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The rolling bearing and gear fault features are generally shown as modulation characteristics of their vibration signals. The empirical envelope (EE) method is an accordingly common demodulation method. However, the EE method has the defects of over- and undershoot, which may lead to demodulation error. According to this, an envelope optimization algorithm -- empirical optimal envelope (EOE) is introduced into the EE method, and an improved empirical envelope (IEE) method is obtained to calculate the instantaneous amplitude and instantaneous frequency of mono-component modulation signal. Furthermore, aiming at the actual measured mechanical vibration signal has multi-component modulation feature, the IEE method is combined with an adaptive signal decomposition method -- local oscillatory characteristic decomposition (LOD) proposed by the author, thereby a new multi-component signal demodulation method based on LOD and IEE is proposed. The proposed method is compared with Hilbert transform (HT) and Teager energy operator (TEO) demodulation methods by the simulation signal and actual measured mechanical vibration signal. The results show that the demodulation effects including edge effects, negative frequency, over- and undershoot of the proposed method are significantly improved and can extract the rolling bearing and gear fault feature information clearly.

Under variable working conditions, the components of gear fault vibration signals had complex time-frequency characteristics that crossing multiple time scales or overlapping time-frequency domains. The traditional decomposition method could not decompose this kind of signals based on local time-scale characteristics. A new MMD method was introduced. The MMD method innovatively regarded the mono-component signals as a linear combination of eigenvectors with different weight coefficients. By iteratively optimizing the weight coefficients, the corresponding component signals were obtained. The problems that large amount of data reduced the decomposition efficiency when MMD analyzed the actual vibration signals with high sampling rate was solved. And the MMD method was applied to analyse gear fault vibration signals under variable rotating speed working conditions.The results show that the method may effectively decompose to the overlapping fault component signals in time-frequency domain, and has obvious advantages compare to the traditional method based on time-scale characteristics.Combined with order analysis, the gear fault feature information may be extracted clearly and accurately. [ABSTRACT FROM AUTHOR]