High-speed train suspension parameter evaluation method

Abstract

The invention provides a high-speed train suspension parameter evaluation method which combines a particle Markov chain Monte Carlo model, a Kriging model and a particle swarm optimization algorithm. According to the method, firstly, based on a vehicle vertical six-degree-of-freedom dynamical model, a PMCMC algorithm is used for carrying out preliminary evaluation on suspension parameters; then, key suspension parameters, namely, the vertical stiffness of a primary spring and the vertical stiffness of an air spring, serve as design variables, the Pearson's correlation coefficient of the vertical acceleration power spectral density of the simulation and actual measurement vehicle body serves as output, and a Kriging proxy model is constructed; meanwhile, with the purpose of minimizing simulation and actually-measured vertical acceleration PSD errors of a vehicle body, key suspension parameters matched with the actual service state are obtained through a PSO algorithm. And taking the obtained key parameters as prior information of a PMCMC algorithm, and taking actually measured vibration data of the train as an observation value to complete posteriori estimation of the suspension parameters.

Description

TECHNICAL FIELD

[0001] The present application relates to a suspension parameter evaluation method, in particular to a high-speed train suspension parameter evaluation method. BACKGROUND

[0002] With the rapid development of high-speed railway technology, the stability, safety and comfort requirements of high-speed trains during operation are increasingly improved. The suspension system, as an important subsystem of the high-speed train bogie, not only determines the overall dynamics stability of the vehicle, but also attenuates the multi-frequency vibration caused by track irregularity excitation to ensure passenger comfort. However, in the long-term complex service environment, the suspension system components will gradually deviate from the initial design value due to wear, aging and environmental factors, which will further cause the degradation of vehicle dynamics performance, and even threaten the safety of train operation. Therefore, accurate suspension parameter evaluation can check whether the current parameters of the train meet the original design range, and further parameter updating of the simulation model can provide accurate initial conditions and parameter correction basis for subsequent dynamics performance optimization.

[0003] At present, the methods for evaluating the suspension parameters of high-speed trains mainly include the methods based on the dynamics model and the data-driven methods, both of which can use sensor measurement data during train operation to evaluate the parameters of the vehicle suspension and related key components. The parameter evaluation research based on the dynamics model is mainly realized through filtering algorithm, but most of the researches only rely on dynamics simulation data for analysis, and the evaluation results are not compared and analyzed with the actual vibration data of the train. In addition, in the posterior evaluation, the prior information cannot be updated based on the measured data to make the prior evaluation closer to the true value. In terms of data-driven methods, the mapping relationship between vibration data and suspension parameters is used to realize the evaluation of suspension parameters, but due to the neglect of the constraints of the bogie dynamics model, multiple sensor data are needed to achieve the accuracy of parameter evaluation, which faces the problems of difficult access to part of the sensor data and high cost. In addition, under the influence of train operating conditions and sensor measurement noise, the evaluation results are prone to errors, and it is difficult to reflect the actual state of the suspension system of the in-service train. SUMMARY

[0004] Preferably, a high-speed train suspension parameter evaluation method, characterized in that it comprises the following steps: Step S1: constructing a vehicle vertical six-degree-of-freedom dynamics model; Step S2: using the PMCMC algorithm to preliminarily evaluate the suspension parameters; Step S3: Taking the key suspension parameters as the design variables, a Kriging surrogate model is constructed with the Pearson correlation coefficient of the simulated and measured vertical acceleration power spectral density of the car body as the output; meanwhile, the PSO algorithm is used to obtain the key suspension parameters matching the actual service state by minimizing the error of the simulated and measured vertical acceleration PSD of the car body; Step S4: Suspension parameter evaluation based on PMCMC-Kriging-PSO.

[0005] Preferably, step S1 specifically includes steps S11-S12; Step S11: Establishing a whole vehicle dynamics model in SIMPACK; Step S111: Building a whole vehicle dynamics simulation model in SIMPACK; Step S112: Adding sensors on different components such as the car body, frame, axle box, wheelset, etc. to obtain post-processing data such as vibration acceleration and angular acceleration.

[0006] Step S12: Building a whole vehicle vertical dynamics model and a state space model; Step S121: Building a multi-rigid-body whole vehicle model of a four-axle vehicle.

[0007] Step S122: Transforming the vertical dynamics model of the railway vehicle into a state space model.

[0008] Preferably, step S2 includes steps S21-S22; Step S21: Implementing the PMCMC algorithm; Step S211: Initializing the parameters; Step S212: At each observation time j ( j =1,2,…), repeat the following steps; step1: Filtering the state space under the current parameter value and sampling ; step2: When the observation value comes, calculate the observation likelihood value of the particle based on the observation model and the particle weight update function to realize resampling, and resample the particles according to the weight to avoid particle degeneration; step3: Calculate the likelihood function approximation value , which is used as the input of MCMC sampling; Step S213: If , save Otherwise, the Metropolis acceptance criterion is used to determine whether to accept the application; the Metropolis acceptance criterion is... To accept probability Evaluate Is it acceptable? If so, save it in the parameter chain. Otherwise Save the data; if the parameter chain has converged, output the MCMC chain; otherwise, save the data. And generate new parameters according to the symmetric normal proposed distribution. ; Step S22: PMCMC algorithm parameter settings; Step S221: In the evaluation of dangling parameters, the covariance of the proposal distribution determines the acceptable range of candidate parameters in each iteration. (Proposal covariance) ;in Represents a 12th-order identity matrix. It was obtained based on the prior range of suspension parameters and repeated trials with an acceptance rate of 40%. Step S222: State process noise in parameter evaluation For vertical irregularities in the track, the state noise covariance controls the noise level during the state update process. for: ; in, For track roughness factors, take ; The sampling time interval, , The train's speed is expressed in m / s. Step S223: The observation noise covariance affects the noise of the observation model. To ensure that the observation noise covariance can adaptively reflect the magnitude differences in the observations of each channel, the following steps are taken: Let it be a diagonal matrix. Among them, the first The calculation of the diagonal elements is as follows; (11) In the formula, It is an empirical coefficient. and They represent the first The maximum and minimum values ​​of each observation during the observation process; Step S224: Based on the vehicle vertical dynamics model and state-space model constructed in step S12, a program is written using Python software to verify the accuracy of the PMCMC algorithm under normal train service conditions, and the number of particles is selected. The evaluation value of each suspension parameter is solved by the PMCMC algorithm, and is compared with the true value of each suspension parameter.

