A method and system for determining a turnout stiffness degradation limit value based on time-varying reliability
By establishing a rigid-flexible coupling dynamic model of the vehicle-turnout system and a probability density evolution equation, the shortcomings of turnout stiffness variation in system reliability assessment are addressed, the precise determination of turnout stiffness degradation limits is achieved, and a balance between safety and efficiency is provided.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SOUTHWEST JIAOTONG UNIV
- Filing Date
- 2026-01-27
- Publication Date
- 2026-06-12
Smart Images
Figure CN122197279A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of track engineering technology, and more specifically, to a method and system for determining the stress degradation limit of turnouts based on time-varying reliability. Background Technology
[0002] During long-term service, the structural rigidity of key components of railway turnouts, such as fasteners and pads, gradually deteriorates. This deterioration directly leads to an increased dynamic response of vehicles when passing through the turnout, affecting not only ride comfort but also operational safety and increasing the risk of derailment.
[0003] However, there is currently a lack of effective means to quantify and assess the evolution of the overall system reliability caused by changes in the stiffness of turnout components. This lack of assessment methods severely restricts the development of preventative maintenance plans. The current technical bottlenecks in reliability assessment and stiffness limit determination for vehicle-turnout systems are as follows: First, existing reliability assessment methods, when dealing with vehicle-turnout coupled systems, fail to establish a quantitative mapping relationship between the time-varying degradation of turnout component stiffness and the overall system reliability. This makes it impossible to accurately assess the system's reliability during long-term service, i.e., it is difficult to directly assess the continuous decline in reliability of the vehicle-turnout system as the turnout structural stiffness deteriorates. Second, existing turnout stiffness limits are mostly static fixed values, failing to consider the dynamic coupling effects of complex loads, environmental changes, and stiffness degradation. This disconnects them from the system's time-varying reliability, resulting in a lack of scientific rigor and engineering adaptability in the limit standards, and an inability to provide precise support for maintenance decisions at different service stages. Summary of the Invention
[0004] The purpose of this invention is to provide a method and system for determining the turnout stiffness degradation limit based on time-varying reliability, so as to improve the above-mentioned problems. To achieve the above objective, the technical solution adopted by this invention is as follows:
[0005] Firstly, this application provides a method for determining the turnout stiffness degradation limit based on time-varying reliability, including:
[0006] Establish the dynamic vibration equation of flexible turnout based on the rigid-flexible coupling dynamic model of vehicle-turnout;
[0007] Random samples were generated using a stratified sphere-Latinization sampling method, and the random samples included random track irregularities and vehicle parameter samples.
[0008] Based on the dynamic vibration equation of flexible turnout, the dynamic equation of vehicle-turnout rigid-flexible coupling is constructed. The dynamic equation is solved according to random samples to generate the extreme value distribution of dynamic response index under different stiffness.
[0009] The probability density evolution equation of the dynamic response index is solved by extreme value distribution, and the probability density function information of the dynamic response index under different stiffnesses is generated.
[0010] The time-varying reliability under different stiffnesses is calculated based on the probability density function information, and the stiffness degradation limit of the turnout is determined by the time-varying reliability.
[0011] Secondly, this application also provides a system for determining the limit of turnout stiffness deterioration based on time-varying reliability, including:
[0012] The module is used to establish the dynamic vibration equation of flexible turnouts based on the vehicle-turnout rigid-flexible coupling dynamic model;
[0013] The generation module is used to generate random samples using a spherical-Latinized partially stratified sampling method, wherein the random samples include random track irregularities and vehicle parameter samples.
[0014] The first calculation module is used to construct the dynamic equation of the vehicle-turnout rigid-flexible coupling based on the dynamic vibration equation of the flexible turnout, solve the dynamic equation according to random samples, and generate the extreme value distribution of the dynamic response index under different stiffness.
[0015] The second calculation module is used to solve the probability density evolution equation of the dynamic response index through the extreme value distribution, and generate the probability density function information of the dynamic response index under different stiffnesses.
[0016] The third calculation module is used to calculate the time-varying reliability under different stiffnesses based on the probability density function information, and to determine the stiffness deterioration limit of the turnout through the time-varying reliability.
[0017] The beneficial effects of this invention are as follows:
[0018] (1) The present invention designs a spherical-Latinized partial stratified sampling method, which decomposes the high-dimensional random parameter space into a low-dimensional subspace, generates a uniform point set in the low-dimensional space and then randomly combines it back into the high-dimensional space, so that the sample points are more evenly distributed and more comprehensively covered in the high-dimensional space, which significantly reduces the variance and error of the reliability assessment results. At the same time, by combining the implicit integral Park method, the total variation non-increase method and the absorbing boundary condition method, stiffness degradation modeling, dynamic solution, probability density evolution calculation and time-varying reliability calculation are realized. This not only ensures the stability and convergence of the solution of the nonlinear dynamic equation, but also realizes the accurate characterization of the probability density evolution process, filling the technical gap that traditional methods cannot quantify the correlation between stiffness time-varying degradation and system reliability.
