A rail vehicle dynamics performance random analysis method, system and computer

Abstract

The present application relates to the field of rail vehicle dynamics, and provides a rail vehicle dynamics performance random analysis method, system and computer, the rail vehicle dynamics performance random analysis method comprising: obtaining a plurality of irregular data sample groups of a track, obtaining a plurality of amplitude coefficient sets; constructing a joint probability distribution model of the plurality of amplitude coefficient sets, obtaining track irregularity excitation; constructing a rail vehicle dynamics simulation model, obtaining a rail vehicle dynamics performance index, and constructing a rail vehicle dynamics performance random model; based on the sparse polynomial chaos basis function set and the rail vehicle dynamics performance random model, obtaining a rail vehicle dynamics performance random proxy model; obtaining a rail vehicle dynamics performance random analysis result of the rail vehicle. Through the above method, the random correlation between the irregular states of different tracks is considered, and the limitations of the analysis of the rail vehicle dynamics performance are reduced.

Description

Technical Field

[0001] This invention relates to the field of rail vehicle dynamics technology, and in particular to a method, system and computer for stochastic analysis of the dynamic performance of rail vehicles. Background Technology

[0002] Rail transit is an important part of the transportation system in modern life. With the development of technology, the speed and load capacity of rail vehicles have gradually improved. Rail vehicles are continuously subjected to high-cycle loads and complex environmental excitations, and their dynamic performance is gradually changing. Continuous analysis of the dynamic performance of rail vehicles plays an important role in driving safety.

[0003] Track irregularities are the primary source of excitation for rail vehicles, directly impacting their operational safety, stability, and comfort. Track irregularities in different sections and at different service periods are constantly changing; for example, long-term service leads to gradual deterioration of the irregularity, while maintenance and polishing improve it. Therefore, studying track irregularities is crucial for analyzing vehicle dynamics.

[0004] However, current research on track irregularities lacks consideration of the stochastic correlations between different track irregularity states. In practice, changes in the irregularity states of the left and right rails within the same section are usually random and correlated. For example, track irregularities in the same direction for the left and right rails, as well as irregularities in the lateral and vertical directions of the same rail, often exhibit strong positive correlations in their amplitude changes, and the correlation structure is quite complex. Whether ignoring the stochastic correlations between track states or using a traditional single linear correlation coefficient matrix, it is difficult to fully reflect the complex stochastic correlations of track irregularities. In particular, traditional methods have significant limitations when analyzing the dynamic performance of rail vehicles using only typical irregularity data samples, and lack comprehensiveness in statistically analyzing the information presented by vehicle dynamic performance under changes in track irregularities. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the present invention aims to provide a method, system, and computer for stochastic analysis of the dynamic performance of rail vehicles. This invention introduces amplitude coefficients to represent the differences in amplitude states of track irregularities across different sections and time periods. By establishing a stochastic model of rail vehicle dynamic performance with the set of amplitude coefficients as input variables, stochastic analysis of rail vehicle dynamic performance can be achieved. This invention aims to solve the problem that existing technologies lack consideration of the stochastic correlation between different track irregularity states, resulting in limitations in the stochastic analysis of rail vehicle dynamic performance and a lack of comprehensive technical solutions.

[0006] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0007] A stochastic analysis method for the dynamic performance of rail vehicles includes the following steps:

[0008] A number of irregular data sample groups of the track are obtained, a typical irregular data sample corresponding to the track is determined from the irregular data sample group, and a number of amplitude coefficient sets are obtained based on the typical irregular data sample and the irregular data sample.

[0009] A joint probability distribution model of several amplitude coefficient sets is constructed, and track irregularity excitation is obtained based on the joint probability distribution model and several typical irregularity data samples.

[0010] A dynamic simulation model of the rail vehicle is constructed based on the rail vehicle, and the dynamic performance index of the rail vehicle is obtained. Based on the dynamic simulation model of the rail vehicle, the dynamic performance index of the rail vehicle, and the track irregularity excitation, a stochastic model of the dynamic performance of the rail vehicle is constructed with the amplitude coefficient as the input variable.

[0011] Construct a set of basis functions for arbitrary polynomial chaotic expansion, and optimize the set of basis functions using an adaptive sparsity method to obtain a sparse polynomial chaotic basis function set. Based on the sparse polynomial chaotic basis function set and the stochastic model of the dynamic performance of the rail vehicle, obtain a stochastic surrogate model of the dynamic performance of the rail vehicle.

[0012] Based on the stochastic proxy model of the track vehicle's dynamic performance, the stochastic analysis results of the track vehicle's dynamic performance are obtained through the ANCOVA global sensitivity method and Monte Carlo simulation.