[0009] Preferably, the step S3 of Kriging-PSO-based key suspension parameter evaluation comprises steps S31-S35. Step S31: data acquisition and processing; step S32: obtaining suspension system parameter samples; step S33: constructing a Kriging surrogate model; step S34: establishing a power spectral density error optimization model; and step S35: solving by a particle swarm algorithm.

[0010] Preferably, the step S4 comprises steps S41-S42. Step S41: suspension parameter evaluation under normal conditions of the train vehicle; Step S411: taking the measured vertical acceleration of the train and the nodding acceleration obtained by simulation as observation values, i.e. The PMCMC algorithm is used to obtain the suspension parameter evaluation value; meanwhile, the suspension parameter evaluation value obtained by the Kriging-PSO algorithm is taken as the prior information in the PMCMC algorithm, and the PMCMC is used to re-calculate the suspension parameter evaluation value. K pz 、 K sz The value is updated as the prior information in the PMCMC algorithm, and the PMCMC is used to re-calculate the suspension parameter evaluation value. Step S412: the suspension parameters obtained by the parameter evaluation based on the PMCMC algorithm and the PMCMC-Kriging-PSO algorithm are substituted into the SIMPACK whole-vehicle dynamics simulation model, the vertical acceleration of the car body is calculated, and the calculated result is compared with the measured vertical acceleration of the car body in time domain and the power spectral density; Step S42: suspension parameter evaluation under fault conditions of the train vehicle; The PMCMC-PSO-Kriging algorithm is used to evaluate the parameters by simulating the fault of the primary spring and the primary vertical damper in the track vehicle SIMPACK model and taking the fault simulation result data as observation values; the PMCMC-Kriging-PSO algorithm is used to evaluate the parameters by setting different fault conditions of the primary spring vertical stiffness and the primary vertical damper of the bogie at one end and the other end in the SIMPACK whole-vehicle model and setting straight-curved running conditions, obtaining the simulation result in the SIMPACK post-processing and taking the simulation result as observation values.

[0011] Compared with the prior art, the present application has the following advantages: (1) The inventor found in practice that it is difficult for the technicians in the prior art to directly measure or accurately evaluate the suspension parameters of the bogie of the high-speed train, the present application takes into account the difference between the simulation test data and the actual monitoring data, and considers the fusion of data and mechanism, which is beneficial to improve the precision of the evaluation of the suspension parameters of the bogie.

[0012] (2) The inventor found that in the evaluation of high-speed train suspension parameters, the dynamic operating characteristics of the bogie suspension system are complex, and due to the significant nonlinear non-Gaussian characteristics of observation noise and system noise, traditional linear evaluation algorithms (such as KF, etc.) are difficult to meet the precision requirements of suspension parameter evaluation, and the standard MCMC algorithm is prone to local convergence in the state space. Therefore, the present application adopts particle Markov chain Monte Carlo (PMCMC) and is based on the vertical dynamics model of the whole train and the state space model to realize the preliminary evaluation of the vertical suspension parameters of the bogie (vertical stiffness of the primary spring, vertical damper of the primary spring, vertical stiffness of the air spring and vertical damper of the secondary spring).

[0013] (3) The inventor found that the PMCMC algorithm can perform posterior evaluation based on prior information and observation data, thereby comprehensively evaluating the parameters. However, relying only on simulation data, the prior information can only be determined by experience, and static prior evaluation is performed. The present application can evaluate the key suspension parameter values (vertical stiffness of the primary spring and vertical stiffness of the air spring) based on the measured vibration data of the train by combining the Kriging-PSO algorithm, and update the obtained result values as new prior distribution in the PMCMC algorithm, thereby reducing the gap between the prior and the true parameters when new data is measured, and making the posterior evaluation closer to the actual state of the suspension system of the in-service train.

[0014] (4) The inventor found that in practice, the suspension system of the high-speed train directly affects the dynamic performance of the train during operation, and the suspension parameters and the train vibration acceleration have nonlinear and strong coupling characteristics. To quantify the influence of the suspension parameters on the prediction accuracy of the car body vibration acceleration, the present application uses power spectrum density (PSD) to evaluate it, because power spectrum density can intuitively reflect the influence of different suspension parameters on the waveform characteristics of the car body acceleration from amplitude and wavelength. In addition, the Pearson correlation coefficient is used as the error evaluation function between the predicted value and the true value power spectrum density. In the present application, the collected car body vertical acceleration is taken as the true value, and 120 groups of car body vertical acceleration results obtained by SIMPACK simulation are taken as the predicted value.

[0015] (5) The inventor found that the suspension parameters that have the greatest impact on the car body vertical vibration include the vertical stiffness of the primary spring ( K pz ) and the vertical stiffness of the air spring ( K sz), the prediction accuracy of the vibration acceleration of the vehicle body is calculated with high cost and low efficiency by simulation or experiment. The Kriging model can capture the nonlinear relationship between variables based on known sample information, and has good prediction accuracy of the model for high-dimensional and nonlinear problems. Therefore, the invention will K pz 、 K sz As input variables, the Pearson correlation coefficient is used as an output variable, and a Kriging surrogate model is used to construct the mapping relationship between the suspension parameters and the Pearson correlation coefficient.