[0019] (2) This invention also establishes a mapping relationship between stiffness and minimum time-varying reliability, and solves in reverse to obtain the stiffness degradation limit of the turnout. This breaks through the limitation of the traditional static limit lacking dynamic adaptability, and directly links the stiffness limit with the time-varying reliability of the system under complex loads and environmental changes, which is more in line with the actual working conditions of the turnout in long-term service. This stiffness degradation limit can provide precise guidance for railway operation and maintenance. When the stiffness of the turnout component is detected to degrade to the limit, timely maintenance or replacement measures can be taken to effectively prevent safety risks such as excessive wheel-rail contact force and abnormal derailment coefficient. At the same time, the evaluation results based on time-varying reliability can predict the evolution trend of the system's safety status, help to formulate preventive operation and maintenance plans, and avoid the waste of resources caused by excessive maintenance while ensuring traffic safety, so as to achieve a balance between safety and efficiency.
[0020] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing embodiments of the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings. Attached Figure Description
[0021] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.
[0022] Figure 1 This is a schematic diagram of the method for determining the turnout stiffness degradation limit based on time-varying reliability as described in an embodiment of the present invention;
[0023] Figure 2 This is a cross-sectional view of the hazardous space in the fork area in an embodiment of the present invention;
[0024] Figure 3 This is a cross-sectional view of the long center rail in the fork area of this invention embodiment;
[0025] Figure 4 This is a schematic diagram of the ball-cutting method in an embodiment of the present invention;
[0026] Figure 5 This is a probability density evolution cloud map in an embodiment of the present invention.
[0027] The markings in the diagram are: 1. Straight main rail; 2. Curved main rail; 3. Side wing rail; 4. Straight wing rail; 5. Long center rail; 6. Fork and point rail; 7. Guard rail; 8. Base plate; 10. Lateral restraint of fasteners; 11. Spacer; 12. Rail head tightness restraint; 13. Bolt; 14. Top rail; 15. External locking device for center rail; 16. Vertical contact between movable rail components and base plate; 17. Under-rail rubber pad; 18. Under-slab rubber pad; 19. Turnout slab; 20. Self-compacting concrete; 21. Base plate; 22. Subgrade surface layer; 23. Ground foundation. Detailed Implementation
[0028] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.
[0029] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.
[0030] Example 1:
[0031] This embodiment provides a method for determining the turnout stiffness degradation limit based on time-varying reliability.
[0032] See Figure 1 The figure shows that the method includes steps S1, S2, S3, S4 and S5.
[0033] Step S1: Establish the dynamic vibration equation of the flexible turnout based on the rigid-flexible coupling dynamic model of the vehicle-turnout;
[0034] Step S1 includes:
[0035] Step S11: Establish a vehicle-turnout rigid-flexible coupling dynamic model that includes the mechanical properties of each part of the turnout structure;
[0036] In this step, to consider the impact of changes in the stiffness of the turnout track structure on the vehicle's dynamic response, a flexible turnout model needs to be established. This model considers the multi-layered structure of the turnout's variable cross-section rails, shared rail base plates, turnout slabs, and slide plates, as well as the complex constraints between layers and between rails. The dynamic modeling of the frog area is as follows: Figure 2 and Figure 3 As shown. Then, combined with the vehicle dynamics model, a rigid-flexible coupling dynamic model of the vehicle-turnout coupling system is formed.
[0037] It should be noted that both the flexible turnout model and the vehicle dynamics model are constructed based on the finite element discretization method. Modal analysis is then performed using finite element software to provide a basis for calculating mechanical parameters.
[0038] Step S12: Define the turnout dynamic equations for the rigid-flexible coupling dynamic model of the vehicle-turnout;
[0039] In this step, the turnout dynamics equation for the flexible turnout model is defined as follows:
[0040] ;
[0041] In the formula, , and These represent the mass matrix, damping matrix, and stiffness matrix of the turnout, respectively. , and These represent the displacement, velocity, and acceleration vectors of the rail node, respectively. This represents the vector of external loads acting on the rail.
[0042] Step S13: Calculate the mode vectors and mode matrices of each mode of the turnout structure based on the turnout dynamics equation and characteristic equation;
[0043] In this step, without considering structural damping, the angular frequencies and mode shape vectors of each mode of the structure are solved using the characteristic equation:
[0044] ;
[0045] In the formula, Indicates the first The angular frequency of the first mode, Indicates the first The mode shape vectors of the first-order modes. Where, the mode shape matrix... It is composed of the vectors of each mode shape.
[0046] Step S14: Based on the modal superposition method, the coordinate vectors in the physical space are transformed into the product of the mode shape matrix and the regular mode shape coordinate vector;
[0047] In this step, the coordinate vector represents the displacement of the rail node. It can be transformed into:
[0048] ;
[0049] In the formula, Represents the coordinate vector of the normal mode shape. Indicates the first The normal mode coordinates of the mode shapes corresponding to the first mode. This represents the total modal order.
[0050] Step S15: Substitute the mode shape vector, the transformed coordinate vector and its time derivative into the dynamic equation to decouple the turnout dynamic equation from the physical space to the modal space, and obtain the dynamic vibration equation of the flexible turnout.
[0051] In this step, the dynamic vibration equation of the flexible turnout is:
[0052] ;
[0053] In the formula, express transpose, and These represent the normal mode velocity vector and the normal mode acceleration vector, respectively.
[0054] Step S2: Generate random samples using the spherical-Latinized partial stratified sampling method. The random samples include random track irregularities and vehicle parameter samples.
[0055] In establishing the rigid-flexible coupling dynamic model of the vehicle-turnout, a large number of uncertain parameters, i.e., high-dimensional random variables, exist, and the distribution of samples in the high-dimensional space becomes extremely sparse. Traditional methods such as cut-ball sampling or Monte Carlo methods, when dealing with high-dimensional random parameters, suffer from insufficient coverage of the parameter space due to the sparse distribution of samples in the high-dimensional space. Consequently, the reliability assessment results have large variance and errors, making it difficult to accurately reflect the true statistical characteristics of the system.