[0013] Furthermore, the plurality of irregularity data sample groups respectively correspond to the lateral irregularity state of the left rail, the vertical irregularity state of the left rail, the lateral irregularity state of the right rail, and the vertical irregularity state of the right rail. Each irregularity data sample group includes a plurality of irregularity data samples. The step of establishing typical irregularity data samples corresponding to the track from the irregularity data sample groups, and obtaining a plurality of amplitude coefficient sets based on the plurality of typical irregularity data samples and the plurality of irregularity data samples, includes:

[0014] Several valid values ​​are extracted from several non-rough data samples, and an effective mean is calculated based on several valid values. The non-rough data sample closest to the effective mean is established as a typical non-rough sample.

[0015] Calculate the ratio of several effective values ​​to the effective values ​​of the typical non-rough sample to obtain several amplitude coefficients, which form an amplitude coefficient set.

[0016] Furthermore, the step of constructing a joint probability distribution model of several sets of amplitude coefficients includes:

[0017] A random vector is formed based on several sets of amplitude coefficients, and several marginal distribution functions are obtained through the random vector;

[0018] A joint probability distribution function is established based on several marginal distribution functions. The correlation between several amplitude coefficient sets in the joint probability distribution function is analyzed by Vine Copula to determine the optimal Copula function and Copula parameters. A joint probability distribution model of several amplitude coefficient sets is constructed based on the joint probability distribution function, the optimal Copula function, and the Copula parameters.

[0019] Furthermore, the specific steps for constructing a dynamic simulation model of a rail vehicle based on the rail vehicle are as follows:

[0020] Based on rail vehicles, a dynamic simulation model of rail vehicles is constructed using the multibody dynamics method.

[0021] Furthermore, the step of obtaining the dynamic performance indicators of the rail vehicle, and constructing a stochastic model of the rail vehicle dynamic performance with the amplitude coefficient as the input variable based on the rail vehicle dynamic simulation model, the rail vehicle dynamic performance indicators, and the track irregularity excitation, includes:

[0022] Obtain a set of track vehicle operation stability indicators, a set of track vehicle operation smoothness indicators, and a set of track vehicle operation quality indicators, and extract track vehicle dynamic performance indicators from the set of track vehicle operation stability indicators, the set of track vehicle operation smoothness indicators, and the set of track vehicle operation quality indicators.

[0023] Obtain the index calculation rules corresponding to the dynamic performance indicators of the rail vehicle;

[0024] Based on the aforementioned rail vehicle dynamics simulation model and the aforementioned index calculation rules, an initial dynamic performance model is obtained;

[0025] Substituting the track irregularity excitation into the initial dynamic performance model, a stochastic model of the track vehicle dynamic performance is obtained with the amplitude coefficient as the input variable.

[0026] Furthermore, the step of constructing a set of basis functions for arbitrary polynomial chaotic expansion and optimizing the set of basis functions using an adaptive sparsity method to obtain a sparse polynomial chaotic basis function set includes:

[0027] Several standard orthogonal polynomial basis functions of arbitrary random variable type are generated recursively by Stieltjes, and a basis function set for arbitrary polynomial chaotic expansion is established based on several of the standard orthogonal polynomial basis functions.

[0028] An adaptive sparse method based on minimum angular regression and hyperbolic truncation is used to optimize the basis function set to obtain a sparse polynomial chaotic basis function set.

[0029] Furthermore, the step of obtaining the stochastic analysis results of the vehicle dynamics performance of the rail vehicle based on the stochastic surrogate model of the rail vehicle dynamics performance, through the ANCOVA global sensitivity method and Monte Carlo simulation, includes:

[0030] Based on the stochastic proxy model of the dynamic performance of the rail vehicle, the first-order global sensitivity is calculated using the ANCOVA global sensitivity method.

[0031] Based on the stochastic proxy model of the track vehicle dynamics performance, the mean, standard deviation, skewness, kurtosis and histogram corresponding to the track vehicle dynamics performance index are calculated by Monte Carlo simulation, and combined with the first-order global sensitivity to form the stochastic analysis results of the track vehicle dynamics performance.

[0032] A stochastic analysis system for the dynamic performance of rail vehicles, applied to a stochastic analysis method for the dynamic performance of rail vehicles as described in the above technical solution, the system comprising:

[0033] The acquisition module is used to acquire several groups of irregular data samples of the track, establish typical irregular data samples corresponding to the track from the irregular data sample groups, and obtain several sets of amplitude coefficients based on the several typical irregular data samples and the several irregular data samples.

[0034] A construction module is used to construct a joint probability distribution model of several amplitude coefficient sets, and to obtain track irregularity excitation based on the joint probability distribution model and several typical irregularity data samples.