[0016] (6) The inventors found that K pz and K sz The vertical vibration of the vehicle body has the greatest impact, and the measured data of the vertical acceleration of the vehicle body is less affected by noise. At the same time, the number of measured samples of the invention is limited, and the vibration response of multiple components (such as the frame, the wheel set, etc.) is considered in the optimization process. The error between the simulation and the measured data in the optimization objective will weaken the constraint of the measured data on parameter evaluation, resulting in unstable optimization solution or falling into local optimum. Therefore, the invention will K pz 、 K sz As design variables, the power spectral density error between the predicted value and the true value of the vertical acceleration of the vehicle body is minimized as the target, and an optimization mathematical model is constructed.

[0017] (7) The inventors found that minimizing the power spectral density error is a single-objective, multi-parameter optimization problem. Particle swarm optimization (PSO) finds the global optimal solution in continuous space by simulating the hunting process of a bird swarm, and has the advantages of simple parameter setting, fast convergence speed, high calculation accuracy, and suitability for proxy model calling. Therefore, the invention uses PSO to solve the key suspension parameters K pz 、 K sz .

[0018] (8) The inventors compared the results of the traditional method of extended Kalman filter algorithm (EKF) in the field of train suspension evaluation to prove the engineering advantages of the method proposed in this study. In addition, to further verify the feasibility of the method proposed in this invention in the case of train failure, the inventors simulated the failure of the primary spring and the primary vertical damper in the track vehicle SIMPACK model, and used the failure simulation result data as the observation value to evaluate the parameters using the method proposed in this invention, which still achieved accurate evaluation of the suspension parameters. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 Technical route diagram for evaluating bogie suspension parameters by using PMCMC-Kriging-PSO algorithm; Figure 2 Schematic diagram of a four-axle vehicle multi-rigid-body whole vehicle model constructed; Figure 3 Schematic diagram of a process for evaluating suspension parameters by using PMCMC algorithm; Figure 4 Schematic diagram of a process for evaluating key suspension parameters by using Kriging-PSO algorithm; Figure 5 Schematic diagram of a process for solving key suspension parameters by using PSO algorithm. DETAILED DESCRIPTION

[0020] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application.

[0021] Therefore, the following detailed description of the embodiments of the present application is not intended to limit the scope of the claimed application, but merely represents some embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of protection of the present application.

[0022] A high-speed train suspension parameter evaluation method, comprising the following steps: Step S1: constructing a vehicle vertical six-degree-of-freedom dynamics model.

[0023] Step S2: performing preliminary evaluation of suspension parameters by using PMCMC algorithm.

[0024] Step S3: taking key suspension parameters as design variables, simulating the Pearson correlation coefficient of the vertical acceleration power spectral density of the vehicle body and the measured vertical acceleration power spectral density of the vehicle body as output, and constructing a Kriging surrogate model. Meanwhile, taking the minimization of the error of the simulated and measured vehicle body vertical acceleration PSD as the target, and obtaining key suspension parameters matching the actual service state by using a particle swarm optimization algorithm.

[0025] Step S4: suspension parameter evaluation based on PMCMC-Kriging-PSO.

[0026] Preferably, step S1 specifically comprises steps S11-S12: Step S11: establishing a whole vehicle dynamics model in SIMPACK.

[0027] Step S111: Construct a vehicle dynamics simulation model in SIMPACK. The primary suspension system includes steel springs, primary vertical dampers, and axle box swing arm devices; the secondary suspension system includes air springs, secondary vertical dampers, secondary lateral dampers, and anti-hunting dampers. The vehicle model uses the measured tread surface of S1002CN. The Hertz nonlinear contact model is used to calculate the contact stress between the vehicle model and the track model, and the FASTSIM algorithm is used to calculate the wheel-rail rolling contact. Furthermore, measured track irregularities, curve radii, and curve superelevation are used as input excitations for the model.

[0028] Step S112: Sensors are added to different components such as the car body, frame, axle boxes, and wheelsets to obtain post-processed data such as vibration acceleration and angular acceleration. Based on the initial suspension parameters of this vehicle model, the value range of the suspension parameters is determined by a 50% fluctuation above and below the initial parameters. The suspension parameter variables are set in the SIMPACK software, with a train speed of 200 km / h, a curve condition, and a sampling frequency of 1000 Hz. The vertical acceleration and nose-dive angular acceleration of the car body, first-position end frame, and second-position end frame in the whole-vehicle simulation model are obtained through post-processing and used as observations in the subsequent PMCMC algorithm suspension parameter evaluation.

[0029] Step S12: Construct the vertical dynamics model and state space model of the whole vehicle.

[0030] Step S121: This invention constructs a multi-rigid-body whole vehicle model for a four-axle vehicle. To improve computational efficiency and reduce model complexity, a stiffness-damped parallel model is used to establish the vertical dynamics model of the whole vehicle, assuming that track irregularities move together in the vertical direction. The whole vehicle vertical dynamics model has a total of 6 degrees of freedom, and the car body, the first-position end frame, and the second-position end frame all consider buoyancy and pitching motions. The whole vehicle vertical dynamics equations are shown in equations (1)-(6): (1) (2) (3) (4) (5) (6) In equations (1)-(6), , These refer to the mass of the car body and the frame, respectively. , These are the head-nodding rotational inertia of the vehicle body and the frame, respectively. , , are the heave displacements of the car body, one-end bogie and two-end bogie, respectively; , , are the pitch displacements of the car body, one-end bogie and two-end bogie, respectively; , are the dampings of the primary and secondary vertical dampers, respectively, including - , - ; , are the stiffnesses of the primary and air springs, respectively, including - , - ; , , , are the track vertical irregularities acting on the four wheelsets, respectively; is the distance between the center of the car body and the center of the one-end or two-end bogie; is the distance between the center of the bogie and the center of the wheelset installed on the bogie.