[0056] Therefore, this step designs a spherical-Latinized partial stratified sampling method to generate uniformly distributed sample points in a high-dimensional space, significantly improving sampling efficiency and coverage, and laying the foundation for high-precision reliability analysis.
[0057] Step S2 includes:
[0058] Step S21: Set high-dimensional random parameters, which include vehicle parameters and track-related basic parameters;
[0059] In this step, vehicle parameters may include primary suspension stiffness, primary suspension damping, secondary suspension stiffness, secondary suspension damping, axle load, wheelset mass, bogie mass, and car body mass. Track-related basic parameters may include wavelength distribution parameters and track irregularity amplitude. Furthermore, the distribution form (e.g., normal distribution, uniform distribution) and value range of each high-dimensional random parameter need to be clearly defined. Simultaneously, the total number of vehicle parameters and track irregularity-related parameters is counted and denoted as the high-dimensional space dimension. .
[0060] Step S22: Divide the high-dimensional space corresponding to the high-dimensional random parameters into multiple low-dimensional subspaces, wherein the low-dimensional subspaces are two-dimensional subspaces or one-dimensional subspaces;
[0061] It should be noted that the sphere-cutting method performs well in low-dimensional spaces, generating uniform point sets with small biases. However, its applicability is limited in high-dimensional spaces due to issues such as decreased convergence speed of bias, complex construction, poor flexibility of point sets, and unclear geometric structure. Therefore, directly generating uniform point sets in high-dimensional spaces is very difficult. However, by decomposing the high-dimensional space into multiple low-dimensional subspaces and then randomly combining these low-dimensional points back into the high-dimensional space, the resulting high-dimensional sample will also have good uniformity, thus achieving significant variance reduction.
[0062] In this step, A high-dimensional space is decomposed into several low-dimensional subspaces according to the principle of two dimensions as the main component and one dimension as a supplement.
[0063] like If it is even, then decompose it into: A mutually independent two-dimensional subspace, if If it is an odd number, then decompose it into: There are two independent two-dimensional subspaces and one one-dimensional subspace.
[0064] It should be noted that the determined high-dimensional random parameters are evenly distributed to each low-dimensional subspace (e.g., two vehicle parameters or one vehicle parameter and one track-related basic parameter are distributed to the same two-dimensional subspace) to ensure that the parameters in each subspace do not overlap and are fully covered.
[0065] Step S23: Generate a uniform point set for each low-dimensional subspace using the principle of spherical cutting or equidistant sampling;
[0066] In this step, the spherical cutting method is used to generate a uniform set of points in the two-dimensional subspace.
[0067] In a two-dimensional subspace, the sphere-filling problem provides a feasible way to construct a uniformly distributed set of representative sample points, such as... Figure 4 As shown, the centers of these non-overlapping spheres form a point set, where, and They represent shaft and Axis. In a sense, it is uniformly distributed in space, and its properties can be quantified by the filling density. These circles form different cycles (layers) outward, and the circles can be numbered counterclockwise along each cycle.
[0068] Therefore, for each two-dimensional subspace, the calculation of the first... Polar coordinates of the centers of the circles :
[0069] ;
[0070] In the formula, The index representing the center of the circle. Indicates the angle cycle number. This represents the cycle number, initially set to 0. , Indicates the maximum number of loops. Indicates the index within the loop. Represents the radius of the circle. and They represent the first The polar radius and polar angle of each circle.
[0071] After Cartesian coordinate transformation, the coordinates of each circle's center are: :
[0072] ;
[0073] In the formula, and They represent the first The x and y coordinates of the center of each circle.
[0074] The coordinates of all the centers of the circles form a uniform set of points in the corresponding two-dimensional subspace, and each point becomes the tangent point.
[0075] In this step, if a one-dimensional subspace exists, equidistant sampling is used to generate the corresponding uniform point set. Specifically, based on the total number of samples required, within the range of values for this one-dimensional parameter, several sample points are drawn at equal intervals to form a one-dimensional uniform point set.
[0076] Step S24: Randomly pair up the uniform point sets of each low-dimensional subspace and combine them into uniform samples in the high-dimensional space.
[0077] In this step, high-dimensional uniform samples are generated by randomly combining low-dimensional uniform point sets.
[0078] when When the number is even, the uniform point sets of each two-dimensional subspace are randomly paired to generate multiple uniform samples:
[0079] ;
[0080] In the formula, Indicates the first A uniform sample, Indicates the first The first two-dimensional subspace One cutting point, Indicates the first The corresponding uniform sample of the th th Point indices of a low-dimensional subspace, , This represents the total number of low-dimensional subspaces. express The transpose of . In this case, Each low-dimensional subspace is a two-dimensional subspace.
[0081] when When the number is odd, multiple uniform samples are generated as follows:
[0082] ;
[0083] In the formula, Indicates the first The first two-dimensional subspace One cutting point, Describe the first in a one-dimensional subspace equidistant sampling points. In this case, the first... Each of the low-dimensional subspaces is a two-dimensional subspace, and the... Each low-dimensional subspace is a one-dimensional subspace.
