Abstract
Abnormal vibration signals of tramcar are mostly nonstationary and nonlinear signals. This study applied the Hilbert–Huang transform (HHT) to analyze abnormal vibration of the tramcar, aiming to overcome the limitations of some traditional time-frequency analysis methods, such as Fourier transform, in dealing with nonstationary and nonlinear signals. Additionally, to address mode aliasing produced during empirical mode decomposition (EMD) used in classical HHT, this study proposed to first use complete EMD with adaptive noise for the decomposition of original vibration data, then eliminate the trend-term components with the calculated correlation coefficients, and finally perform denoising on high-frequency noisy components using the wavelet threshold method. After weighted reconstruction using denoised high-frequency components and low-frequency information components, data processing was finally optimized via HHT. Taking a tramcar as an example, the Hilbert spectra of the vertical acceleration of axle box were plotted via HHT, and the time-instantaneous, frequency-instantaneous energy 3D relations were obtained for the location of impact points. Further, the vibration characteristics were analyzed and quality indexes were calculated in combination with the marginal spectra so as to judge the reasons for abnormal vibration and failure modes of the tramcar. The results revealed that the proposed method was feasible and effective in vibration feature extraction and vibration impact analysis for tramcars.
Highlights
Aiming at the problems of mode aliasing in the EMD method used in the classical Hilbert–Huang transform (HHT), this article proposes to decompose the original vibration data using the fully adaptive noise set empirical mode decomposition (CEEMDAN), eliminate the trend-term component by the correlation coefficient method, and denoise the high-frequency noisy component using the wavelet threshold method and weighted reconstruction of the highfrequency component and low-frequency information component after denoising, the optimization process of Hilbert Huang transform is carried out
Taking a tram as the research object, the Hilbert spectrum of axle box vertical acceleration is obtained through HHT, the corresponding relationship of time-instantaneous frequency-instantaneous energy is obtained, and the impact point is located
Based on the local characteristic time scale of signal, HHT decomposed complex signals into limited intrinsic mode function (IMF) components and performed feature extraction on various IMF components of the tramcar vibration signal, which could effectively identify both trend and state of abnormal vibrations, thereby laying a foundation for the identification of tramcar failure modes. e impact on the operating tramcar induced the corresponding inherent frequencies, which could lead to the change in the distribution of the instantaneous energy with instantaneous frequency
Summary
Traditional time-frequency methods mainly adopted the kurtosis value, mean square value, effective value, probability density function, and wavelet analysis to judge abnormal vibration. Both the kurtosis value and the effective value could show the position and degree of the impact points in time domain but could not reflect the characteristic frequencies of the excited abnormal vibration. After adding the positive and negative auxiliary white noises in pairs to the original signal x(t), EMD decomposition was performed on the novel signal so as to derive the first-order IMF component c1(t). K 1 where ci denotes each IMF component after decomposition and includes different components from high- to low-frequency bands and rk(t) denotes the residual signal
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