by solving the dual problem, the solution of equation (4) can be obtained:
Figure BDA0003907998750000116
in the formula: n is a radical of sv The number of the support vectors;
Figure BDA0003907998750000121
and alpha i Is a lagrange multiplier; k (x) i And x) is a kernel function.
In order to eliminate the influence of the unbalance of the numerical values of the parameters of different dimensions on the prediction result, the original data is normalized by adopting a maximum and minimum method, and the calculation formula is as follows:
Figure BDA0003907998750000122
in the formula: x is the number of min Is the minimum value in the data series; x is a radical of a fluorine atom max Is the maximum value in the data series.
Taking four random variables in the section 2.1 as input samples, taking wheel-rail dynamic response as output samples, taking the vertical acceleration of the vehicle body as an example, taking the front 20 groups of training samples in the result obtained by calculation in the section 2.2 as sample data of a regression model of a support vector machine to carry out modeling, and then verifying the model by using 5 groups of test data to ensure the reliability of the model. Before calculation, input and output samples are normalized, and a normalization formula is shown as a formula (9). The result of the parameter selection for the kernel function parameter g and the penalty factor c is shown in fig. 5.
As can be seen from the analysis of fig. 5, the values of the optimized kernel function parameter g and the penalty factor c are 0.125 and 2.828, respectively. Substituting the optimal values of the parameters c and g into the SVR model, wherein the real value and the predicted value of the vertical acceleration of the vehicle body are shown in figure 6, and the error between the real value and the predicted value is shown in figure 7.
As can be seen from fig. 6 and 7, the variation law of the vehicle vertical acceleration predicted by the SVR is substantially the same as the actual vehicle vertical acceleration, the correlation coefficient between the two is 0.993, and the mean square error is 0.004, so that the wheel-rail power system mapping model established based on the SVR in this embodiment has high fitting degree and accuracy.
2.4 analysis of parameter sensitivity
In order to research the influence degree of the four random variables on the dynamic response of the wheel-track system, the sensitivity coefficient of each random variable on the dynamic response of the wheel-track system needs to be defined so as to quantitatively analyze the influence degree of each random variable. Assume that the random variable is represented by S 1 Change to S 2 The dynamic response of the wheel-track system is controlled by M 1 Change to M 2 Then the sensitivity coefficient of the random variable is defined as:
Figure BDA0003907998750000123
in the formula: gamma ray 1 、γ 2 、γ 3 、γ 4 And gamma 5 The random variables are respectively the sensitivity coefficients of the random variables to the vertical acceleration of the vehicle body, the vertical wheel-rail force, the wheel load shedding rate, the vertical displacement of the steel rail and the vertical displacement of the track slab.
When the sensitivity coefficient of a certain random variable is calculated, the other random variables are taken as initial values, the initial values of the fastener rigidity, the mortar elastic modulus, the mortar void length and the pier settlement are respectively taken as 20mm, 7000MPa, 3m and 2mm, and the calculation results are shown in table 3 and fig. 8.
TABLE 3 sensitivity coefficient of random variable to dynamic response of wheel-rail system
Figure BDA0003907998750000131
As can be seen from analysis of table 3 and fig. 8, the influence of pier settlement on the vertical acceleration of the vehicle body is most significant, and the vertical force of the wheel rail, the wheel weight load shedding rate, the vertical displacement of the steel rail and the vertical displacement of the track plate are more sensitive to the mortar void length. Therefore, the vertical force of the wheel rail, the wheel weight load shedding rate, the vertical displacement of the steel rail and the vertical displacement of the track plate are selected as research objects when the influence of mortar void on the long-term service performance of the wheel rail system is evaluated.
TABLE 4 solution time comparison of the two models
Figure BDA0003907998750000132
As can be seen from the data in table 4, the time for solving for 1 time is 738.41 times that of the SVR mapping model, and the calculation efficiency of the SVR nonlinear mapping model is improved by 99.86%; and (3) solving for 100 ten thousand times, wherein the SVR nonlinear mapping model only takes 13.85s, and the train-track-bridge dynamic model cannot be completed. Therefore, the SVR nonlinear mapping model has the advantages of high efficiency, suitability for large sample calculation and the like.
