CN117313559A - Data-driven vehicle track coupling dynamics method - Google Patents
Data-driven vehicle track coupling dynamics method Download PDFInfo
- Publication number
- CN117313559A CN117313559A CN202311611457.1A CN202311611457A CN117313559A CN 117313559 A CN117313559 A CN 117313559A CN 202311611457 A CN202311611457 A CN 202311611457A CN 117313559 A CN117313559 A CN 117313559A
- Authority
- CN
- China
- Prior art keywords
- vehicle
- track
- data
- fourier
- dynamics
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000000034 method Methods 0.000 title claims abstract description 88
- 230000008878 coupling Effects 0.000 title claims abstract description 59
- 238000010168 coupling process Methods 0.000 title claims abstract description 59
- 238000005859 coupling reaction Methods 0.000 title claims abstract description 59
- 230000004044 response Effects 0.000 claims abstract description 22
- 238000012549 training Methods 0.000 claims abstract description 20
- 210000002569 neuron Anatomy 0.000 claims abstract description 14
- 238000012360 testing method Methods 0.000 claims abstract description 10
- 230000001537 neural effect Effects 0.000 claims abstract description 6
- 238000012795 verification Methods 0.000 claims abstract description 5
- 230000008569 process Effects 0.000 claims description 22
- 230000001133 acceleration Effects 0.000 claims description 14
- 230000006870 function Effects 0.000 claims description 14
- 230000010354 integration Effects 0.000 claims description 13
- 238000006073 displacement reaction Methods 0.000 claims description 12
- 238000011156 evaluation Methods 0.000 claims description 8
- 230000003993 interaction Effects 0.000 claims description 6
- 230000004913 activation Effects 0.000 claims description 5
- 238000013528 artificial neural network Methods 0.000 claims description 4
- 238000013016 damping Methods 0.000 claims description 4
- 238000013507 mapping Methods 0.000 claims description 3
- 239000011159 matrix material Substances 0.000 claims description 3
- 230000000737 periodic effect Effects 0.000 claims description 3
- 238000004364 calculation method Methods 0.000 description 10
- 238000013135 deep learning Methods 0.000 description 7
- 238000010586 diagram Methods 0.000 description 7
- 238000004088 simulation Methods 0.000 description 7
- 230000008901 benefit Effects 0.000 description 4
- 230000006872 improvement Effects 0.000 description 4
- 239000000725 suspension Substances 0.000 description 4
- 229910000831 Steel Inorganic materials 0.000 description 3
- 238000011161 development Methods 0.000 description 3
- 238000005516 engineering process Methods 0.000 description 3
- 239000010959 steel Substances 0.000 description 3
- ORILYTVJVMAKLC-UHFFFAOYSA-N Adamantane Natural products C1C(C2)CC3CC1CC2C3 ORILYTVJVMAKLC-UHFFFAOYSA-N 0.000 description 2
- 101100346171 Arabidopsis thaliana MORC3 gene Proteins 0.000 description 2
- 101100346177 Arabidopsis thaliana MORC5 gene Proteins 0.000 description 2
- 101100346179 Arabidopsis thaliana MORC7 gene Proteins 0.000 description 2
- 101100168604 Candida albicans (strain SC5314 / ATCC MYA-2876) CRH12 gene Proteins 0.000 description 2
- 101100168607 Saccharomyces cerevisiae (strain ATCC 204508 / S288c) UTR2 gene Proteins 0.000 description 2
- 238000005299 abrasion Methods 0.000 description 2
- 238000013461 design Methods 0.000 description 2
- 230000000694 effects Effects 0.000 description 2
- 238000010801 machine learning Methods 0.000 description 2
- 238000011160 research Methods 0.000 description 2
- 230000003595 spectral effect Effects 0.000 description 2
- 238000001228 spectrum Methods 0.000 description 2
- 238000013459 approach Methods 0.000 description 1
- 230000000712 assembly Effects 0.000 description 1
- 238000000429 assembly Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000015556 catabolic process Effects 0.000 description 1
- 238000007418 data mining Methods 0.000 description 1
- 238000013136 deep learning model Methods 0.000 description 1
- 238000006731 degradation reaction Methods 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 230000007246 mechanism Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000005457 optimization Methods 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 230000009467 reduction Effects 0.000 description 1
- 238000004611 spectroscopical analysis Methods 0.000 description 1
- 238000010200 validation analysis Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N3/00—Computing arrangements based on biological models
- G06N3/02—Neural networks
