Local-instantaneous Spectrum For Dynamic Response Of High-speed Vehicle-track Coupling System

Vehicle-track coupling system is a nonlinear and nonstationary system. Since the traditional spectrum analysis based on Fourier transform describes time history of vehicle-track coupling system either in time domain or frequency domain, the time varying characteristics of dynamic response of vehicle-track system cannot be reflected. Although traditional time-frequency methods such as Short-time Forier transform (STFT) and wavelet transform (WT) can show some nonstationary characteristics to a certain extent, there are some obvious shortcomings. For instance, the basis function must be predetermined, so the computational procedure is not self-adaptive. If the original data is severely distorted, some sub-harmonics may be introduced in the results and the spectrum does not make physical sense. As we known, a time series, x(t), is stationary, if, for allt, it satisfies the traditional definition of stationarity. In practice, we can only have limited time spans; therefore, even to check these definitions, we have to make approximations. Few of the data sets, from either natural phenomena or artificial sources, can satisfy these definitions; consequently, no one even bothers using them for checking the stationarity. Based on linear algebra, as we known, nonlinearity is defined on input vs. output. But in reality, since the results depend on initial conditions as well as loading, such an approach is not practical:natural system is not clearly defined and inputs and outputs are hard to ascertain and quantify.Local-instantaneous spectrum analysis method based on empirical mode decomposition (EMD) and ensemble empirical mode decomposition (EEMD) are recently developed by Norden E.Huang and Zhaohua Wu, respectively. This method consists of two steps. The first step is to decompose the data according to their intrinsic characteristic scales into a number of intrinsic mode function (IMF) components by applying the empirical mode decomposition or ensemble empirical mode decomposition. In this way, the data are expanded in a basis derived from the data itself. The second step is to calculate the local instantaneous frequency and instantaneous amplitude of the IMF components and construct time-frequency-energy and time-frequency-amplitude distribution. This method has very high resolution in both time domain and frequency domain, can clearly and accurately give the local-instantaneous spectrum. This method can be used to analyze any data, but is of particular relevance with regard to the analysis of amplitude and frequency modulated signals. Therefore we can define nonlinearity and non-stationarity based on data characteristics:intra-wave frequency modulation and inter-wave frequency modulation, which is a sure signal of nonlinearity and non-stationarity.This dissertation is concentrated on the advanced local-instantaneous spectrum analysis method based on EMD/EEMD and its application on the local-instantaneous spectrum analysis of vehicle-track coupling system, and includes the following research contents:(1) Introduce the latest development on the field of EMD/EEMD method and the responding local-instantaneous spectrum theory, including the decomposition process of EMD/EEMD, the definition and the meaning of intrinsic mode function (IMF), methods for computing the instantaneous frequency (IF) and the responding local-instantaneous spectrum, the filtering properties of the empirical mode decomposition, the confidence limit for the EMD/EEMD, and the physical and mathematical understanding of EMD/EEMD. Propose a criterion for distinguishing noise components from signal components based on the insight gleaned from recent studies of the statistical properties of white noise. Discuss the condition and criterion for EMD decomposition of two synthetic harmonics ranging from one to five orders, study the influence of the number of siftings on the decomposition results, and propose an extrema criterion for EMD decomposition of two synthetic harmonics. Propose a method to eliminate local strong disturbance from signal by applying the linear interpolation EMD method.(2) Introduce the basic characteristics and mathematical model of time varying nonlinear and non-stationary dynamic system; compares traditional spectrum methods with local-instantaneous spectrum method in dealing with nonlinear and non-stationary dynamic response. Based on local-instantaneous spectrum method, define the index and degree of nonlinearity and non-stationarity. The validity is confirmed by numerical examples.(3) Build a typical high speed vehicle-track coupling system model; introduce the local-instantaneous spectrum method and the proposed method for quantifying nonlinearity and non-stationarity into the dynamic response analysis of vehicle-track coupling system. Study the influences of typical wheels and rails irregularity on local-instantaneous spectrum and degree of nonlinearity and non-stationarity, including out-of-round wheels, harmonic track irregularity, rails corrugation, yaw damper failure, etc. Two complicated cases, the combined irregularity of wheels out-of-roundness and track harmonic irregularity and the combined irregularity of wheels out-of-roundness and high speed low disturbance random track irregularity, are also studied.(4) Study the change of running performance (including wheels wear, running stability, and comfortable index) of typical high speed train in a period of vehicle maintenance. Study the local-instantaneous spectrum, the degree of nonlinearity and non-stationarity of vehicle vibration after different running distance. The effects of wheels profile reshaping on the local-instantaneous spectrum, the degree of nonlinearity and non-stationarity of vehicle vibration are also learned. Finally, use an example to demonstrate the efficiency and usefulness of the proposed linear interpolation EMD method in eliminating local strong disturbance from signal.