[0084] Step S25: Transform the uniform samples into vehicle parameter samples that conform to a preset distribution through equal probability transformation;
[0085] In this step, the uniform samples are transformed into vehicle parameter samples that conform to a preset distribution by using the inverse function of the joint cumulative distribution function:
[0086] ;
[0087] In the formula, Indicates the first Vehicle parameter samples corresponding to a uniform sample This represents the inverse function of the joint cumulative distribution function. The joint cumulative distribution function needs to be derived from the distribution form of the corresponding vehicle parameters.
[0088] Step S26: Obtain the power spectral density function of the orbital random irregularities;
[0089] In this step, the power spectral density function is obtained based on the power spectral density of the track irregularity spectrum of ballastless track in China.
[0090] Step S27: Superimpose multiple sinusoidal simulations onto the power spectral density function to generate a random track irregularity function;
[0091] By superimposing multiple sinusoidal simulated random signals onto the power spectral density function, a random harmonic function, namely the orbital random irregularity function, is constructed.
[0092] Step S28: Adjust the harmonic amplitude in the track random irregularity function using vehicle parameter samples to generate a track random irregularity sample corresponding to each vehicle parameter sample.
[0093] Step S3: Construct the dynamic equation of vehicle-turnout rigid-flexible coupling based on the dynamic vibration equation of flexible turnout, solve the dynamic equation according to random samples, and generate the extreme value distribution of dynamic response index under different stiffness.
[0094] In step S3, the construction of the dynamic equations for the rigid-flexible coupling of the vehicle and the turnout based on the dynamic vibration equations of the flexible turnout includes:
[0095] Step S301: Define the vehicle dynamics equations for the rigid-flexible coupling dynamics model of the vehicle-turnout;
[0096] Step S302: Establish the mechanical coupling relationship between the dynamic vibration equation of the flexible turnout and the dynamic equation of the vehicle through the wheel-rail contact algorithm, and obtain the dynamic equation of the rigid-flexible coupling between the vehicle and the turnout.
[0097] In step S3, solving the dynamic equations based on random samples to generate extreme value distributions of dynamic response indices under different stiffnesses includes:
[0098] Step S31: Obtain the mechanical properties of the turnout component at each stiffness during the stiffness degradation process, wherein the mechanical properties include stiffness matrix, mass matrix and damping matrix;
[0099] In this step, measured data on stiffness degradation of turnout components (fasteners, rail pads, under-slab pads, etc.) during service are collected to establish a stiffness degradation sequence. For each stiffness in the stiffness degradation sequence, the mechanical properties of the turnout in the finite element model are updated.
[0100] Step S32: Convert the random irregularity sample of the track into an external load vector in the physical space, and convert the external load vector into the modal space through the modal superposition method to obtain the modal load vector;
[0101] In this step, the random irregularity samples of the track are transformed into external load vectors in physical space. The load is applied at the rail joint. Transforming to modal space yields the modal load vector, i.e. .
[0102] Step S33: Input the modal load vector, mechanical properties and random samples into the dynamic equation to obtain the sample dynamic equation corresponding to each random sample under different stiffness;
[0103] For each stiffness, the stiffness matrix, mass matrix, and damping matrix of the turnout are extracted. Then, the stiffness matrix, mass matrix, and damping matrix of the vehicle are updated by combining the vehicle parameter samples. These are then substituted into the dynamic equation to obtain the sample dynamic equation corresponding to each random sample under different stiffnesses.
[0104] Step S34: Solve the dynamic equation for each sample using the Park method to obtain the time series of dynamic response indexes for each random sample under different stiffnesses;
[0105] To address medium- and high-frequency impacts in the turnout area, and to ensure stable convergence of the results, the unconditionally stable implicit integral algorithm Park method is chosen for solving the dynamic equations.
[0106] Set time step Meanwhile, the vehicle-turnout coupling system is a nonlinear dynamic system. For a nonlinear dynamic system, at any given moment... The sample dynamics equation can be expressed as:
[0107] ;
[0108] In the formula, , and Let these represent the mass, damping, and stiffness matrices of the vehicle-turnout coupling system, respectively. , and Representing time respectively The displacement, velocity, and acceleration vectors of the vehicle-turnout coupling system. , and Representing time respectively Compared to time The change in dynamic response, Indicates time Load matrix of vehicle-turnout coupling system.
[0109] The Park method makes the following basic assumptions:
[0110] ;
[0111] ;
[0112] In the formula, , and Representing time respectively The displacement, velocity, and acceleration vectors of the vehicle-turnout coupling system. and Representing time respectively Displacement and velocity of the vehicle-turnout coupling system at that time This represents a linear combination operator of historical responses, used to indicate the contribution of past responses to the current prediction. , , and All represent integral coefficients.
[0113] Understandable , , Therefore, substituting the basic assumptions into the sample dynamics equations yields:
[0114] ;
[0115] ;
[0116] ;
[0117] In the formula, Represents the equivalent stiffness matrix. This represents the equivalent load matrix.
[0118] The Park method performs numerical integration based on the dynamic response of the first three time steps, and uses Newmark at the start of the iteration. β The calculation is performed using a method. In implicit integral algorithms for wheel-rail system dynamics, a common iteration error limit is used to control the accuracy of each element in the generalized displacement matrix (including displacement and rotation), ensuring that the 2-norm of the displacement increment matrix is less than 10. -8 Practice has shown that directly judging the accuracy of wheel-rail contact force can more fully guarantee the convergence of calculation, including that at a certain moment, for each wheel-rail contact pair, the relative error of the contact normal force and tangential force between two iterations is less than 0.1%.