- G06N3/04—Architecture, e.g. interconnection topology
- G06N3/042—Knowledge-based neural networks; Logical representations of neural networks
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N3/00—Computing arrangements based on biological models
- G06N3/02—Neural networks
- G06N3/04—Architecture, e.g. interconnection topology
- G06N3/0464—Convolutional networks [CNN, ConvNet]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2111/00—Details relating to CAD techniques
- G06F2111/10—Numerical modelling
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Landscapes
- Engineering & Computer Science (AREA)
- Theoretical Computer Science (AREA)
- Physics & Mathematics (AREA)
- Evolutionary Computation (AREA)
- General Engineering & Computer Science (AREA)
- Artificial Intelligence (AREA)
- Software Systems (AREA)
- General Physics & Mathematics (AREA)
- Health & Medical Sciences (AREA)
- General Health & Medical Sciences (AREA)
- Mathematical Physics (AREA)
- Computing Systems (AREA)
- Molecular Biology (AREA)
- Life Sciences & Earth Sciences (AREA)
- Biomedical Technology (AREA)
- Biophysics (AREA)
- Computational Linguistics (AREA)
- Data Mining & Analysis (AREA)
- Geometry (AREA)
- Computer Vision & Pattern Recognition (AREA)
- Medical Informatics (AREA)
- Computer Hardware Design (AREA)
- Vehicle Body Suspensions (AREA)
- Feedback Control In General (AREA)
Abstract
The invention discloses a data-driven vehicle track coupling dynamics method, which relates to the technical field of railways and track traffic and comprises the following steps: establishing a vehicle-track coupling power system; the method comprises the steps of expressing a coupling dynamics equation of a vehicle-track coupling power system into a unified form by utilizing a dynamics system numerical solution method; generating input and output parameters of a training set, a verification set and a test set of the vehicle track coupling dynamics model; establishing fourier neuron operators to map any initial conditions to their solutions; providing a branch Fourier neural operator architecture, establishing a data-driven vehicle track coupling dynamics model, using BFNO as backbone, and then connecting a fully-connected network; converting the data from the time domain to the frequency domain using a fourier convolution layer; extracting the characteristics of the frequency domain data, combining through a full-connection layer, and outputting the dynamic response of the last layer of vehicle-track coupling power system; the method can realize rapid and accurate solution of the coupling dynamics of the vehicle track.
Description
Technical Field
The invention relates to the technical field of railways and rail transit, in particular to a data-driven vehicle rail coupling dynamics method.
Background
The dynamic model and the solving method of the vehicle track coupling system have important significance for the related researches such as high-speed train operation safety and riding comfort evaluation, vibration and noise reduction structure design, wheel and rail abrasion prediction, rail damage degradation mechanism and the like. The numerical result of the method is used for determining the reasons of actual engineering problems such as non-circles of wheels, rail wave abrasion, vibration or noise sources and the like, and providing theoretical guidance for formulating effective solutions of the problems. Therefore, it is important to efficiently and accurately solve the dynamic response of the vehicle rail coupling system.
Therefore, a great deal of students develop a series of researches on how to save calculation time while ensuring the solving precision. For the three-dimensional vehicle-track coupling dynamics model, nearly half of the calculation cost is spent on solving the wheel-track contact, while when the three-dimensional vehicle-track coupling dynamics model is coupled with other large flexible structures, a single working condition usually takes several hours or even tens of hours, some students purposefully propose parallel calculation methods to reduce the calculation time, and efficient parallel calculation methods are proposed based on MP and API (application program interface) to improve the numerical calculation efficiency. There are also some researchers working to develop iterative methods to increase computational efficiency and save computer memory. In this approach, iteration within each time step is avoided, and updated iteration strategies are developed to improve convergence properties.