3. Mortar filling layer void length reliability based on SVR nonlinear mapping model
3.1 random sampling
The four random variables are randomly sampled for 100 ten thousand times by adopting a Latin hypercube sampling method, and the generated random variable samples are substituted into the SVR nonlinear mapping model established by 2.3 sections for calculation, so that a probability density distribution diagram and an accumulated probability curve of the vertical acceleration of the vehicle body, the vertical force of the wheel rail, the load shedding rate of the wheel weight, the vertical displacement of the steel rail and the vertical displacement of the track plate can be respectively obtained, and the probability density distribution diagram and the accumulated probability curve are respectively shown in fig. 9 and fig. 10.
3.2 mortar void length different grade control standard limit value
Based on a reliability theory, taking the reliability probability when the power response amplification factor is greater than a certain value as a division basis of a mortar void length control standard, and taking a mortar void length value corresponding to the amplification factor as a control limit value; states of the wheel-rail system when the reliable probability that the dynamic response amplification factor is greater than a certain value is 50%, 30% and 10% are evaluated as first-level, second-level and third-level mortar void length control standards, respectively, and division results of the mortar void length control standards are shown in fig. 11.
The range of the power response amplification coefficient of the wheel-rail system under different mortar void length control standard grades is shown in table 5.
TABLE 5 mortar void length control Standard partition Definitions
Figure BDA0003907998750000141
After determining the standard grade of mortar void length control and the corresponding dynamic response amplification coefficient of a wheel-rail system, solving the mortar void length limit values under the control standards of different grades by using an SVR nonlinear mapping model, wherein the different grade control standard limit values of the mortar void length are shown in Table 6 at different train running speeds when the fastener rigidity A =50kN/mm, the mortar elastic modulus B =7000MPa and the pier settlement D =5 mm;
TABLE 6 mortar void length different grade control standard limit value
Figure BDA0003907998750000142
Figure BDA0003907998750000151
As can be seen from table 6, the mortar void length limit under the vehicle dynamic response control decreases first and then increases with the increase of the speed, while the void length limit under the track dynamic response control increases with the increase of the speed, because the track dynamic response is more sensitive to the mortar void length than the vehicle dynamic response, and when the train running speed is 250-300 km/h, the influence of the train running speed on the vehicle dynamic response is greater than the mortar void length, when the train running speed reaches 350km/h, the influence of the mortar void length on the vehicle dynamic response is more significant, and the track dynamic response is more sensitive to the mortar void length; when the running speeds of the train are 250km/h, 300km/h and 350km/h respectively, the control limit values of the I level, the II level and the III level of the mortar void length are 3.932, 4.337 and 4.766m respectively; 3.948, 4.363 and 4.778m;3.991, 4.386 and 4.803m.
In summary, the invention adopts MATLAB to establish a train sub-model, ANSYS to establish a track-bridge sub-model, the two sub-models are assembled into a train-track-bridge coupling system dynamic model through a wheel-track contact relation, and the train-track-bridge coupling system dynamic model is compared with a literature model for verification; then, considering the rigidity of a fastener, the elastic modulus of mortar, the void length of the mortar and the randomness of pier settlement based on a Latin hypercube sampling method, designing a test point by adopting a Box-Behnken method, carrying out coupled dynamic model calculation, extracting train and structural response index values, establishing a wheel-rail power system nonlinear mapping model based on support vector machine regression (SVR) analysis and predicting, and carrying out comparison verification by adopting a true value and a predicted value; and finally, based on the SVR mapping model, solving the reliability probability of the response index amplification coefficient distribution in different ranges, and taking the reliability probability when the response index amplification coefficient is larger than a certain value as the division basis of the mortar filling layer void length control standard, thereby obtaining the mortar filling layer void length limit value.