[0119] Wherein, the solution obtained at each time step is Then, the spatial relative position of the rail wheelset is updated, and the normal and tangential forces at the contact point are calculated using a wheel-rail contact algorithm. The obtained normal and tangential forces are then written into a matrix according to their position and direction of action. In the next iteration, the dynamic response results of the vehicle passing through the turnout are obtained, which means that the time series of dynamic response indexes corresponding to each random sample under different stiffness can be obtained.
[0120] Dynamic response indicators can include safety indicators such as wheel-rail vertical force, wheel-rail lateral force, derailment coefficient, and wheel load reduction rate.
[0121] Step S35: Perform statistical analysis on the time series of dynamic response indices to generate the extreme value distribution of dynamic response indices under different stiffnesses.
[0122] Step S35 includes:
[0123] Step S351: Obtain the extreme values of the dynamic response index through the time series of the dynamic response index;
[0124] Step S352: For each stiffness, collect the extreme values of each dynamic response index of all random samples to obtain the set of extreme values under that stiffness;
[0125] Step S353: Perform statistical analysis on the extreme value set for each stiffness to generate the extreme value distribution of multiple dynamic response indices under different stiffnesses.
[0126] Step S4: Solve the probability density evolution equation of the dynamic response index through the extreme value distribution to generate the probability density function information of the dynamic response index under different stiffnesses;
[0127] Step S4 includes:
[0128] Step S41: Define the dynamic response index as a state variable. ;
[0129] Step S42: Establish the probability density evolution equation of the state variables and fit the initial probability density function of the state variables;
[0130] In this step, it is assumed that no random source is eliminated or introduced during the stiffness degradation process of the nonlinear dynamic system, and therefore the nonlinear dynamic system follows the probability conservation condition. Based on this, the probability density evolution equation under a certain stiffness is established:
[0131] ;
[0132] In the formula, Indicates at time The probability density function under the given conditions, Represents the state variable over time The deterministic rate of change in evolution.
[0133] Step S43: Under different stiffnesses, iteratively solve the probability density evolution equation based on the initial probability density function to obtain the probability density function of the current time step;
[0134] In this step, the method of non-increasing total variation is used for numerical solution.
[0135] In step S43, obtaining the probability density function for the current time step includes:
[0136] Step S431: Obtain the range of values by the extreme value distribution of the state variables, discretize the range of values to obtain grid points and grid step size;
[0137] This step is based on the grid step size. The range of values is evenly divided into multiple grid intervals, resulting in multiple grid points.
[0138] Step S432: Discretize the service time to obtain the time step;
[0139] Step S433: Define the stability coefficients using the grid step size and time step size;
[0140] In this step, the stability coefficient Used to control numerical stability, specifically:
[0141] ;
[0142] In the formula, Indicates the time step. This indicates the grid step size.
[0143] Step S434: Calculate the mixed flux of each grid point based on the initial probability density function, and update the probability density of each grid point at the current time step using the mixed flux and stability coefficient;
[0144] In this step, at each time step Grid points The probability density at a given point, whose flux difference form can be written as:
[0145] ;
[0146] In the formula, and These represent the time steps. and time step Time grid points The probability density at that location, and These represent the time steps. Time grid points and grid points Mixed flux at the location.
[0147] The mixed flux can be calculated using one-sided flux, probability density difference, etc., thus yielding:
[0148] ;
[0149] In the formula, and These represent the time steps. Time grid points and grid points One-sided flux at the location, and These represent the time steps. Half-grid points and half grid points The probability density difference at the point, Represents a deterministic rate of change. This indicates taking the absolute value. and These represent points at half grid points. and half grid points The flux limiter at the location.
[0150] in, It is a stability correction factor, which, while maintaining the TVD properties, introduces an appropriate amount of dissipation to ensure format stability. and It is typically a factor less than 1, which applies a correction to the numerical flux based on the data from the numerical solution. The one-sided flux is calculated using the deterministic rate of change and the corresponding probability density.
[0151] Therefore, the complete numerical flux form of the probability density can be written as:
[0152]
[0153] To ensure that the above equation does not simplify to the one-sided form or the Laks-Wendloff form, the following is required: .
[0154] By using the sequential difference ratio, it is possible to determine whether abrupt changes occur in the curve, and to make corresponding corrections to the flux limiter. and To correct the flux limiter:
[0155] ;
[0156] In the formula, and These represent the forward order difference ratio and the reverse order difference ratio, respectively. , and These represent the time steps. Half-grid points , and The probability density difference at the point, , , and These represent the time steps. Time grid points , , and The probability density at that location.
[0157] Step S435: Calculate the total variation at the current time step using the probability density of adjacent grid points;
[0158] In this step, the discrete form of the total variation is defined as:
[0159] ;
[0160] In the formula, Indicates time step The total variation.
[0161] Step S436: Determine whether the TVD requirement is met by the total variation between two adjacent time steps. If yes, generate the probability density function of the current time step using the probability density of each grid point in the current time step. Otherwise, adjust the stability coefficient and recalculate the probability density function of the current time step.
[0162] In this step, TVD requires that the total variation does not increase, that is, the total variation at the current time step is not greater than the total variation at the previous time step.
[0163] Step S44: Use the probability density function of the current time step as the initial probability density function of the next time step, and perform the next iteration until the probability density functions of all time steps under different stiffness are generated.
[0164] Step S45: Generate the probability density function information of the dynamic response index under different stiffnesses by using the probability density function of all time steps under different stiffnesses.