With the development of computer technology and big data mining technology, domestic and foreign scholars turn to a Machine Learning (ML) method and a Deep Learning (DL) method to solve the problem of multi-body dynamics including vehicle-track coupling dynamics, and the calculation of the whole vehicle track system by using the deep learning has the following advantages: (1) Complex wheel-rail contact, nonlinear suspension assemblies, and high degrees of freedom in a vehicle-rail system typically result in an intricate nonlinear relationship between system inputs and system dynamic responses. While conventional linear models present challenges in accurately capturing nonlinear relationships, deep learning methods can model complex nonlinear functions using multi-layer neural networks. (2) Through extensive data training, deep learning methods can capture a wide range of features and patterns. Although the training process of the deep learning method may be relatively time consuming due to the complex network, once the training steps are completed, the computation speed of the deep learning method is significantly faster than that of a traditional multi-body dynamics model.
Disclosure of Invention
In order to solve the problems in the prior art, the invention aims to provide a data-driven vehicle track coupling dynamics method, which can realize rapid and accurate solution of vehicle track coupling dynamics and considers the applicability of the method under different high-speed railway train body parameters and running speeds.
In order to achieve the above purpose, the invention adopts the following technical scheme: a data-driven vehicle track coupling dynamics method, comprising the steps of:
step 1, establishing a vehicle-track coupling power system;
step 2, using a dynamics system numerical solution method to express a coupling dynamics equation of the vehicle-track coupling power system into a unified form:
；
in the method, in the process of the invention,respectively a mass, damping and stiffness matrix of the vehicle-track coupling power system,the generalized displacement vector, the generalized velocity vector and the generalized acceleration vector of the vehicle-track coupling power system are respectively; />A generalized load vector for a vehicle-rail coupled powertrain;
step 3, generating input and output parameters of a training set, a verification set and a test set of the vehicle track coupling dynamics model through a dynamics system numerical solution method;
step 4, establishing a Fourier neuron operatorAny initial conditions +.>Mapping to its solution->The neuron operator comprises a local nonlinear activation function +.>And non-local integration operator, i.e. Fourier convolution operator +.>；
Step 5, providing a branch Fourier neural operator framework, separating the vehicle body from other components, constructing a vehicle body branch for outputting the response of each degree of freedom of the vehicle body, and outputting the response of each degree of freedom of the bogie, wheel set and track by other branches;
step 6, establishing a data-driven vehicle track coupling dynamics model, using a branch Fourier neuron operator based on a graph convolution kernel network theory as backbone, and then connecting a fully-connected network; converting the data from the time domain to the frequency domain using a fourier convolution layer; and extracting the characteristics of the frequency domain data, combining through the full connection layer, and outputting the dynamic response of the last layer of vehicle-track coupling power system.
As a further improvement of the present invention, the step 1 specifically includes:
assuming that the body, the framework and the wheel set of the vehicle are all rigid bodies, treating the track as an Euler-Bernoulli beam supported by a series of force elements, and connecting the vehicle and the track subsystem through wheel-track interaction forces; the wheel rail interaction force comprises a wheel rail normal contact force and a tangential creeping force.
As a further improvement of the present invention, in step 2, the dynamics system numerical solution method is specifically as follows:
predicting the displacement and the speed of the next step by using the displacement, the speed and the acceleration of the first two steps, solving the acceleration of the next step according to a system coupling dynamics equation, and repeating the steps in a circulating way; the integration format is as follows:
；
in the method, in the process of the invention,is the time integration step length; subscript->Representing the current step, the previous step and the next step respectively; />And->Is an independent parameter that controls the characteristics of the integration method.
As a further improvement of the present invention, in step 3, the input parameters include vehicle system parameters, track system parameters, vehicle speed, track irregularity parameters, and the output parameters are dynamic responses of the vehicle-track coupled power system.
As a further development of the invention, in step 4, the neuron operatorThe definition is as follows:
；
in the method, in the process of the invention,is a point-by-point neural network that promotes the input to a higher dimension channel space and outputs by projecting it back to the target dimension; />The number of layers is the number of network layers; />Is a point-by-point linear operator; />Is an integral kernel operator.
The fourier convolution operatorThe definition is as follows:
；
in the method, in the process of the invention,representing fourier transforms and their inverse; />Is the fourier transform of the periodic function; />Representing the input after lifting to the higher dimensional channel space; />Representing the Fourier mode, +.>Is to limit the input to the lowest +.>Fixed truncation of the fourier mode.
As a further development of the invention, in step 6, the vehicle track coupling dynamics model obtains a gradient during training from the following loss function:
；
in the method, in the process of the invention,respectively data loss, first derivative loss and second derivative loss,is the corresponding weight parameter; />The true value and the predicted value obtained by the neuron operator, respectively.