[0035] The dynamics module is used to construct a dynamics simulation model of a rail vehicle based on the rail vehicle, obtain the dynamics performance index of the rail vehicle, and construct a stochastic model of the dynamics performance of the rail vehicle with the amplitude coefficient as the input variable based on the dynamics simulation model of the rail vehicle, the dynamics performance index of the rail vehicle, and the track irregularity excitation.

[0036] The proxy module is used to construct a set of basis functions for arbitrary polynomial chaotic expansion, and to optimize the set of basis functions using an adaptive sparsity method to obtain a sparse polynomial chaotic basis function set. Based on the sparse polynomial chaotic basis function set and the stochastic model of the dynamic performance of the rail vehicle, a stochastic proxy model of the dynamic performance of the rail vehicle is obtained.

[0037] The analysis module is used to obtain the stochastic analysis results of the vehicle dynamics performance of the rail vehicle based on the stochastic surrogate model of the rail vehicle dynamics performance, through the ANCOVA global sensitivity method and Monte Carlo simulation.

[0038] A computer includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements a stochastic analysis method for the dynamic performance of a rail vehicle as described in the above technical solution.

[0039] Compared with the prior art, the beneficial effects of the present invention are as follows: By acquiring several sets of irregularity data samples, several sets of amplitude coefficients are extracted to describe the irregularity state of the track. The effect of the overall deterioration or improvement of the track irregularity amplitude due to the change of state is approximately equivalent to the change of the amplitude coefficient set, which facilitates the further establishment of the joint probability distribution model to describe the stochastic correlation changes in the evolution of different track irregularity states. By establishing the track vehicle dynamics simulation model, coupling the track vehicle dynamics performance index with the track vehicle dynamics simulation model, and then substituting the track irregularity excitation, a stochastic model of track vehicle dynamics performance that reflects the impact of track irregularity state on the stability, smoothness, and running quality of the track vehicle is obtained. The complex correlation between different track irregularity states propagates to the stochastic model of track vehicle dynamics performance along with the track irregularity excitation. By establishing the stochastic proxy model of track vehicle dynamics performance based on adaptive sparse arbitrary polynomial chaotic expansion, it is beneficial to reduce the amount of computation. Combined with ANCOVA sensitivity analysis and Monte Carlo simulation, stochastic analysis of track vehicle dynamics performance is realized. Attached Figure Description

[0040] Figure 1 This is a flowchart of a stochastic analysis method for the dynamic performance of a rail vehicle according to the first embodiment of the present invention;

[0041] Figure 2 This is a structural block diagram of a stochastic analysis system for the dynamic performance of a rail vehicle according to the second embodiment of the present invention.

[0042] The following detailed description, in conjunction with the accompanying drawings, will further illustrate the present invention. Detailed Implementation

[0043] To facilitate understanding of the present invention, a more complete description will be given below with reference to the accompanying drawings. Several embodiments of the invention are illustrated in the drawings. However, the invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.

[0044] It should be noted that when a component is said to be "fixed to" another component, it can be directly on the other component or there may be an intervening component. When a component is said to be "connected to" another component, it can be directly connected to the other component or there may be an intervening component. The terms "vertical," "horizontal," "left," "right," and similar expressions used in this document are for illustrative purposes only.

[0045] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0046] Please see Figure 1 The first embodiment of the present invention provides a method for stochastic analysis of the dynamic performance of a rail vehicle, comprising the following steps:

[0047] Step S10: Obtain several groups of irregular data samples of the track, establish typical irregular data samples corresponding to the track from the groups of irregular data samples, and obtain several sets of amplitude coefficients based on the several typical irregular data samples and the several irregular data samples.

[0048] An amplitude coefficient is introduced to describe the evolution of track irregularities in different sections and time periods. The overall deterioration or improvement of track irregularity amplitude caused by changes in condition is approximated by an equivalent method, which facilitates the statistical analysis of track condition and the changes in dynamic performance of rail vehicles affected by track irregularities through mathematical methods.

[0049] In step S10, the plurality of irregularity data sample groups correspond respectively to the lateral irregularity state of the left rail, the vertical irregularity state of the left rail, the lateral irregularity state of the right rail, and the vertical irregularity state of the right rail. The irregularity data sample group includes a plurality of irregularity data samples. Step S10 further includes:

[0050] S110: Extract several valid values ​​from several non-rough data samples, calculate an effective mean based on several valid values, and establish the non-rough data sample closest to the effective mean as a typical non-rough sample;

[0051] Preferably, the track irregularity data is measured by collecting four sets of irregularity data samples corresponding to the lateral irregularity of the left rail, the vertical irregularity of the left rail, the lateral irregularity of the right rail, and the vertical irregularity of the right rail, respectively, and establishing a typical irregularity sample in each set of irregularity data samples.