[0031] Step S122: transform the track vehicle vertical dynamics model into a state space model as follows, the continuous-time quantities are , and the discrete-time quantities are ; (7) (8) In equations (7)-(8), , , , is the system state matrix, is the disturbance matrix, is the output matrix; is the observation vector of the system at time , i.e., the observed values of each parameter in at time ; Since equation (7) is a continuous function of time t , let the sampling period be , and let , then the discrete quantities are defined as , Therefore , ; the discretized state space model can be obtained by discretizing equation (7) and combining equation (8) as follows: ​​​​ (9) (10) In the formula, This refers to the sampling time sequence number in the discrete model; , These are the state noise vector and the observation noise vector, respectively. , , It is by The determined matrix This is a vector of physical parameters for the vehicle system, namely mass, moment of inertia, and suspension stiffness / damping. , , Based on The value is derived from the vehicle system dynamics equations and transformed according to the definition of state variables.

[0032] Step S2: Preliminary assessment of suspension parameters based on PMCMC, including steps S21-S22.

[0033] This invention employs the particle-independent Metropolis-Hastings (MH) algorithm to implement the PMCMC algorithm. Its core idea is: under unknown parameters... Under the following assumption The vehicle body and frame acceleration values ​​obtained through SIMPACK simulation at any time are Using particle filtering to evaluate state variables Then, the corresponding observed likelihood values ​​are calculated. Finally, new parameters are obtained by sampling based on the MH criterion. And determine whether to accept the parameter as an evaluation value. .

[0034] Step S21: Implement the PMCMC algorithm.

[0035] Step S211: Initialize parameters. Set initial values ​​for the parameters. and particle number M， Let the parameter sample index From the initial distribution Extract N Particles .

[0036] Step S212: At each observation time j ( j =1,2,…), repeat the following steps.

[0037] Step 1: Filter the state space under the current parameter values. Perform sampling; Step 2: When the observed value Upon arrival, calculate the observation likelihood value of the particle based on the observation model and update the weight of the particle with the particle weight update function Resample the particle according to the weight Resample the particle to avoid particle degeneracy Step 3: Calculate the approximation value of the likelihood function Take this value as the input of MCMC sampling Step S213: If , save in the parameter chain, otherwise enter the Metropolis acceptance criterion to determine whether to accept

[0038] The Metropolis acceptance criterion is expressed as , and the acceptance probability is evaluated whether it is acceptable, and if accepted, save in the parameter chain, otherwise save . If the parameter chain has converged, output the MCMC chain, otherwise , and generate a new parameter according to the symmetric normal proposal distribution.

[0039] Step S22: Parameter setting of PMCMC algorithm

[0040] Step S221: The covariance of the proposal distribution in the hanging parameter evaluation determines the acceptance range of the candidate parameter in each iteration process, and the proposal covariance . Among them represents a 12-order unit matrix, is obtained based on the prior range of the hanging parameter and the acceptance rate of 40% repeated test.

[0041] Step S222: State process noise in parameter evaluation is vertical track irregularity, and state process noise covariance controls the noise size in state update process, and state noise covariance is: ; Among them, is the track roughness factor, and ; is the sampling time interval, , is the train running speed, unit: m / s.

[0042] Step S223: Observation noise covariance affects the observation model. In order to make the observation noise covariance adaptively reflect the magnitude difference of each channel observation value, is a diagonal matrix, The calculation of the first diagonal element is as follows.

[0043] (11) wherein, is an empirical coefficient, and respectively represent the maximum and minimum values of the first observation during the observation process.

[0044] Step S224: Based on the whole vehicle vertical dynamics model and the state space model constructed in step S12, a program is written using Python software to verify the accuracy of the PMCMC algorithm under normal service state of the train, and the number of particles is selected, and the evaluation value of each suspension parameter is solved by the PMCMC algorithm, and compared with the true value of each suspension parameter. The results show that each parameter can realize effective convergence and is close to the initial design value, indicating that the PMCMC algorithm is reliable.

[0045] Step S3: Key suspension parameter evaluation based on Kriging-PSO, including steps S31-S35.

[0046] This step relates to the method for obtaining key suspension parameters (primary spring vertical stiffness and air spring vertical stiffness) in suspension parameter evaluation. The Kriging surrogate model is introduced into the PSO algorithm, and based on the measured vibration data of the train, the evaluation value of the key parameter matching the suspension state of the high-speed train is obtained, so as to update the prior information in the PMCMC algorithm.

[0047] Step S31: Data acquisition and processing.

[0048] The measured data used is collected by the on-board state monitoring system during normal operation. Preferably, in the present application, the historical measured vibration data of a certain type of motor train unit running at 200 km / h on an actual line is used, and the detection length is 300 km. The detection data only includes two-way (vertical, lateral) acceleration sensors placed on the train body center and the frame, the sampling frequency is 1000 Hz, and does not involve sensitive data such as passenger information, scheduling records, etc. and removes identification information such as train number, running date and specific line name, and the present application only uses desensitized acceleration time history for suspension parameter evaluation. According to the acceleration data processing method in GB5599-2019 "Dynamics Performance Evaluation and Test Identification Specification for Rolling Stock", the measured and simulated vertical accelerations of the train body and the frame are all subjected to 0.1~10 Hz band-pass filtering.

[0049] Preferably, as in the acquired vehicle measured data, the nodding acceleration of the vehicle body and the frame is missing, the section with smaller root mean square (RMS) of lateral acceleration is selected as the approximate straight line working condition, and the nodding acceleration of the vehicle body and the frame obtained by simulating the SIMPACK vehicle model under the same working condition is taken as the supplement of the observation data.

[0050] Step S32: acquiring suspension system parameter samples.

