Unbalance, fatigue crack and rotor-stator rub are the three common and important faults in a rotor-bearing system. They are originally interconnected each other, and their vibration behaviors do often show strong nonlinear and transient characteristic, especially when more than one of them coexist in the system. This article is aimed to study the vibration response of the rotor system in presence of multiple rotor faults such as unbalance, crack, and rotor-stator rub, using local mean decomposition-based time-frequency representation. Equations of motion of the multi-faulted Jeffcott rotor, including unbalance, crack, and rub, are presented. By solving the motion equations, steady-state vibration response is obtained in presence of multiple rotor faults. As a comparison, Hilbert-Huang transformation, based on empirical mode decomposition, is also applied to analyze the multi-faults data. By the study some diagnostic recommendations are derived.
A class of methods is presented for wholly estimating direction of arrival (DOA) of convolutively mixed sources in the frequency domain, which is based on independent component analysis (ICA). Convolutive mixtures of multiple sources in the spatio-temporal domain are firstly reduced to instantaneous mixtures by using the well-known short-time Fourier transformation (STFT) technique. From the time-frequency mixture in each frequency bin, one frequency respond matrix of the mixing system from sources to sensors is identified by some instantaneous ICA algorithms. Furthermore, DOAs of the multiple sources is estimated by using a whole estimating strategy. Consequently, all mixtures in total frequency bins contribute to a final estimation set, in which the source directions are shown as several direction clusters and/or local maxima. Experimental results indicate that the ICA based methods have some advantages over the well-known MUSIC (MUltiple SIgnal Classification) method not only on estimation precision of multiple source directions, but also on potential applicability under some especial conditions.
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