[0052] S120: Calculate the ratio of several effective values ​​to the effective values ​​of the typical non-rough sample to obtain several amplitude coefficients to form an amplitude coefficient set.

[0053] The irregularity data sample can be used to derive an amplitude coefficient. Through a typical irregularity sample, all amplitude coefficients of the corresponding irregularity data sample group are calculated and formed into a set. Each amplitude coefficient set represents a track irregularity state, so as to quantify the multi-faceted and multi-directional irregularity states of the left rail lateral, left rail vertical, right rail lateral and right rail vertical within a segment.

[0054] Step S20: Construct a joint probability distribution model of several amplitude coefficient sets, and obtain track irregularity excitation based on the joint probability distribution model and several typical irregularity data samples;

[0055] Preferably, a track irregularity excitation function is established based on the typical irregularity data samples and the product of the amplitude coefficients corresponding to the typical irregularity data samples. Based on the track irregularity excitation function and the joint probability distribution model, the track irregularity excitation is obtained. Understandably, the track irregularity excitation is considered a random quantity. However, during service, the changes in the state of track irregularities in the left rail lateral, left rail vertical, right rail lateral, and right rail vertical directions often exhibit similarities. The left and right rails are connected, and the lateral and vertical directions are the main directions for measuring rail irregularities. The four irregularity states have relatively complex stochastic correlations. The excitation of track irregularities on the dynamic performance of rail vehicles is defined by the amplitude coefficient set and its joint probability distribution, describing the stochastic correlation changes in track irregularity states. Through the track irregularity excitation, track irregularities and the stochastic correlations between various irregularities can be propagated to the analysis of vehicle performance, avoiding the problem that a single coefficient cannot describe the complexity of rail irregularities, and facilitating a more comprehensive and accurate analysis.

[0056] Step S20 includes:

[0057] S210: A random vector is formed based on several sets of amplitude coefficients, so as to obtain several marginal distribution functions through the random vector;

[0058] Preferably, the set of amplitude coefficients is used as random variables to establish the random vector, and nonparametric kernel density estimation is used to determine the marginal distribution of all variables in the random vector.

[0059] S220: Establish a joint probability distribution function based on several marginal distribution functions, analyze the correlation between several amplitude coefficient sets in the joint probability distribution function through Vine Copula, so as to determine the optimal Copula function and Copula parameters, and construct a joint probability distribution model of several amplitude coefficient sets based on the joint probability distribution function, the optimal Copula function and the Copula parameters.

[0060] Preferably, according to Sklar's theorem, the multivariate joint probability distribution function can be obtained through multiple marginal distribution functions, Copula functions, and Copula parameters. Specifically, the Copula function can be the Vine Copula function. Based on Vine Copula theory, an initial joint probability distribution model of the four amplitude coefficient sets is constructed through C-Vine Copula and D-Vine Copula. The correlation between the four variables is analyzed, and the optimal Copula type and Copula parameters for each connection point are solved. Specifically, the Vine Copula function is optimized using maximum likelihood to obtain the optimal Copula function.

[0061] Step S30: Construct a dynamic simulation model of the rail vehicle based on the rail vehicle, obtain the dynamic performance index of the rail vehicle, and construct a stochastic model of the dynamic performance of the rail vehicle with the amplitude coefficient as the input variable based on the dynamic simulation model of the rail vehicle, the dynamic performance index of the rail vehicle and the track irregularity excitation.

[0062] Preferably, based on multibody dynamics simulation and the dynamic performance indicators of the rail vehicle, and in conjunction with the track irregularity excitation, a stochastic model of the rail vehicle's dynamic performance is established. This stochastic model reflects the relationship between the rail vehicle's dynamic performance and multiple track irregularity states with stochastic correlation, thus providing intuitive data analysis for the rail vehicle's dynamic performance.

[0063] Step S30 includes:

[0064] S310: Based on rail vehicles, a dynamic simulation model of rail vehicles is constructed using the multibody dynamics method.

[0065] Preferably, the dynamic simulation model of the rail vehicle is constructed in multibody dynamics software, specifically, UM or Simpack software can be used.

[0066] S320: Obtain the set of track vehicle operation stability indicators, the set of track vehicle operation smoothness indicators, and the set of track vehicle operation quality indicators, and extract track vehicle dynamic performance indicators from the set of track vehicle operation stability indicators, the set of track vehicle operation smoothness indicators, and the set of operation quality indicators.