[0051] Optimal Latin Hypercube Sampling (OLHS) is a widely used design space sampling method for acquiring data samples. Compared with random sampling or orthogonal experimental design, OLHS can achieve more uniform coverage of the design space by optimizing the distribution of sample points. The present application adopts the Optimal Latin Hypercube Sampling (OLHS) method to acquire key parameter samples of the suspension system, takes the 11 suspension parameters selected by the present application as the sampling objects, the sample number is 120, and the sampling results are substituted into the DOE module of the SIMPACK software for batch calculation, and finally the vertical acceleration values of the vehicle body in the 120 groups of results are extracted by Matlab.

[0052] Step S33: constructing a Kriging surrogate model.

[0053] Step S331: taking the vertical acceleration of the vehicle body collected in step S31 as the true value, and taking the 120 groups of vertical acceleration results of the vehicle body obtained by SIMPACK simulation in step S32 as the predicted value. To quantify the influence of the suspension parameters on the prediction accuracy of the vehicle body vibration acceleration, because the power spectrum density can intuitively reflect the influence of different suspension parameters on the waveform characteristics of the vehicle body acceleration from the amplitude and wavelength, the present application adopts the power spectrum density (Power Spectrum Density, PSD) for evaluation. In addition, the Pearson correlation coefficient is used as the error evaluation function between the predicted value and the true value power spectrum density, and the Pearson correlation coefficient of the power spectrum density is calculated as follows: (12) In the formula, represents the mathematical expectation, and are the power spectrum densities of the predicted value and the true value respectively, is the Pearson correlation coefficient of the power spectrum density, and the value range of the Pearson correlation coefficient is [-1, 1], indicates complete positive correlation, indicates complete negative correlation, indicates no linear correlation.

[0054] Step S332: the present application takes the vertical stiffness of the primary spring ( Kpz ) and air spring vertical stiffness ( K sz ) as input variables, and Pearson correlation coefficient as output variable, the Kriging surrogate model is established. 100 groups of 120 groups of calculated Pearson correlation coefficients are used as training data, and the remaining 20 groups of data are used as a validation set to verify the accuracy of the surrogate model. The determination coefficient of the model reaches 0.932, and the accuracy meets the requirements of engineering application.

[0055] Step S333: In order to verify that the Kriging surrogate model is accurate and reliable, radial basis function (Radial Basis Function, RBF) and random forest (Random Forest, RF) are used to construct K pz , K sz The Pearson correlation coefficient of the power spectral density of the vehicle body vertical acceleration is used to compare the accuracy of the Kriging surrogate model with RBF and RF surrogate models. The results show that the determination coefficients of RBF and RF surrogate models are 0.735 and 0.897 respectively, and the accuracy of the Kriging model is the highest among the three surrogate models.

[0056] Step S34: An error optimization model of power spectral density is established.

[0057] The present application will K pz , K sz As a design variable, the power spectral density error between the predicted value and the true value of the vehicle body vertical acceleration is minimized as the target, and the optimization mathematical model is constructed as follows: (13) In the formula, is the error between the predicted value and the true value of the vehicle body vertical acceleration, is the predicted value of the vehicle body vertical Kriging surrogate model, is the vertical suspension parameter K pz , K sz .

[0058] Step S35: Particle swarm algorithm is used for solution.

[0059] Step S351: As can be seen from formula (13), minimizing the power spectral density error is a single-target, multi-parameter optimization problem. The present application uses particle swarm optimization (Particle Swarm Optimization, PSO) to solve the problem.

[0060] Preferably, according to the constraint condition in formula (13), the influence of the order of magnitude between targets is eliminated by using the normalization method, and the PSO algorithm is set as follows: the population number is initialized to 100, the iteration number is 100 times, the maximum inertia weight and the minimum inertia weight are set to 0.9 and 0.4 respectively, and are set to 1 and 2 respectively. The PSO algorithm is realized by using Python, and the suspension parameters obtained by searching by using the PSO algorithm are K pz , K sz optimal solution.

[0061] Step S352: In order to analyze the stability of the PSO optimization result and verify whether it is susceptible to the influence of the initial population number, the algorithm is run multiple times under the same parameter setting, and different initial population number values are adjusted each time. The optimal target function value of each run is unchanged, compared with the optimal solution when the initial population number is 100, the change range of the optimal solution of the suspension parameters is less than 1x10 -4 , and the PSO algorithm can stably converge to the same global optimal solution.

[0062] Step S4: Suspension parameter evaluation based on PMCMC-Kriging-PSO.

[0063] The PMCMC algorithm can perform posterior evaluation based on prior information and observation data, thereby comprehensively evaluating the parameters. However, only relying on simulation data, the prior information can only be determined by experience, and static prior evaluation is performed. By combining the Kriging-PSO algorithm, the present application can evaluate the key suspension parameter values based on the measured vibration data of the train, and update the obtained result values as new prior distribution in the PMCMC algorithm, thereby reducing the gap between the prior and the true parameters when new data is measured, and making the posterior evaluation closer to the actual state of the suspension system of the in-service train.

[0064] Step S41: Suspension parameter evaluation under normal conditions of the train vehicle.

[0065] Step S411: The measured vertical acceleration of the train and the nodding acceleration obtained by simulation are taken as observation values, i.e. , and the suspension parameter evaluation value is obtained by using the PMCMC algorithm. At the same time, the value of K pz , K sz obtained based on the Kriging-PSO algorithm is updated as the prior information in the PMCMC algorithm, and the suspension parameter evaluation values are recalculated by using the PMCMC.

[0066] Step S412: Substitute the suspension parameters obtained by parameter evaluation based on the PMCMC algorithm and the PMCMC-Kriging-PSO algorithm into the SIMPACK whole vehicle dynamics simulation model, and calculate the vehicle body vertical acceleration result, and compare it with the measured vehicle body vertical acceleration time domain waveform and power spectral density of the train.