As a further improvement of the invention, also comprises the following steps ofrLSEThe value is used as an evaluation index of the vehicle track coupling dynamics model:
；
in the method, in the process of the invention,sequence index representing output->Is true value +.>Is a predicted value.
The beneficial effects of the invention are as follows:
1. the method can realize rapid and accurate solution of the coupling dynamics of the vehicle track, and obtain the dynamic response of the vehicle body, the bogie, the wheel set and the steel rail below the wheel set by inputting the parameters of the vehicle system, the parameters of the track system and the track irregularity data; the invention is verified under different conditions of China high-speed railway trains and speeds, can achieve better prediction effects in time domains and frequency domains, helps railway operators to design vehicle track structure parameters and provides technical support for vehicle running stability evaluation.
2. The data driving method provided by the invention has the advantages that the system displacement, the speed and the acceleration are combined under the optimal super-parameterrLSEThe losses are respectively 4.30%, 4.53% and 6.48%, good prediction effects can be achieved in the time domain and the frequency domain, and the method can be used for evaluating the running comfort of the high-speed train.
Drawings
FIG. 1 is a flow chart of embodiment 1 of the present invention;
FIG. 2 is a schematic diagram of a vehicle-track coupled power system according to embodiment 1 of the present invention;
FIG. 3 is a schematic diagram of a simulation sample of track irregularity in embodiment 1 of the present invention;
FIG. 4 is a schematic diagram of a Fourier convolution operator in embodiment 1 of the present invention;
FIG. 5 is a frame diagram of a vehicle track coupling dynamics model in embodiment 1 of the present invention;
FIG. 6 is a diagram showing the parameter ranges in embodiment 2 of the present invention;
FIG. 7 is a schematic diagram of training and test loss in example 2 of the present invention;
FIG. 8 is a comparison of a vehicle track coupling dynamics model and a multi-body dynamics simulation method in example 2 of the present invention;
FIG. 9 is a frequency domain comparison chart of a vehicle track coupling dynamics model and a multi-body dynamics simulation method in embodiment 2 of the present invention;
fig. 10 is a schematic diagram of the vehicle body vertical stability index and the vehicle body lateral stability index in example 2 of the present invention.
Detailed Description
Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
Example 1
As shown in fig. 1, a data-driven vehicle track coupling dynamics method includes the steps of:
step 1, as shown in fig. 2, a vehicle-rail coupling power system is established, and the vehicle body, the framework and the wheel set are assumed to be rigid bodies, each rigid body has five degrees of freedom, the whole vehicle subsystem has 35 degrees of freedom, the rail is regarded as a Bernoulli-Euler beam supported by a series of force elements, and the vehicle and the rail subsystem are connected through wheel-rail interaction forces. The wheel-rail interaction force mainly comprises a wheel-rail normal contact force and a tangential creep force, which are calculated through the combination of a Hertz nonlinear contact theory, a Kalker linear theory and a Shen-Herrick-Elkins nonlinear model.
Step 2, a dynamic system numerical solution method (a method), wherein a vehicle-track coupling dynamic equation can be expressed in a unified form as shown in a formula (1). In the method, in the process of the invention,mass, damping and stiffness matrix of the vehicle-rail coupled powertrain, respectively, < >>A generalized displacement vector which is a coupling system; />Generalized for coupling systemsA velocity vector; />A generalized acceleration vector that is a coupled system; />A generalized load vector for a vehicle-rail coupled powertrain; difficult to display expression, is with->And->Related nonlinear process quantities.
(1)；
The Dian method belongs to an explicit two-step numerical integration method, and the basic principle is as follows: and predicting the displacement and the speed of the next step by using the displacement, the speed and the acceleration of the first two steps, solving the acceleration of the next step according to a system motion equation, and repeating the steps. The integration format is shown in formula (2). In the method, in the process of the invention,is the time integration step length; subscript->Representing the current step, the previous step and the next step respectively; />And->Is an independent parameter that controls the characteristics of the integration method.
(2)；
And 3, data preparation, wherein input and output parameters of a model training set, a verification set and a test set are generated by a Zha method, wherein the input parameters comprise vehicle system parameters, track system parameters, vehicle speed and track irregularity, and the output parameters are dynamic responses of the system (35 degrees of freedom responses of the vehicle system and 24 degrees of freedom responses of a steel rail below a wheel pair).