[0067] S330: Obtain the index calculation rules corresponding to the dynamic performance index of the rail vehicle;

[0068] S340: Based on the aforementioned track vehicle dynamics simulation model and the aforementioned index calculation rules, an initial dynamic performance model is obtained;

[0069] S350: Substitute the track irregularity excitation into the initial dynamic performance model to obtain a stochastic model of the track vehicle dynamic performance with the amplitude coefficient as the input variable.

[0070] Preferably, S320~S350 are based on GB / T The 5599-2019 standard specifies the operational stability, operational smoothness, and operational quality indicators for rail vehicles. This standard establishes the dynamic performance indicators for rail vehicles and provides calculation methods for these indicators. The operational stability indicators include, but are not limited to, derailment coefficient, wheel load reduction rate, and wheel-axle lateral force. The operational smoothness indicators include, but are not limited to, lateral smoothness, vertical smoothness, and comfort. The operational quality indicators include, but are not limited to, lateral and vertical operational quality. Specifically, taking the operational smoothness indicator as an example of the rail vehicle's dynamic performance indicators, the vibration acceleration measurement of the floor plate 1000mm off-center from the bogie body is used as a basis. The vibration acceleration amplitude is determined based on the Fourier transform spectrum of the vibration acceleration. Combined with the vibration frequency, the calculation rules for the rail vehicle's dynamic performance indicators are obtained. The vector of the rail vehicle's dynamic performance indicators is considered the output vector. The model parameters affecting the operational smoothness of the rail vehicle and the track irregularity excitation form the input vector. The amplitude coefficient in the track irregularity excitation is a variable to realize the propagation of track irregularity in the rail vehicle's dynamic performance system.

[0071] Step S40: Construct a set of basis functions for arbitrary polynomial chaotic expansion, and optimize the set of basis functions using an adaptive sparsity method to obtain a sparse polynomial chaotic basis function set. Based on the sparse polynomial chaotic basis function set and the stochastic model of the dynamic performance of the rail vehicle, obtain a stochastic surrogate model of the dynamic performance of the rail vehicle.

[0072] Understandably, traditional polynomial chaotic expansions, when dealing with complex problems, experience a combinatorial explosion in the number of polynomial terms required as the dimension of the random variables increases with the order of the dimension, resulting in enormous computational costs and significant limitations. Furthermore, considering the arbitrariness of the joint probability distribution model, traditional standard Hermitian polynomial chaotic expansions and generalized polynomial chaotic expansions can only handle a limited number of probability distribution types. Therefore, a recursive relation is used to generate standard orthogonal polynomial basis functions for any type of random variable, constructing a basis function set for arbitrary polynomial chaotic expansion. This set is then used to process the stochastic model of the track vehicle dynamics performance that propagates the stochastic correlation of the track irregularity excitation. Further, considering the large total number of terms in the basis function set under standard truncation, resulting in a large computational cost per model iteration, an adaptive sparse method is used to process the basis function set, effectively reducing the computational cost. This leads to higher computational efficiency for the stochastic proxy model of the track vehicle dynamics performance.

[0073] Step S40 includes:

[0074] S410: Generate several standard orthogonal polynomial basis functions of arbitrary random variable type by recursively generating Stieltjes, and establish a basis function set for arbitrary polynomial chaotic expansion based on the several standard orthogonal polynomial basis functions;

[0075] S420: The basis function set is optimized using an adaptive sparse method based on minimum angular regression and hyperbolic truncation to obtain a sparse polynomial chaotic basis function set.

[0076] Preferably, in steps S410-S420, the stochastic surrogate model for the dynamic performance of the rail vehicle is a PCE stochastic surrogate model with finite variance. For the basis function set, an original candidate set is constructed using a hyperbolic truncation scheme. Based on minimum angular regression, the regression quantities most correlated with the current residual in the candidate set are gradually added to the effective set to achieve the selection of the basis function set for the optimal arbitrary polynomial chaotic expansion. Furthermore, the sparse polynomial chaotic basis function set is processed using a modified leave-one-out error formula to obtain an adaptive sparse polynomial chaotic basis function set. The adaptive sparse polynomial chaotic basis function set has the optimal approximation accuracy. The least squares method is used to calculate the expansion coefficients of the adaptive sparse polynomial chaotic basis function set to establish the stochastic surrogate model for the dynamic performance of the rail vehicle.

[0077] Step S50: Based on the stochastic surrogate model of the track vehicle dynamics performance, obtain the stochastic analysis results of the track vehicle dynamics performance through the ANCOVA global sensitivity method and Monte Carlo simulation.