[0067] In addition, to further prove the engineering advantages of the method of the present research, the evaluation results of the traditional method of the train suspension evaluation field, the extended Kalman filter algorithm (EKF), are compared. The comparison results show that the Pearson correlation coefficient of the EKF algorithm is improved by 0.107. It is verified that the high-speed train suspension parameter evaluation method based on the PMCMC-Kriging-PSO algorithm can accurately realize parameter evaluation.

[0068] Step S42: Suspension parameter evaluation under train vehicle failure conditions.

[0069] By simulating the failure of primary springs and primary vertical dampers in the track vehicle SIMPACK model, and using the failure simulation result data as the observation value, the PMCMC-PSO-Kriging algorithm is used to evaluate the parameters. In the SIMPACK whole vehicle model, different failure conditions of the primary spring vertical stiffness and the primary vertical damper damping of the one-end and two-end bogies are set, and the straight-curved running conditions are set. The simulation results are obtained in the SIMPACK post-processing and used as observation values, and the PMCMC-Kriging-PSO algorithm is used to evaluate the parameters.

[0070] The failure is divided into three working conditions of primary spring vertical stiffness failure, secondary vertical damper damping failure and simultaneous failure of both. When the primary spring vertical stiffness is reduced to about 0.5 times the normal value, the results show that the evaluation values of the primary and secondary vertical dampers can converge to the true value near the iteration of about 50 steps. When the primary vertical damper damping is reduced to about 0.5 times the normal value, the evaluation value of the secondary vertical damper damping can also converge to the true value near the iteration of about 50 steps. When the primary spring vertical stiffness and the primary vertical damper damping are simultaneously reduced to about 0.5 times the normal value, the evaluation value of the secondary vertical damper damping can still converge to the true value near the iteration of about 50 steps.

[0071] Preferably, the evaluated suspension parameters are used to further update the dynamics model, which can reduce the gap between the simulation model and the service vehicle.

[0072] Taking the case where the vertical stiffness of the primary spring is reduced to 50% of its normal value as an example, the dynamic performance of the vehicle was monitored. Four dynamic performance parameters were mainly selected: left / right lateral acceleration of the train body, left / right derailment coefficient of the first wheelset, lateral wheel-rail force of the first wheelset, vertical wheel-rail force of the first wheelset, and wheel load reduction rate of the first wheelset. The simulation results of the vehicle under fault conditions were used as observations, and the suspension parameter evaluation values ​​obtained by the proposed method were substituted into the simulation model for recalculation. Finally, the dynamic performance parameter results obtained under the initial and evaluation values ​​under fault conditions were compared. The results show that the maximum absolute error of the compared dynamic performance parameters does not exceed 0.07, indicating that the proposed method can reduce the calculation error of the dynamic performance parameters in the simulation model.

[0073] A comparison with existing technologies reveals that the main advantages of the high-speed train suspension parameter evaluation method proposed in this invention are at least the following: (1) Using the dynamic results obtained from the SIMPACK simulation as the observation values, the suspension parameters were evaluated using the PMCMC algorithm. The results showed that all parameters could achieve effective convergence and were close to the initial design values, indicating that the PMCMC algorithm is reliable.

[0074] (2) A Kriging surrogate model was established with key suspension parameters (vertical stiffness of primary spring and vertical stiffness of air spring) as input and Pearson correlation coefficient between simulation and measured values ​​as output. The determination coefficient of the model reached 0.932, and the accuracy met the requirements of engineering applications.

[0075] (3) A power spectral density error optimization model was constructed. Based on the predicted values ​​of the Kriging model, the PSO algorithm was used to solve for the key suspension parameters, and the optimization results were updated with the prior information of the PMCMC algorithm to obtain the final parameter evaluation values. By analyzing the simulation results of the initial design parameters and the parameters evaluated by the PMCMC-Kriging-PSO algorithm with the power spectral density of the measured vertical acceleration of the train body, the Pearson correlation coefficients were 0.323 and 0.958, respectively. The Pearson correlation coefficient of the method in this paper was improved by 0.107 compared with that of the EKF algorithm. This verifies that the high-speed train suspension parameter evaluation method based on the PMCMC-Kriging-PSO algorithm can accurately achieve parameter evaluation.

[0076] (4) Based on the proposed method's ability to accurately evaluate suspension parameters, the PMCMC-Kriging-PSO algorithm was further used to verify the method under vehicle fault conditions. It still effectively evaluates all suspension parameters with high accuracy. The simulation model was updated using the evaluated parameters, and compared with the vehicle dynamic performance parameters under the initial parameters. The maximum absolute error of the compared dynamic performance parameters did not exceed 0.07, indicating that the proposed method can reduce the calculation error of the simulation model's dynamic performance parameters.

[0077] The above examples are only used to illustrate the present application and are not intended to limit the technical solutions described in the present application. Although the present application has been described in detail with reference to the above various embodiments, the present application is not limited to the above specific embodiments. Therefore, any modification or equivalent replacement of the present application; and all technical solutions and improvements without departing from the spirit and scope of the application are all included in the scope of the claims of the present application.

Claims

1. A method for evaluating suspension parameters of high-speed trains, characterized in that: Includes the following steps: Step S1: Construct a six-degree-of-freedom vertical dynamic model of the vehicle; Step S2: Perform preliminary evaluation of suspension parameters using the PMCMC algorithm; Step S3: Using key suspension parameters as design variables and the Pearson correlation coefficient of the simulated and measured vertical acceleration power spectral density of the vehicle body as output, construct a Kriging surrogate model; at the same time, with the goal of minimizing the PSD error between the simulated and measured vertical acceleration of the vehicle body, use the PSO algorithm to obtain key suspension parameters that match the actual service conditions. Step S4: Evaluation of suspension parameters based on PMCMC-Kriging-PSO.