[0165] Taking the wheel load reduction rate as an example, when the wheel load reduction rate is a state variable, after obtaining the probability density function information, it is plotted as follows: Figure 5 The probability density evolution cloud diagram shown is shown in which each curve is a probability density function under different stiffness, and is obtained by converting the total weight through time, that is, the total weight is the cumulative throughput during the service time.
[0166] Step S5: Calculate the time-varying reliability under different stiffnesses based on the probability density function information, and determine the stiffness deterioration limit of the turnout through the time-varying reliability.
[0167] Step S5 includes:
[0168] Step S51: Transform the probability density function information through high-dimensional random parameters to obtain the joint probability density function, and set the absorbing boundary conditions through the joint probability density function;
[0169] In this step, a high-dimensional set of random parameters is set. , Including all high-dimensional random parameters. (Through...) and get Simultaneously, the probability density evolution equation is obtained:
[0170] ;
[0171] In the formula, Indicates at time State variable values High-dimensional random parameters The joint probability density function at time , Indicates by and The deterministic rate of change of the state vector is determined.
[0172] If the sample response exceeds the safety region, the corresponding random sample will contribute to the failure probability rather than the reliability. Therefore, an absorption boundary condition is set:
[0173] ;
[0174] In the formula, Represents the failure domain, once the state variable... The value exceeds the safety domain and becomes invalid when it reaches the failure domain. The safety domain is determined by railway safety standards.
[0175] Step S52: For each stiffness, the residual probability density within the safety region is obtained by integrating the joint probability density function, where the safety region is the allowable range of values for the dynamic response index.
[0176] It should be noted that for the joint probability density function After setting the absorbing boundary conditions, the remaining joint probability density can be obtained. The physical meaning of the absorbing boundary condition is that once the sample response exceeds the safe region, the relevant probability will not return to the safe region. Therefore, its residual probability density can be expressed as:
[0177] ;
[0178] In the formula, Indicates at time The residual probability density function under the given conditions, Represents a set of high-dimensional random parameters The value space of .
[0179] Step S53: Integrate the residual probability density over the safe region to obtain the time-varying reliability curve of each stiffness with respect to service time;
[0180] In this step, the time-varying reliability for each stiffness at different service times is:
[0181] ;
[0182] In the formula, Indicates time-varying reliability. Indicates a security domain.
[0183] In different calculations corresponding Then, the time-varying reliability curve of each stiffness with respect to service time can be plotted.
[0184] Step S54: Extract the minimum time-varying reliability over the service life from the time-varying reliability curve for each stiffness.
[0185] Step S55: Establish the mapping relationship between stiffness and minimum time-varying reliability, and obtain the mapping relationship curve;
[0186] Step S56: Based on the mapping relationship curve, find the stiffness value that satisfies the minimum time-varying reliability equal to the preset target threshold, and use this stiffness value as the stiffness deterioration limit of the turnout.
[0187] In this step, the stiffness degradation limit is... This refers to the safety maintenance limit for the stiffness of turnout components. When the real-time detected component stiffness exceeds... At this point, the reliability of the entire vehicle-turnout coupling system remains above the safety baseline under the most unfavorable conditions, indicating a safe state. However, if testing reveals that the stiffness of a component has degraded to equal to or below the safety baseline... If this happens, it means that the system reliability has reached or fallen below the safety threshold, and the component must be maintained or replaced to prevent safety accidents from occurring.
[0188] Example 2:
[0189] This embodiment provides a turnout stiffness degradation limit determination system based on time-varying reliability, the system comprising:
[0190] The module is used to establish the dynamic vibration equation of flexible turnouts based on the vehicle-turnout rigid-flexible coupling dynamic model;
[0191] The generation module is used to generate random samples using a spherical-Latinized partially stratified sampling method, wherein the random samples include random track irregularities and vehicle parameter samples.
[0192] The first calculation module is used to construct the dynamic equation of the vehicle-turnout rigid-flexible coupling based on the dynamic vibration equation of the flexible turnout, solve the dynamic equation according to random samples, and generate the extreme value distribution of the dynamic response index under different stiffness.
[0193] The second calculation module is used to solve the probability density evolution equation of the dynamic response index through the extreme value distribution, and generate the probability density function information of the dynamic response index under different stiffnesses.
[0194] The third calculation module is used to calculate the time-varying reliability under different stiffnesses based on the probability density function information, and to determine the stiffness deterioration limit of the turnout through the time-varying reliability.
[0195] The generation module includes:
[0196] The setting unit is used to set high-dimensional random parameters, which include vehicle parameters and track-related basic parameters.
[0197] A splitting unit is used to split the high-dimensional space corresponding to high-dimensional random parameters into multiple low-dimensional subspaces, wherein the low-dimensional subspace is a two-dimensional subspace or a one-dimensional subspace.
[0198] The first generation unit is used to generate a uniform set of points for each low-dimensional subspace by means of the spherical cutting method or equidistant sampling.
[0199] Pairing units are used to randomly pair uniform point sets in each low-dimensional subspace to form uniform samples in a high-dimensional space.
[0200] The first conversion unit is used to convert uniform samples into vehicle parameter samples that conform to a preset distribution through equal probability transformation.
[0201] The first acquisition unit is used to acquire the power spectral density function of random irregularities in the orbit;
[0202] The second generation unit is used to superimpose multiple sinusoidal simulations on the power spectral density function to generate a random irregularity function of the orbit.
[0203] The third generation unit is used to adjust the harmonic amplitude in the track random irregularity function through vehicle parameter samples, and generate a track random irregularity sample corresponding to each vehicle parameter sample.