[0078] The ANCOVA global sensitivity method can handle the random correlation of parameters and, combined with Monte Carlo simulation, estimate the mean, standard deviation, skewness, kurtosis, histogram and other statistical quantities of the dynamic performance indicators of rail vehicles, thereby realizing the analysis and evaluation of random statistical information of the dynamic performance of rail vehicles.

[0079] Step S50 includes:

[0080] S510: Based on the stochastic surrogate model of the dynamic performance of the rail vehicle, calculate the first-order global sensitivity using the ANCOVA global sensitivity method;

[0081] S520: Based on the stochastic proxy model of the track vehicle dynamics performance, the mean, standard deviation, skewness, kurtosis and histogram corresponding to the track vehicle dynamics performance index are calculated by Monte Carlo simulation, and combined with the first-order global sensitivity to form the stochastic analysis results of the track vehicle dynamics performance.

[0082] Preferably, in S510~S520, the first-order global sensitivity represents the variance contribution of the parameter to the response. The first-order global sensitivity includes two parts: one part is the variance contribution of the independent action of the amplitude coefficient variable to the dynamic performance of the rail vehicle, and the other part is the variance contribution of the correlation or interaction effect of the amplitude coefficient variable to the dynamic performance of the rail vehicle.

[0083] Please see Figure 2 The second embodiment of the present invention provides a stochastic analysis system for the dynamic performance of rail vehicles, applied to a stochastic analysis method for the dynamic performance of rail vehicles as described in the first embodiment above. The system includes:

[0084] The acquisition module 10 is used to acquire several groups of irregular data samples of the track, establish typical irregular data samples corresponding to the track from the groups of irregular data samples, and obtain several sets of amplitude coefficients based on the several typical irregular data samples and the several irregular data samples.

[0085] In the acquisition module 10, several sets of irregularity data samples correspond to the lateral irregularity of the left rail, the vertical irregularity of the left rail, the lateral irregularity of the right rail, and the vertical irregularity of the right rail, respectively. Each set of irregularity data samples includes several irregularity data samples. The acquisition module 10 further includes:

[0086] The first unit is used to extract several valid values ​​from several irregular data samples, calculate an effective mean based on several valid values, and establish the irregular data sample closest to the effective mean as a typical irregular sample.

[0087] The second unit is used to calculate the ratio of several effective values ​​to the effective values ​​of the typical non-rough samples, and obtain several amplitude coefficients to form an amplitude coefficient set.

[0088] Construction module 20 is used to construct a joint probability distribution model of several amplitude coefficient sets, and obtain track irregularity excitation based on the joint probability distribution model and several typical irregularity data samples;

[0089] The construction module 20 includes:

[0090] The third unit is used to form a random vector based on several sets of amplitude coefficients, so as to obtain several marginal distribution functions through the random vector;

[0091] The fourth unit is used to establish a joint probability distribution function based on several marginal distribution functions, analyze the correlation between several amplitude coefficient sets in the joint probability distribution function through VineCopula, so as to determine the optimal Copula function and Copula parameters, and construct a joint probability distribution model of several amplitude coefficient sets based on the joint probability distribution function, the optimal Copula function and the Copula parameters.

[0092] The dynamics module 30 is used to construct a dynamics simulation model of the rail vehicle based on the rail vehicle, obtain the dynamics performance index of the rail vehicle, and construct a stochastic model of the dynamics performance of the rail vehicle with the amplitude coefficient as the input variable based on the dynamics simulation model of the rail vehicle, the dynamics performance index of the rail vehicle and the track irregularity excitation.

[0093] The dynamics module 30 includes:

[0094] The fifth unit is used to construct dynamic simulation models of rail vehicles using multibody dynamics methods.

[0095] The sixth unit is used to acquire the set of track vehicle operation stability indicators, the set of track vehicle operation smoothness indicators, and the set of track vehicle operation quality indicators, and to extract track vehicle dynamic performance indicators from the set of track vehicle operation stability indicators, the set of track vehicle operation smoothness indicators, and the set of track vehicle operation quality indicators.

[0096] The seventh unit is used to obtain the index calculation rules corresponding to the dynamic performance indicators of the rail vehicle;

[0097] The eighth unit is used to obtain the initial dynamic performance model based on the aforementioned rail vehicle dynamics simulation model and the aforementioned index calculation rules;

[0098] The ninth unit is used to substitute the track irregularity excitation into the initial dynamic performance model to obtain a stochastic model of the track vehicle dynamic performance with the amplitude coefficient as the input variable.

[0099] The proxy module 40 is used to construct a set of basis functions for arbitrary polynomial chaotic expansion, and to optimize the set of basis functions using an adaptive sparsity method to obtain a sparse polynomial chaotic basis function set. Based on the sparse polynomial chaotic basis function set and the stochastic model of the dynamic performance of the rail vehicle, a stochastic proxy model of the dynamic performance of the rail vehicle is obtained.