The track irregularity existing on the actual line is formed by superposition of random irregularities with different wavelengths, different phases and different amplitudes, and is a complex random process related to the line mileage. The Power Spectral Density (PSD) is the most commonly used statistical function that represents random track irregularities, which are generally considered as a smooth random process, and the statistical features of random track irregularities can only be obtained from field measurements. In engineering, PSD maps are typically used to describe the relationship between spectral density and corresponding frequencies. A spatial domain simulation sample of track irregularities was generated using classical spectroscopy and the chinese high-speed ballastless track spectrum was used as a PSD function, as shown in fig. 3.
Step 4, establishing a neuron operator (FNO) principleAny initial conditions +.>Mapping to its solution->The neuron operator comprises a non-local integration operator +.>And a local nonlinear activation function->. The definition of the neuron operator is shown in formula (3). In (1) the->Is a point-by-point neural network that promotes the input to a higher dimensional channel space and outputs it by projecting it back to the target dimension.
(3)；
As shown in fig. 4, fourier convolution operatorThe definition of (2) is shown as formula (4), wherein +.>Representing the fourier transform and its inverse, < >>Is the fourier transform of a periodic function, +.>Is a fixed truncation that limits the input to the lowest K fourier mode.
(4)；
And 5, providing a Branch Fourier Neural Operator (BFNO), wherein the Fourier neural operator consists of frequency truncation of each layer, and only allows the lowest K Fourier mode to transmit input information. Although frequency truncation ensures discretization invariance of the FNO, selecting an appropriate number of active modes K is still challenging because it is task-specific and requires careful superparameter selection. Setting K too small results in too few frequency patterns and insufficient information to learn the solution operator, resulting in an under fit. K with too many effective frequency modes may cause FNO to insert noise into the high frequency components, resulting in an increase in overfitting and computational costs.
For a vehicle rail system, the frequency domain ranges of the vehicle body, bogie, wheel set and rail are different, and setting the same K value may result in under-fitting or over-fitting. To solve these problems, a Branch Fourier Neural Operator (BFNO) architecture has been proposed that separates the vehicle body from other components, constructing vehicle body branches for outputting the response of each degree of freedom of the vehicle body, and other branches for outputting the response of each degree of freedom of the bogie, wheel set and track.
And 6, establishing a data-driven vehicle track coupling dynamics model (PINO-VTSCD), wherein the model uses BFNO based on graph convolution kernel network theory as a backbone and then connects a fully-connected network as shown in figure 5. The fourier convolution layer is used to transform the data from the time domain to the frequency domain. And extracting the characteristics of the frequency domain data, combining through the full connection layer, and outputting the dynamic response of the last layer of system. The convolution operation is implemented using a Fast Fourier Transform (FFT).
And 7, in the training process, the PINO-VTSCD obtains gradients from the following three types of loss functions.
(5)；
In the method, in the process of the invention,data loss is performed respectively. The first derivative loss and the second derivative loss are inspired by the actual demands of engineering science, and many physical phenomena are often not obviously related to the solution of the control equation, but are closely related to the derivative of the solution of the control equation. For example, in nature, the sound emitted by vibration of an object tends to be directly related to the vibration velocity (first derivative), while the human body is generally sensitive to acceleration (second derivative). Undoubtedly, use +.>It must have a positive impact on the accuracy of the derivatives of the output results, as the deep learning model can see the true solutions of these derivatives.
Step 8, adoptrLSEThe value was used as an evaluation index for the present model. The calculation is shown in formula (6).
(6)；
In the method, in the process of the invention,sequence index representing output->Is true value +.>Is a predicted value.
Step 9, training a model, wherein the solution optimizer adopts Adam, the initial learning rate is set to be 1e-3, and the initial learning rate is reduced to 75% every 30 steps; the activation function adopts an ELU function, so that the full-connection layer has the advantage of negative input, and the training stability is promoted; the Batch Size is taken to be 32 and the maximum number of iterations is taken to be 300.
And 10, model testing, namely inputting test set data into a model to obtain a test result.