2. The method for evaluating suspension parameters of a high-speed train as described in claim 1, characterized in that: Step S1 specifically includes steps S11-S12; Step S11: Establish the vehicle dynamics model in SIMPACK; Step S111: Construct a vehicle dynamics simulation model in SIMPACK; the primary suspension system includes steel springs, primary vertical dampers, and axle box swing arm devices, while the secondary suspension system includes air springs, secondary vertical dampers, secondary lateral dampers, and anti-hunting dampers; the vehicle model uses the measured tread surface of S1002CN, and the Hertz nonlinear contact model is used to calculate the contact stress between the vehicle model and the track model, while the FASTSIM algorithm is used to calculate the wheel-rail rolling contact; in addition, measured track irregularities, curve radius, and curve superelevation are used as input excitations for the model; Step S112: Sensors are added to different components such as the car body, frame, axle box, and wheelsets to obtain post-processed data such as vibration acceleration and angular acceleration. Based on the initial suspension parameters of the vehicle, the value range of the suspension parameters is determined by a 50% fluctuation above and below the initial parameters. In the SIMPACK software, the variables of each suspension parameter are set, the train running speed is 200 km / h, the curve condition is used, and the sampling frequency is 1000 Hz. The vertical acceleration and nose-nodding angular acceleration of the car body, the first end frame, and the second end frame in the whole vehicle simulation model are obtained through post-processing and used as observation values ​​in the subsequent PMCMC algorithm suspension parameter evaluation. Step S12: Construct the vertical dynamics model and state space model of the whole vehicle; Step S121: Construct a multi-rigid-body whole vehicle model for a four-axle vehicle; use a stiffness-damping parallel model to establish the vertical dynamics model of the whole vehicle, and assume that the track irregularities move together in the vertical direction; the vertical dynamics model of the whole vehicle has a total of 6 degrees of freedom, and the car body, the first end frame and the second end frame all consider the floating and nodding motion; the vertical dynamics equations of the whole vehicle are shown in equations (1)-(6): (1) (2) (3) (4) (5) (6) In equations (1)-(6), , These refer to the mass of the vehicle body and the mass of the frame, respectively. , These are the head-nodding rotational inertia of the car body and the frame, respectively. , , These are the floating and sinking displacements of the car body, the first end frame, and the second end frame, respectively. , , These are the head angle displacements of the car body, the first end frame, and the second end frame, respectively. , These are the primary and secondary vertical dampers, including... - , - ; , These are the vertical stiffnesses of primary springs and air springs, including... - , - ; , , , The vertical unevenness of the track acting on the four wheelsets is respectively. This is half the vehicle's fixed distance, i.e., the distance from the center of the vehicle body to the center of the first or second end frame. It is half the wheelbase of the bogie, that is, the distance from the center of the frame to the center of the axle of the wheelset mounted on the frame; Step S122: Transform the vertical dynamics model of the rail vehicle into a state-space model as follows, with the continuous time quantities denoted as... Discrete time quantities are denoted as ; (7) (8) In equations (7)-(8), , , , For the system state matrix, For the perturbation matrix, This is the output matrix; For the system at time The observation vector, i.e. The parameters in time Observed values; Since equation (7) is about time t A continuous function, with a sampling period of . ,make Then the discrete quantity is defined as , ,therefore , Discretizing equation (7) and combining it with equation (8) yields the following discretized state-space model: (9) (10) In the formula, This refers to the sampling time sequence number in the discrete model; , These are the state noise vector and the observation noise vector, respectively. , , It is by The determined matrix This is a vector of physical parameters for the vehicle system, namely mass, moment of inertia, and suspension stiffness / damping. , , Based on The value is derived from the vehicle system dynamics equations and transformed according to the definition of state variables.

3. The method for evaluating suspension parameters of a high-speed train as described in claim 2, characterized in that: Step S2 includes steps S21-S22; Step S21: Implement the PMCMC algorithm; Step S211: Initialize parameters; set initial parameter values. and particle number M， Let the parameter sample index From the initial distribution Extract N Particles ; Step S212: At each observation time j ( j =1,2,…), repeat the following steps; Step 1: Filter the state space under the current parameter values. Perform sampling; Step 2: When the observed value Upon arrival, the observed likelihood value of the particle is calculated based on the observation model. With particle weight update function To achieve resampling, based on weights Particles are resampled to prevent particle degradation; Step 3: Calculate the approximate value of the likelihood function. This value is used as the input for MCMC sampling; Step S213: If Then save it in the parameter chain. Otherwise, it will proceed to the Metropolis acceptance criteria to determine whether to accept the application. Metropolis acceptance criteria are To accept probability Evaluate Is it acceptable? If so, save it in the parameter chain. Otherwise Save the data; if the parameter chain has converged, output the MCMC chain; otherwise, save the data. And generate new parameters according to the symmetric normal proposed distribution. ; Step S22: PMCMC algorithm parameter settings; Step S221: In the evaluation of dangling parameters, the covariance of the proposal distribution determines the acceptable range of candidate parameters in each iteration. (Proposal covariance) ;in Represents a 12th-order identity matrix. It was obtained based on the prior range of suspension parameters and repeated trials with an acceptance rate of 40%. Step S222: State process noise in parameter evaluation For vertical irregularities in the track, the state noise covariance controls the noise level during the state update process. for: ； in, For track roughness factors, take ; The sampling time interval, , The train's speed is expressed in m / s. Step S223: The observation noise covariance affects the noise of the observation model. To ensure that the observation noise covariance can adaptively reflect the magnitude differences in the observations of each channel, the following steps are taken: Let it be a diagonal matrix. Among them, the first The calculation of the diagonal elements is as follows; (11) In the formula, It is an empirical coefficient. and They represent the first The maximum and minimum values ​​of each observation during the observation process; Step S224: Based on the vehicle vertical dynamics model and state-space model constructed in step S12, a program is written using Python software to verify the accuracy of the PMCMC algorithm under normal train service conditions, and the number of particles is selected. The evaluation values ​​of each suspension parameter are obtained by using the PMCMC algorithm and compared with the actual values ​​of each suspension parameter.