[0100] The proxy module 40 includes:

[0101] Unit 10 is used to recursively generate several standard orthogonal polynomial basis functions of arbitrary random variable types using Stieltjes, and to establish a set of basis functions for arbitrary polynomial chaotic expansion based on several of the standard orthogonal polynomial basis functions;

[0102] Unit 11 is used to optimize the basis function set using an adaptive sparse method based on minimum angular regression and hyperbolic truncation, to obtain a sparse polynomial chaotic basis function set.

[0103] Analysis module 50 is used to obtain stochastic analysis results of the vehicle dynamic performance of the rail vehicle based on the stochastic surrogate model of the rail vehicle dynamic performance, through the ANCOVA global sensitivity method and Monte Carlo simulation.

[0104] The analysis module 50 includes:

[0105] The twelfth unit is used to calculate the first-order global sensitivity based on the stochastic surrogate model of the dynamic performance of the rail vehicle using the ANCOVA global sensitivity method.

[0106] The thirteenth unit is used to calculate the mean, standard deviation, skewness, kurtosis and histogram corresponding to the dynamic performance index of the rail vehicle through Monte Carlo simulation based on the stochastic proxy model of the rail vehicle dynamic performance, so as to form the stochastic analysis result of the vehicle dynamic performance of the rail vehicle in combination with the first-order global sensitivity.

[0107] The third embodiment of the present invention provides a computer, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements a stochastic analysis method for the dynamic performance of a rail vehicle as described in the first embodiment above.

[0108] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0109] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A method of stochastic analysis of the dynamic behavior of a railway vehicle, characterized in that, The method comprises the following steps: a plurality of irregular data sample groups of a track are obtained, a typical irregular data sample corresponding to the track is determined from the irregular data sample groups, a plurality of amplitude coefficient sets are obtained based on the typical irregular data sample and the irregular data sample; the irregular data sample groups correspond to the lateral irregular state of the left track, the vertical irregular state of the left track, the lateral irregular state of the right track and the vertical irregular state of the right track, the step of determining the typical irregular data sample from the irregular data sample groups and obtaining a plurality of amplitude coefficient sets based on the typical irregular data sample and the irregular data sample comprises: a plurality of effective values are extracted from the irregular data sample, the effective mean value is calculated based on the effective values, and the irregular data sample closest to the effective mean value is determined as the typical irregular sample; the ratio of the effective value to the effective value of the typical irregular sample is calculated to obtain a plurality of amplitude coefficients to form an amplitude coefficient set; a joint probability distribution model of the plurality of amplitude coefficient sets is constructed, and a track irregular excitation is obtained based on the joint probability distribution model and the typical irregular data sample; the step of constructing the joint probability distribution model of the plurality of amplitude coefficient sets comprises: a random vector is formed based on the plurality of amplitude coefficient sets to obtain a plurality of marginal distribution functions through the random vector; a joint probability distribution function is established based on the plurality of marginal distribution functions, the correlation between the plurality of amplitude coefficient sets in the joint probability distribution function is analyzed through Vine Copula, the optimal Copula function and Copula parameter are determined, and the joint probability distribution model of the plurality of amplitude coefficient sets is constructed based on the joint probability distribution function, the optimal Copula function and the Copula parameter; a track vehicle dynamics simulation model is constructed based on a track vehicle, a track vehicle dynamics performance index is obtained, and a track vehicle dynamics performance random model with the amplitude coefficient as the input variable is constructed based on the track vehicle dynamics simulation model, the track vehicle dynamics performance index and the track irregular excitation; a basis function set of arbitrary polynomial chaos expansion is constructed, the basis function set is optimized by using an adaptive sparse method to obtain a sparse polynomial chaos basis function set, and a track vehicle dynamics performance random proxy model is obtained based on the sparse polynomial chaos basis function set and the track vehicle dynamics performance random model; the track vehicle dynamics performance random analysis result of the track vehicle is obtained through the ANCOVA global sensitivity method and Monte Carlo simulation based on the track vehicle dynamics performance random proxy model.

2. The method according to claim 1, wherein, the step of constructing the track vehicle dynamics simulation model based on the track vehicle comprises: a track vehicle dynamics simulation model is constructed based on the track vehicle by using the multi-body dynamics method.