Example 2
A data-driven vehicle track coupling dynamics method, comprising:
1. 10000 sets of training set data, 2000 sets of validation set data and 2000 sets of test set data were generated together using a Zha-based multi-body dynamics simulation (MBS). The input parameters comprise vehicle system parameters, track system parameters, vehicle speed and track irregularity, and the output parameters are dynamic response of the system (35 degrees of freedom response of the vehicle system and 24 degrees of freedom response of the lower steel rail of the wheel pair). Operating vehicle parameters including mass, suspension and operating speed are considered variable. FIG. 6 shows the body mass range [ ]) Moment of inertia of bogie pitch (+)>) Longitudinal stiffness of each axle side main suspension) And vertical damping of the bogie side sub-suspension (+)>). CRH2, CRH3, high-speed railway train,Both CRH5 and CRH380 parameters are within these ranges.
2. Establishing a data-driven vehicle track coupling dynamics model (PINO-VTSCD), selecting model super-parameters by Bayesian optimization with the aim of maximally improving the model performance on a verification set, and finally determining: in the vehicle body branch, three fourier layers and four full connection layers were designed, each layer having a width set to 100 and 120, respectively. Also in the other branches, three fourier layers and four fully connected layers were designed, the width of each layer being set to 200. Other parameters and techniques used by the model include: the training method comprises the steps of (1) a small batch technology (batch size=32) to reduce the calculation cost, (2) an Adam optimizer to update the local learning rate in the training process and enhance the robustness of a network, (3) setting the initial learning rate to be 1e-3 and reducing the initial learning rate to 75% every 30 steps, and (4) an ELU activation function (used for a full connection layer) has the advantage of negative input and improves the training stability.
3. The training and test loss curves for the model are shown in fig. 7. After 300 rounds, the system displacement, velocity and acceleration reached 4.30%, 4.53% and 6.48%, respectivelyrLSEDespite the fact that no derivative is provided during training. The comparison results of the PINO-VTSCD model and the multi-body dynamics simulation method are shown in fig. 8, only 6 responses in 59 degrees of freedom are shown in the figure for clarity, and (a) - (d) in fig. 8 respectively represent vehicle body heave, vehicle body roll, first bogie roll, second bogie roll, third bogie roll and second bogie roll, and the displacement, speed and acceleration results obtained by using the PINO-VTSCD model have good precision. Fig. 9 shows the spectrum corresponding to track irregularities, car bodies, bogies, wheel sets and underlying rails of the wheel sets. The dominant frequency range of the track irregularity is between 0.1Hz and 25Hz, and the estimated value and the true value are identical in the frequency domain within the dominant frequency range of the track irregularity.
4. The PINO-VTSCD model can be used for remarkably improving the calculation speed. To perform the 3s simulation, the multi-body dynamics model calculated in MATLAB takes approximately 20 minutes, 214.73 seconds and 209.21 seconds in UM and simack software, respectively. In contrast, the PINO-VTSCD model running in Python requires only 3.69 seconds (on a device equipped with an Intel Core i9-12900K processor and a Nvidia GeForce RTX 3060 Super graphics processing unit).
5. And verifying the applicability of the PINO-VTSCD to different CRH train groups and different speeds. The selected CRH train consist is CRH2, CRH3, CRH5 and CRH380. Selected speeds include 250 km/h, 300 km/h and 350 km/h. The evaluation index results for each CRH training set are shown in table 1.
Table 1 evaluation index results for each CRH train group
As is evident from Table 1, all of the train groupsrLSEAre all lower. By calculating the average evaluation index of the 4 trains,rLSE5.01 percent, and meets the engineering requirements. The stability of the running vehicle was further evaluated using the Sprling index, and the stability index of the obtained vertical and lateral accelerations was calculated as shown in FIG. 10.
The foregoing examples merely illustrate specific embodiments of the invention, which are described in greater detail and are not to be construed as limiting the scope of the invention. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the invention, which are all within the scope of the invention.
