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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.