3. The method according to claim 1, wherein the method is characterized by, The step of acquiring the rail vehicle dynamics performance index, constructing a rail vehicle dynamics performance random model with the amplitude coefficient as an input variable based on the rail vehicle dynamics simulation model, the rail vehicle dynamics performance index and the track irregularity excitation includes: Acquiring a set of rail vehicle running stability indexes, a set of rail vehicle running smoothness indexes and a set of rail vehicle running quality indexes, and extracting a rail vehicle dynamics performance index from the set of vehicle running stability indexes, the set of vehicle running smoothness indexes and the set of running quality indexes; Acquiring an index calculation rule corresponding to the rail vehicle dynamics performance index; Based on the rail vehicle dynamics simulation model and the index calculation rule, an initial dynamics performance model is obtained; The track irregularity excitation is substituted into the initial dynamics performance model to obtain a rail vehicle dynamics performance random model with the amplitude coefficient as an input variable.

4. The method according to claim 1, wherein The step of constructing a basis function set of arbitrary polynomial chaos expansion and optimizing the basis function set by using an adaptive sparse method to obtain a sparse polynomial chaos basis function set includes: A basis function set of arbitrary polynomial chaos expansion is established based on a plurality of standard orthogonal polynomial basis functions of arbitrary random variable types generated by Stieltjes recursion; The basis function set is optimized by using an adaptive sparse method based on minimum angle regression and hyperbolic truncation to obtain a sparse polynomial chaos basis function set.

5. The method of claim 1, wherein the method comprises: The step of obtaining a rail vehicle dynamics performance random analysis result of the rail vehicle based on the rail vehicle dynamics performance random proxy model by ANCOVA global sensitivity method and Monte Carlo simulation includes: Based on the rail vehicle dynamics performance random proxy model, a first-order global sensitivity is calculated by ANCOVA global sensitivity method; Based on the rail vehicle dynamics performance random proxy model, the mean, standard deviation, skewness, kurtosis and histogram corresponding to the rail vehicle dynamics performance index are calculated by Monte Carlo simulation to form a rail vehicle dynamics performance random analysis result of the rail vehicle in combination with the first-order global sensitivity.

6. A system for random analysis of the dynamic performance of a railway vehicle, applied to a method for random analysis of the dynamic performance of a railway vehicle according to any one of the preceding claims 1 to 5, characterized in that, The system includes: An acquisition module is configured to acquire a plurality of track irregularity data sample groups, determine a typical irregularity data sample corresponding to the track from the irregularity data sample groups, and obtain a plurality of amplitude coefficient sets based on a plurality of typical irregularity data samples and a plurality of irregularity data samples. In the acquisition module, a plurality of irregularity data sample groups correspond to a lateral irregularity state of a left rail, a vertical irregularity state of the left rail, a lateral irregularity state of a right rail and a vertical irregularity state of the right rail, respectively, and each irregularity data sample group includes a plurality of irregularity data samples. The first unit is configured to extract a plurality of effective values from a plurality of irregularity data samples, calculate an effective mean based on a plurality of effective values, and determine the irregularity data sample closest to the effective mean as a typical irregularity sample. a second unit configured to calculate ratios of the effective values of the several typical irregularity samples to the effective value of the typical irregularity sample to obtain a plurality of amplitude coefficient sets; a construction module configured to construct a joint probability distribution model of the plurality of amplitude coefficient sets, and obtain track irregularity excitations based on the joint probability distribution model and the plurality of typical irregularity data samples; the construction module comprises: a third unit configured to form a random vector based on the plurality of amplitude coefficient sets to obtain a plurality of marginal distribution functions through the random vector; a fourth unit configured to establish a joint probability distribution function based on the plurality of marginal distribution functions, analyze correlations between the plurality of amplitude coefficient sets in the joint probability distribution function through VineCopula to determine an optimal Copula function and Copula parameters, and construct a joint probability distribution model of the plurality of amplitude coefficient sets based on the joint probability distribution function, the optimal Copula function and the Copula parameters; a dynamics module configured to construct a track vehicle dynamics simulation model based on a track vehicle to obtain track vehicle dynamics performance indicators, and construct a track vehicle dynamics performance random model with the amplitude coefficients as input variables based on the track vehicle dynamics simulation model, the track vehicle dynamics performance indicators and the track irregularity excitations; a proxy module configured to construct a basis function set of arbitrary polynomial chaos expansion, optimize the basis function set by using an adaptive sparse method to obtain a sparse polynomial chaos basis function set, and obtain a track vehicle dynamics performance random proxy model based on the sparse polynomial chaos basis function set and the track vehicle dynamics performance random model; an analysis module configured to obtain a track vehicle dynamics performance random analysis result based on the track vehicle dynamics performance random proxy model through ANCOVA global sensitivity method and Monte Carlo simulation.

7. A computer comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor executes the computer program to implement the track vehicle dynamics performance random analysis method in any one of claims 1-5.

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