[0204] The first computing module includes:
[0205] The second acquisition unit is used to acquire the mechanical properties of the turnout component at each stiffness during the stiffness degradation process. The mechanical properties include stiffness matrix, mass matrix and damping matrix.
[0206] The second conversion unit is used to convert random irregularity samples of the track into external load vectors in the physical space, and to convert the external load vectors into modal space through modal superposition method to obtain modal load vectors;
[0207] The input unit is used to input the modal load vector, mechanical properties and random samples into the dynamic equation to obtain the sample dynamic equation corresponding to each random sample under different stiffness.
[0208] The first solution unit is used to solve the dynamic equation for each sample using the Park method, and obtain the time series of dynamic response indexes for each random sample under different stiffness.
[0209] The sharing unit is used to perform statistical analysis on the time series of dynamic response indicators and generate the extreme value distribution of dynamic response indicators under different stiffnesses.
[0210] The second calculation module includes:
[0211] Define a unit to define the dynamic response index as a state variable;
[0212] The fitting unit is used to establish the probability density evolution equation of the state variables and fit the initial probability density function of the state variables.
[0213] The second solving unit is used to iteratively solve the probability density evolution equation based on the initial probability density function under different stiffness conditions to obtain the probability density function of the current time step.
[0214] The iterative unit is used to take the probability density function of the current time step as the initial probability density function of the next time step and perform the next iteration until the probability density functions of all time steps under different stiffness are generated.
[0215] The fourth generation unit is used to generate the probability density function information of the dynamic response index under different stiffnesses by using the probability density function of all time steps under different stiffnesses.
[0216] It should be noted that the specific methods by which each module performs operations in the system described in the above embodiments have been described in detail in the embodiments related to the method, and will not be elaborated here.
[0217] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
[0218] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.
Claims
1. A method for determining a turnout stiffness deterioration limit value based on time-varying reliability, characterized in that, include: Establish the dynamic vibration equation of flexible turnout based on the rigid-flexible coupling dynamic model of vehicle-turnout; Random samples were generated using a stratified sphere-Latinization sampling method, and the random samples included random track irregularities and vehicle parameter samples. Based on the dynamic vibration equation of flexible turnout, the dynamic equation of vehicle-turnout rigid-flexible coupling is constructed. The dynamic equation is solved according to random samples to generate the extreme value distribution of dynamic response index under different stiffness. The probability density evolution equation of the dynamic response index is solved by extreme value distribution, and the probability density function information of the dynamic response index under different stiffnesses is generated. The time-varying reliability under different stiffnesses is calculated based on the probability density function information, and the stiffness degradation limit of the turnout is determined by the time-varying reliability.
2. The time varying reliability based determination of switch stiffness deterioration limit method of claim 1, wherein, The method of generating random samples using stratified partial stratification with cut-ball-Latinization includes: Set high-dimensional random parameters, which include vehicle parameters and track-related basic parameters; The high-dimensional space corresponding to the high-dimensional random parameters is divided into multiple low-dimensional subspaces, wherein the low-dimensional subspaces are two-dimensional subspaces or one-dimensional subspaces. By using the principle of slicing the ball or equidistant sampling, a uniform set of points is generated for each low-dimensional subspace; The uniform point sets of each low-dimensional subspace are randomly paired and combined into uniform samples in the high-dimensional space. The uniform samples are transformed into vehicle parameter samples that conform to a preset distribution through equal probability transformation. Obtain the power spectral density function for random irregularities in the orbit; Multiple sinusoidal simulations are superimposed on the power spectral density function to generate a random track irregularity function; By adjusting the harmonic amplitude in the track random irregularity function using vehicle parameter samples, a track random irregularity sample corresponding to each vehicle parameter sample is generated.
3. The time varying reliability based determination of switch stiffness deterioration limit method of claim 1, wherein, The step of solving the dynamic equations based on random samples to generate extreme value distributions of dynamic response indices under different stiffnesses includes: The mechanical properties of a turnout component at each stiffness during stiffness degradation are obtained, and the mechanical properties include stiffness matrix, mass matrix and damping matrix; The random irregularity samples of the track are transformed into external load vectors in the physical space. The external load vectors are then transformed into modal space using the modal superposition method to obtain modal load vectors. By inputting the modal load vector, mechanical properties, and random samples into the dynamic equations, the sample dynamic equations corresponding to each random sample under different stiffnesses are obtained. The Park method was used to solve the dynamic equation for each sample, and the time series of dynamic response indexes for each random sample under different stiffnesses were obtained. Statistical analysis was performed on the time series of dynamic response indices to generate extreme value distributions of dynamic response indices under different stiffnesses.
4. The time varying reliability based determination of switch stiffness deterioration limit method of claim 1, wherein, The process of solving the probability density evolution equation of the dynamic response index through extreme value distribution to generate probability density function information of the dynamic response index under different stiffnesses includes: Define the dynamic response index as a state variable; Establish the probability density evolution equation of the state variables and fit the initial probability density function of the state variables; Under different stiffnesses, the probability density evolution equation is iteratively solved based on the initial probability density function to obtain the probability density function of the current time step; The probability density function of the current time step is used as the initial probability density function of the next time step, and the next iteration is performed until the probability density functions of all time steps under different stiffness are generated. By using the probability density functions of all time steps under different stiffnesses, the probability density function information of the dynamic response index under different stiffnesses is generated.