The analysis result shows that: the rail bridge coupling dynamic model established by the invention is accurate and reliable; the wheel-rail power system nonlinear mapping model established by the support vector machine has high fitting precision and can be used for predicting the power response of the wheel-rail system; the pier settlement has the most obvious influence on the vertical acceleration of the vehicle body, and the mortar void length has the most obvious influence on the vertical force of the wheel rail, the wheel weight load shedding rate, the vertical displacement of the steel rail and the vertical displacement of the track plate; when the train speed is 250km/h, 300km/h and 350km/h respectively, the I-grade, II-grade and III-grade control limit values of the mortar void length are 3.932, 4.337 and 4.766m respectively; 3.948, 4.363 and 4.778m;3.991, 4.386 and 4.803m, which practically provides a more definite and safe limiting threshold value for the reliability of the void length of the mortar filling layer of the in-service bridge-ballastless track system; in addition, the train-track-bridge coupling dynamic model established by the invention is not only suitable for the reliability analysis of the void length of the mortar filling layer, but also can be properly improved and used aiming at other track diseases, and has good applicability and popularization value.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description is for clarity only, and those skilled in the art should integrate the description, and the embodiments may be combined as appropriate to form other embodiments understood by those skilled in the art.

Claims (10)

1. A method for analyzing the reliability of the void length of a mortar filling layer of an in-service bridge-ballastless track system is characterized by comprising the following steps: the method comprises the following steps:
s1: establishing a train-track-bridge coupling dynamic model: establishing a train sub-model based on a multi-body dynamics theory; establishing a ballastless track-bridge sub-model based on a finite element theory; assembling the train sub-model and the ballastless track-bridge sub-model based on the wheel-track contact relationship to obtain a train-track-bridge coupling dynamic model;
s2: and (3) model verification: verifying the correctness of the established train-track-bridge coupling dynamic model;
s3: obtaining a sample: selecting the rigidity of the fastener, the elastic modulus of mortar, the void length of the mortar and the rigidity of the fastener as random variables; obtaining an SVR test point sample based on Design-Expert software by adopting a Box-Behnken test Design method;
s4: establishing a wheel-rail power system mapping model: based on the SVR principle, establishing a dynamic nonlinear mapping model of the train-track-bridge system, namely a wheel-track power system mapping model, by adopting the SVR test point sample obtained in the step S3, and verifying the model to ensure the reliability of the model;
s5: and (3) analyzing parameter sensitivity: respectively defining the sensitivity coefficients of the random variables to the vertical acceleration of a vehicle body, the vertical wheeltrack force, the wheelload shedding rate, the vertical displacement of a steel rail and the vertical displacement of a track plate; analyzing the sensitivity of the vertical acceleration of the vehicle body, the vertical wheeltrack force, the wheelweight load shedding rate, the vertical displacement of the steel rail and the vertical displacement of the track plate to the mortar void length; determining a research object for analyzing the reliability of the mortar void length;
s6: controlling standard limit values of different grades of the mortar void length: based on a reliability theory, taking the reliability probability when the power response amplification factor is greater than a certain value as a division basis of a mortar void length control standard, and taking a mortar void length value corresponding to the amplification factor as a control limit value; and then calculating the mortar void length limit value under the control standards of different grades through a wheel-rail power system mapping model.
2. The method for analyzing the reliability of the void length of the mortar filling layer of the in-service bridge-ballastless track system according to claim 1, wherein: in the step S1, the train submodel is established in MATLAB and consists of 1 train body, 2 bogies and 4 wheel pairs; a suspension system among the vehicle body, the bogie and the wheel set is simulated by a spring-damping unit; the car body and the two bogies consider 5 degrees of freedom of transverse movement, sinking and floating, side rolling, nodding and shaking, each wheel pair considers 4 degrees of freedom of transverse movement, sinking and floating, side rolling and shaking, and the car body, the framework and the wheel pair are assumed to be rigid bodies.
3. The method for analyzing the reliability of the void length of the mortar filling layer of the in-service bridge-ballastless track system according to claim 1, wherein: in the step S1, the ballastless track-bridge submodel is established in ANSYS; the ballastless track mainly comprises steel rails, fasteners, track plates, a CA mortar layer, a base plate and a 'two-cloth-one-film' sliding layer; the steel rail, the track plate, the base plate and the bridge are all simulated by adopting a beam unit; the fastener and the CA mortar layer are simulated by a spring-damping unit; the sliding layer is simulated by adopting a one-way compression spring.