Claims (7)
1. A method of data-driven vehicle track coupling dynamics, comprising the steps of:
step 1, establishing a vehicle-track coupling power system;
step 2, using a dynamics system numerical solution method to express a coupling dynamics equation of the vehicle-track coupling power system into a unified form:
；
in the method, in the process of the invention,respectively a mass, damping and stiffness matrix of the vehicle-track coupling power system,the generalized displacement vector, the generalized velocity vector and the generalized acceleration vector of the vehicle-track coupling power system are respectively; />A generalized load vector for a vehicle-rail coupled powertrain;
step 3, generating input and output parameters of a training set, a verification set and a test set of the vehicle track coupling dynamics model through a dynamics system numerical solution method;
step 4, establishing a Fourier neuron operatorAny initial conditions +.>Mapping to its solution->The neuron operator comprises a local nonlinear activation function +.>And non-local integration operators, i.e. Fourier convolution operators；
Step 5, providing a branch Fourier neural operator framework, separating the vehicle body from other components, constructing a vehicle body branch for outputting the response of each degree of freedom of the vehicle body, and outputting the response of each degree of freedom of the bogie, wheel set and track by other branches;
step 6, establishing a data-driven vehicle track coupling dynamics model, using a branch Fourier neuron operator based on a graph convolution kernel network theory as backbone, and then connecting a fully-connected network; converting the data from the time domain to the frequency domain using a fourier convolution layer; and extracting the characteristics of the frequency domain data, combining through the full connection layer, and outputting the dynamic response of the last layer of vehicle-track coupling power system.
2. The method of data driven vehicle track coupling dynamics according to claim 1, characterized in that step 1 comprises in particular: assuming that the body, the framework and the wheel set of the vehicle are all rigid bodies, treating the track as an Euler-Bernoulli beam supported by a series of force elements, and connecting the vehicle and the track subsystem through wheel-track interaction forces; the wheel rail interaction force comprises a wheel rail normal contact force and a tangential creeping force.
3. The data-driven vehicle track coupling dynamics method according to claim 1, characterized in that in step 2, the dynamics system numerical solving method is specifically as follows:
predicting the displacement and the speed of the next step by using the displacement, the speed and the acceleration of the first two steps, solving the acceleration of the next step according to a system coupling dynamics equation, and repeating the steps in a circulating way; the integration format is as follows:
；
in the method, in the process of the invention,is the time integration step length; subscript->Representing the current step, the previous step and the next step respectively; />And->Is an independent parameter that controls the characteristics of the integration method.
4. The method of claim 1, wherein in step 3, the input parameters include vehicle system parameters, track system parameters, vehicle speed, track irregularity parameters, and the output parameters are dynamic responses of the vehicle-track coupled power system.
5. A data driven vehicle track coupling dynamics method according to claim 3, characterized in that in step 4, the neuron operatorThe definition is as follows:
；
in the method, in the process of the invention,is a point-by-point neural network that promotes the input to a higher dimension channel space and outputs by projecting it back to the target dimension; />The number of layers is the number of network layers; />Is a point-by-point linear operator; />In order to integrate the kernel operator,
the fourier convolution operatorThe definition is as follows:
；
in the method, in the process of the invention,representing fourier transforms and their inverse; />Is the fourier transform of the periodic function; />Representing the input after lifting to the higher dimensional channel space; />Representing the Fourier mode, +.>Is to limit the input to the lowest +.>Fixed truncation of the fourier mode.
6. The data-driven vehicle rail coupling dynamics method according to claim 5, characterized in that in step 6, the vehicle rail coupling dynamics model obtains a gradient from the following loss function during training:
；
in the method, in the process of the invention,respectively data loss, first derivative loss and second derivative loss,is the corresponding weight parameter; />The true value and the predicted value obtained by the neuron operator, respectively.