5. The method for determining the turnout stiffness deterioration limit based on time-varying reliability according to claim 4, characterized in that, The process of obtaining the probability density function for the current time step includes: The range of values is obtained by the extreme value distribution of the state variables, and the range of values is discretized to obtain grid points and grid step size; The service time is discretized to obtain the time step; Stability coefficients are defined by grid step size and time step size; The mixed flux of each grid point is calculated based on the initial probability density function, and the probability density of each grid point at the current time step is updated by the mixed flux and the stability coefficient. The total variation at the current time step is calculated using the probability density of adjacent grid points; The TVD requirement is determined by the total variation between two adjacent time steps. If it is, the probability density function of the current time step is generated by the probability density of each grid point in the current time step. Otherwise, the stability coefficient is adjusted and the probability density function of the current time step is recalculated.
6. The method for determining the turnout stiffness deterioration limit based on time-varying reliability according to claim 1, characterized in that, The method of determining the stiffness degradation limit of a turnout through time-varying reliability includes: The probability density function information is transformed by high-dimensional random parameters to obtain the joint probability density function, and the absorbing boundary conditions are set by the joint probability density function. For each stiffness, the residual probability density within the safety region is obtained by integrating the joint probability density function, where the safety region is the allowable range of values for the dynamic response index. Integrating the residual probability density over the safe region yields the time-varying reliability curve for each stiffness over the service time. For each stiffness, the minimum minimum reliability during the service life is extracted from the time-varying reliability curve. Establish the mapping relationship between stiffness and minimum time-varying reliability, and obtain the mapping relationship curve; Based on the mapping relationship curve, find the stiffness value that satisfies the minimum time-varying reliability equal to the preset target threshold, and use this stiffness value as the stiffness deterioration limit of the turnout.
7. A system for determining the limit of turnout stiffness deterioration based on time-varying reliability, characterized in that, include: The module is used to establish the dynamic vibration equation of flexible turnouts based on the vehicle-turnout rigid-flexible coupling dynamic model; The generation module is used to generate random samples using a spherical-Latinized partially stratified sampling method, wherein the random samples include random track irregularities and vehicle parameter samples. The first calculation module is used to construct the dynamic equation of the vehicle-turnout rigid-flexible coupling based on the dynamic vibration equation of the flexible turnout, solve the dynamic equation according to random samples, and generate the extreme value distribution of the dynamic response index under different stiffness. The second calculation module is used to solve the probability density evolution equation of the dynamic response index through the extreme value distribution, and generate the probability density function information of the dynamic response index under different stiffnesses. The third calculation module is used to calculate the time-varying reliability under different stiffnesses based on the probability density function information, and to determine the stiffness deterioration limit of the turnout through the time-varying reliability.
8. The turnout stiffness degradation limit determination system based on time-varying reliability according to claim 7, characterized in that, The generation module includes: The setting unit is used to set high-dimensional random parameters, which include vehicle parameters and track-related basic parameters. A splitting unit is used to split the high-dimensional space corresponding to high-dimensional random parameters into multiple low-dimensional subspaces, wherein the low-dimensional subspace is a two-dimensional subspace or a one-dimensional subspace. The first generation unit is used to generate a uniform set of points for each low-dimensional subspace by means of the spherical cutting method or equidistant sampling. Pairing units are used to randomly pair uniform point sets in each low-dimensional subspace to form uniform samples in a high-dimensional space. The first conversion unit is used to convert uniform samples into vehicle parameter samples that conform to a preset distribution through equal probability transformation. The first acquisition unit is used to acquire the power spectral density function of random irregularities in the orbit; The second generation unit is used to superimpose multiple sinusoidal simulations on the power spectral density function to generate a random irregularity function of the orbit. The third generation unit is used to adjust the harmonic amplitude in the track random irregularity function through vehicle parameter samples, and generate a track random irregularity sample corresponding to each vehicle parameter sample.
9. The turnout stiffness degradation limit determination system based on time-varying reliability according to claim 7, characterized in that, The first computing module includes: The second acquisition unit is used to acquire the mechanical properties of the turnout component at each stiffness during the stiffness degradation process. The mechanical properties include stiffness matrix, mass matrix and damping matrix. The second conversion unit is used to convert random irregularity samples of the track into external load vectors in the physical space, and to convert the external load vectors into modal space through modal superposition method to obtain modal load vectors; The input unit is used to input the modal load vector, mechanical properties and random samples into the dynamic equation to obtain the sample dynamic equation corresponding to each random sample under different stiffness. The first solution unit is used to solve the dynamic equation for each sample using the Park method, and obtain the time series of dynamic response indexes for each random sample under different stiffness. The sharing unit is used to perform statistical analysis on the time series of dynamic response indicators and generate the extreme value distribution of dynamic response indicators under different stiffnesses.
10. The turnout stiffness degradation limit determination system based on time-varying reliability according to claim 7, characterized in that, The second calculation module includes: Define a unit to define the dynamic response index as a state variable; The fitting unit is used to establish the probability density evolution equation of the state variables and fit the initial probability density function of the state variables. The second solving unit is used to iteratively solve the probability density evolution equation based on the initial probability density function under different stiffness conditions to obtain the probability density function of the current time step. The iterative unit is used to take the probability density function of the current time step as the initial probability density function of the next time step and perform the next iteration until the probability density functions of all time steps under different stiffness are generated. The fourth generation unit is used to generate the probability density function information of the dynamic response index under different stiffnesses by using the probability density function of all time steps under different stiffnesses.