4. The method for analyzing the reliability of the void length of the mortar filling layer of the in-service bridge-ballastless track system according to claim 1, wherein: in the step S1, the concrete steps of assembling the train sub-model and the ballastless track-bridge sub-model based on the wheel-track contact relationship to obtain the train-track-bridge coupling dynamic model are as follows:
s1-1: performing modal analysis on the ballastless track-bridge submodel to obtain a full binary file storing the overall mass, rigidity and damping matrix of the submodel;
s1-2: converting the binary file into a Harwell-Boeing file by adopting an HBMAT command, and converting the Harwell-Boeing file into a sparse matrix form by Python; extracting the positions of the quality, rigidity and damping matrix nodes in the binary file by utilizing HBMAT, and generating a Mapping file;
s1-3: and (3) associating the Mapping file and the sparse matrix of the ballastless track-bridge sub-model with the train sub-model by adopting a wheel-rail contact relation, and establishing a train-track-bridge coupling dynamic model.
5. The method for analyzing the reliability of the void length of the mortar filling layer of the in-service bridge-ballastless track system according to claim 4, wherein: according to the established train-track-bridge coupling dynamic model, the wheel-track normal force is subjected to Hertz contact simulation, and the wheel-track transverse force takes the creep force into consideration.
6. The method for analyzing the reliability of the void length of the mortar filling layer of the in-service bridge-ballastless track system according to claim 1, wherein: in the step S2, the model verification requires that the calculation result of the established model is compared with the calculation result of the comparison model, the vertical displacement variation trends of the beam end and the midspan steel rail are basically consistent, and the amplitude error is not more than 5% at most.
7. The method for analyzing the reliability of the void length of the mortar filling layer of the in-service bridge-ballastless track system according to claim 1, wherein: in step S3, the random variable, wherein: the settlement value of the bridge pier is 2-10 m and is subject to uniform distribution; the void length of the mortar is 3-5 m and is subject to uniform distribution; the rigidity of the fastener follows the truncation normal distribution, the mean value is 30, and the standard deviation is 23.33; the elastic modulus of the mortar follows normal distribution, the mean value is 8500, and the standard deviation is 500.
8. The method for analyzing the reliability of the void length of the mortar filling layer of the in-service bridge-ballastless track system according to claim 1, wherein: in the step S4, the mapping model of the wheel-rail power system takes the rigidity of a random variable fastener, the elastic modulus of mortar, the void length of mortar and the rigidity of the fastener as input samples, and takes the wheel-rail power response as an output sample; normalizing the input and output samples; and modeling by taking a part of SVR test point samples as sample data, and verifying the established wheel-rail power system mapping model by using the rest of SVR test point samples.
9. The method for analyzing the reliability of the void length of the mortar filling layer of the in-service bridge-ballastless track system according to claim 1, wherein: in step S5, in the parameter sensitivity analysis, when the sensitivity coefficient of a certain random variable is calculated, the other random variables are all taken as initial values; initial values of the rigidity of the fastener, the elastic modulus of the mortar, the void length of the mortar and the settlement of the pier are respectively 20mm, 7000MPa, 3m and 2mm.
10. The method for analyzing the reliability of the void length of the mortar filling layer of the in-service bridge-ballastless track system according to claim 1, wherein: in step S6, the control standard limit values of different grades of the mortar void length are as follows: and evaluating the states of the wheel-rail system when the reliable probability of the dynamic response amplification coefficient of the wheel-rail system being greater than a certain value is 50%, 30% and 10% as I-grade, II-grade and III-grade mortar void length control standards.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115964920A (en) * 2023-03-16 2023-04-14 武汉大学 Method for estimating void length of CA mortar bed of ballastless track based on finite element simulation

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115964920A (en) * 2023-03-16 2023-04-14 武汉大学 Method for estimating void length of CA mortar bed of ballastless track based on finite element simulation

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