7. The data driven vehicle track coupling dynamics method according to claim 6, further comprising employingrLSEThe value is used as an evaluation index of the vehicle track coupling dynamics model:
；
in the method, in the process of the invention,sequence index representing output->Is true value +.>Is a predicted value.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202311611457.1A CN117313559B (en) | 2023-11-29 | 2023-11-29 | Data-driven vehicle track coupling dynamics method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202311611457.1A CN117313559B (en) | 2023-11-29 | 2023-11-29 | Data-driven vehicle track coupling dynamics method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN117313559A true CN117313559A (en) | 2023-12-29 |
| CN117313559B CN117313559B (en) | 2024-01-26 |
Family
ID=89274092
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202311611457.1A Active CN117313559B (en) | 2023-11-29 | 2023-11-29 | Data-driven vehicle track coupling dynamics method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN117313559B (en) |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111046484A (en) * | 2019-10-25 | 2020-04-21 | 西南交通大学 | Vehicle-track coupling dynamics analysis method considering longitudinal vibration |
| CN111079322A (en) * | 2018-10-19 | 2020-04-28 | 株洲中车时代电气股份有限公司 | Train system dynamics modeling method and simulation method thereof |
| CN115203896A (en) * | 2022-06-10 | 2022-10-18 | 西南交通大学 | Modeling method of high-speed train axle box bearing dynamic model |
| CN116011125A (en) * | 2023-03-23 | 2023-04-25 | 成都理工大学 | Response prediction method for uncertain axle coupling system |
| US20230367994A1 (en) * | 2022-05-13 | 2023-11-16 | NEC Laboratories Europe GmbH | Hyper network machine learning architecture for simulating physical systems |
-
2023
- 2023-11-29 CN CN202311611457.1A patent/CN117313559B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111079322A (en) * | 2018-10-19 | 2020-04-28 | 株洲中车时代电气股份有限公司 | Train system dynamics modeling method and simulation method thereof |
| CN111046484A (en) * | 2019-10-25 | 2020-04-21 | 西南交通大学 | Vehicle-track coupling dynamics analysis method considering longitudinal vibration |
| US20230367994A1 (en) * | 2022-05-13 | 2023-11-16 | NEC Laboratories Europe GmbH | Hyper network machine learning architecture for simulating physical systems |
| CN115203896A (en) * | 2022-06-10 | 2022-10-18 | 西南交通大学 | Modeling method of high-speed train axle box bearing dynamic model |
| CN116011125A (en) * | 2023-03-23 | 2023-04-25 | 成都理工大学 | Response prediction method for uncertain axle coupling system |
Non-Patent Citations (1)
| Title |
|---|
| 陈双喜;林建辉;陈建政;: "基于改进的EMD方法提取车辆-轨道垂向耦合系统动态特性", 振动与冲击, no. 08 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN117313559B (en) | 2024-01-26 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Jiang et al. | Multi-parameter and multi-objective optimisation of articulated monorail vehicle system dynamics using genetic algorithm | |
| Zhang et al. | Study on dynamics of coupled systems in high-speed trains | |
| Zhang et al. | Establishment and validation of a locomotive–track coupled spatial dynamics model considering dynamic effect of gear transmissions | |
| CN104765916B (en) | A kind of Dynamics Performance of High Speed Trains parameter optimization method | |
| CN102496064B (en) | Method for acquiring unevenness of track | |
| CN114169422A (en) | Subway rail corrugation identification method and system based on vehicle vibration and noise combined test | |
| Fu et al. | High-speed railway bogie fault diagnosis using LSTM neural network | |
| CN113656899B (en) | Rail fastener parameter optimization method based on vehicle rail coupling theory | |
| CN109766635B (en) | Optimized layout method for state perception sensor of mechanical part of locomotive | |
| CN112464368A (en) | Method for evaluating adhesion coefficient of wheel rail | |
| Xu et al. | Fault diagnosis method of wheelset based on EEMD-MPE and support vector machine optimized by quantum-behaved particle swarm algorithm | |
| Alfi et al. | Effect of motor connection on the critical speed of high-speed railway vehicles | |
| Chen et al. | Mechanism of track random irregularity affecting dynamic characteristics of rack vehicle | |
| CN117313559B (en) | Data-driven vehicle track coupling dynamics method | |
| CN111444574A (en) | Sensor layout optimization method based on dynamic analysis | |
| Sun et al. | Modelling of periodic slab track using time-frequency hybrid Green's function method and its application to vehicle-track dynamic interaction | |
| Wang et al. | Parameter optimization of multi-suspended equipment to suppress carbody vibration of high-speed railway vehicles: a comparative study | |
| Hur et al. | Steering performance evaluation of active steering bogie to reduce wheel wear on test line | |
| CN115659492A (en) | Complex equipment nonlinear vibration model parameter optimization method | |
| CN115544763A (en) | Road surface flatness prediction method, system and medium | |
| CN112836294B (en) | Vehicle-track coupling dynamics model correction method | |
| CN114357630A (en) | Real-time simulation platform for train dynamics | |
| CN111950150B (en) | Modeling and simulation method and system for twisted orbit test | |
| Huang et al. | Optimization of vehicle suspension parameters based on simpack/isight simulation of wheel eccentric out-of-roundness | |
| Zheng et al. | A novel deep learning architecture and its application in dynamic load monitoring of the vehicle system |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |