Uncertainty Analysis Of EMU Traction Motor Rotor System Based On BSVR

The traction motor rotor system is an essential component of the mechanical traction drive system of the electric multiple units(EMU),researching its dynamic characteristics under the influence of uncertainties is an important indicator for the correct assessment of the safety and reliability of the EMU.In investigating the effects of uncertain inputs on system outputs,Monte Carlo Simulation(MCS)based uncertainty analysis methods usually require large sampling of the input variables and repeated execution of complex simulation models to obtain the uncertainty response.In contrast,the surrogate model approach attempts to use machine learning theory to construct an approximation of the original simulation model,which can substantially reduce the computational burden for uncertainty analysis.Among many surrogate models,the Bayesian Support Vector Regression(BSVR)model based on "structural risk minimization" and Bayesian inference framework has obvious advantages in dealing with high-dimensional nonlinear problems.In fact,the traction motor rotor system of EMU is generally characterized by complex models,high dimensionality and nonlinearity.Therefore,this paper introduces and develops the BSVR model method,which is used to systematically study the propagation law and influence mechanism of stochastic uncertainty in the dynamic characteristics of the traction motor system of the EMU.The main contents can be summarized as follows:(1)An efficient BSVR-based uncertainty analysis method is investigated.Firstly,a new adaptive sampling method is proposed for the adaptive selection problem of experimental design of the BSVR agent model.Then,a new adaptive BSVR surrogate model is constructed by combining the proposed adaptive sampling method and BSVR,and used for the response stochastic analysis problem.The effectiveness of the proposed adaptive BSVR surrogate model is verified using six mathematical algorithms of different complexity,and the results show that the new adaptive BSVR surrogate model proposed in this paper has better performance in terms of accuracy and efficiency when compared with the adaptive BSVR surrogate model built using other adaptive algorithms.Secondly,a new surrogate model method PC-BSVR is proposed to address the high cost and low efficiency of Monte Carlo Simulation(MCS)in calculating Sobol global sensitivity metrics by combining Polynomial Chaos Expansion(PCE)and BSVR.In this method,a complete PCE agent model is established using the BSVR technique and polynomial chaos kernel function,and then the coefficients of PCE are obtained by solving the BSVR problem,and based on the solved PCE coefficients,the Sobol global sensitivity index can be efficiently calculated.Both mathematical and engineering examples show that the proposed PC-BSVR surrogate model has equal accuracy and higher efficiency in computing Sobol global sensitivity indexes compared to MCS.(2)The deterministic dynamics of the traction motor rotor system of the EMU under the combined effect of initial shaft bending and unbalance failure is studied.Firstly,based on the finite element theory of beam rotor,the steady-state dynamics equations of the system under the joint action of unbalance and shaft bending faults are derived,and then the first-order resonant steady-state response(including the peak response as well as the critical speed)is used as the key response quantity to establish the model function of the traction motor rotor system.Furthermore,a stochastic parametric model of the traction motor rotor system of the EMU is established based on the deterministic model with reasonable consideration of the uncertain parameters contained in the system.The influence of uncertainty parameters on the resonant steady-state response of the traction motor rotor was studied qualitatively by analyzing the deterministic dynamics of the model parameters,boundary conditions and fault parameters at different values,and the results showed that the model parameters and boundary conditions had a large influence on the peak resonant steady-state response and the critical speed,while the fault parameters only affected the peak resonant steady-state response.(3)Using the proposed efficient uncertainty analysis method,the uncertainty analysis of the resonance steady-state response of the EMU traction motor rotor system is carried out.First,the stochastic resonance steady-state response is analyzed by using the adaptive BSVR method,and its statistical distribution law under the influence of an input random variable that obeys an independent normal distribution is studied,and the stochastic resonance steady-state response is affected by the coefficient of variation of the input random variable law.Secondly,based on PC-BSVR,the global sensitivity index of stochastic resonance steady-state response to uncertain input parameters is calculated,and the importance of each input random variable in the system to the output response uncertainty is evaluated.Finally,the relevant laws are summarized.In conclusion,this paper fully considers the three types of uncertainties contained in the traction motor rotor system of the EMU and the complex and high-dimensional characteristics of the rotor system,and completes the stochastic analysis and global sensitivity analysis of the resonant steady-state response of the traction motor rotor system of the EMU based on the adaptive BSVR and PC-BSVR surrogate models,respectively.