4. The method for evaluating suspension parameters of a high-speed train as described in claim 3, characterized in that: Step S3: Evaluation of key suspension parameters based on Kriging-PSO, including steps S31-S35; Step S31: Data acquisition and processing; Step S32: Obtain suspension system parameter samples; Step S33: Construct Kriging surrogate model; Step S34: Establish power spectral density error optimization model; Step S35: Solve using particle swarm optimization algorithm.

5. The method for evaluating suspension parameters of a high-speed train as described in claim 4, characterized in that: In step S31: the measured data used is collected by the on-board condition monitoring system during normal operation; the detection data only includes the biaxial acceleration sensor placed at the center of the train body and frame, with a sampling frequency of 1000 Hz, and does not involve sensitive data such as passenger information and dispatch records. The train number, running date and specific line name are removed, and the desensitized acceleration time history is used to evaluate the suspension parameters.

6. The method for evaluating suspension parameters of a high-speed train as described in claim 5, characterized in that: In step S32: The optimal Latin hypercube sampling method is used to obtain key parameter samples of the suspension system. The selected suspension parameters are used as sampling objects, with a sample size of 120. The sampling results are then substituted into the SIMPACK software for batch calculation, and the vertical acceleration values ​​of the vehicle body are extracted from the 120 sets of results.

7. The method for evaluating suspension parameters of a high-speed train as described in claim 6, characterized in that: Step S33: Construct the Kriging proxy model; Step S331: The vertical acceleration of the vehicle body collected in step S31 is taken as the true value. Step S32: 120 sets of vertical acceleration results of the vehicle body are obtained through SIMPACK simulation as predicted values. Power spectral density is used for evaluation. Pearson correlation coefficient is used as the error evaluation function between the predicted value and the true value power spectral density. The Pearson correlation coefficient of power spectral density is calculated as follows: (12) In the formula, Represents mathematical expectation, and These are the predicted and actual power spectral densities, respectively. Let be the Pearson correlation coefficient of the power spectral density, and let the value of the Pearson correlation coefficient be in the range of [-1, 1]. Indicates a perfect positive correlation. Indicates a completely negative correlation. Indicates wireless correlation; Step S332: Adjust the vertical stiffness of a series of springs ( K pz ) and air spring vertical stiffness ( K sz Using the input variable and the Pearson correlation coefficient as the output variable, a Kriging surrogate model is established. Step S333: Constructing [data] using radial basis functions and random forests respectively. K pz , K sz A surrogate model for the Pearson correlation coefficient with the vertical acceleration power spectral density of the vehicle body was used, and the accuracy of the Kriging surrogate model was compared with that of the RBF and RF surrogate models.

8. The method for evaluating suspension parameters of a high-speed train as described in claim 7, characterized in that: In step S34: ... K pz , K sz As a design variable, with the objective of minimizing the power spectral density error between the predicted and actual values ​​of the vehicle's vertical acceleration, the following optimization mathematical model is constructed: (13) In the formula, This represents the error between the predicted and actual values ​​of the vehicle's vertical acceleration. The vertical Kriging surrogate model predicts the values ​​for the vehicle body. Vertical suspension parameters K pz , K sz .

9. The method for evaluating suspension parameters of a high-speed train as described in claim 8, characterized in that: Step S35 includes steps S351-S352; Step S351: Use the particle swarm optimization algorithm to minimize the power spectral density error; according to the constraints in equation (13), use the normalization method to eliminate the influence of orders of magnitude between targets. The particle swarm optimization algorithm is set as follows: the initial population size is 100, the number of iterations is 100, and the maximum inertia weight is... and minimum inertia weight Set them to 0.9 and 0.4 respectively. and The suspension parameters are set to 1 and 2 respectively, and obtained by searching using the particle swarm optimization algorithm. K pz , K sz Optimal solution; Step S352: To analyze the stability of the particle swarm optimization results and verify whether they are easily affected by the initial population size, the algorithm is run multiple times under the same parameter settings, with different initial population values ​​adjusted each time.

10. The method for evaluating suspension parameters of a high-speed train as described in claim 9, characterized in that: Step S4 includes steps S41-S42; Step S41: Evaluation of suspension parameters of train vehicles under normal conditions; Step S411: Use the measured vertical acceleration of the train and the simulated head-nodding acceleration as the observed values, i.e. The suspension parameter evaluation values ​​were obtained using the PMCMC algorithm; simultaneously, the values ​​obtained based on the Kriging-PSO algorithm were... K pz , K sz The values ​​are updated with prior information from the PMCMC algorithm, and the evaluation values ​​of each suspension parameter are recalculated using PMCMC. Step S412: Substitute the suspension parameters obtained from parameter evaluation based on the PMCMC algorithm and the PMCMC-Kriging-PSO algorithm into the SIMPACK vehicle dynamics simulation model, calculate the vertical acceleration result of the vehicle body, and compare it with the time-domain waveform and power spectral density of the measured vertical acceleration of the train body. Step S42: Evaluation of suspension parameters in the event of train vehicle malfunction; By simulating primary spring and primary vertical damper failures in the SIMPACK model of a rail vehicle, and using the failure simulation results as observations, the parameters were evaluated using the PMCMC-PSO-Kriging algorithm. In the SIMPACK whole vehicle model, different failure conditions were set for the primary spring vertical stiffness and primary vertical damper damping of the bogie at the first and second ends, respectively, and straight-curve running conditions were set. The simulation results were obtained in the SIMPACK post-processing and used as observations, and the parameters were evaluated using the PMCMC-Kriging-PSO algorithm.

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