Rotating machines have been widely used in industrial engineering. The fault diagnosis of rotating machines plays a vital important role to reduce the catastrophic failures and heavy economic loss. However, the measured vibration signal of rotating machinery often represents non-linear and non-stationary characteristics, resulting in difficulty in the fault feature extraction. As a statistical measure, entropy can quantify the complexity and detect dynamic change through taking into account non-linear behavior of time series. Therefore, entropy can be served as a promising tool to extract the dynamic characteristics of rotating machines. Recently, many studies have applied entropy in fault diagnosis of rotating machinery. This paper aims to investigate the applications of entropy for the fault characteristics extraction of rotating machines. First, various entropy methods are briefly introduced. Its foundation, application and some improvements are described and discussed. The review is divided into eight parts: Shannon entropy, Rényi entropy, approximate entropy, sample entropy, fuzzy entropy, permutation entropy, and other entropy methods. In each part, we will review the applications using the original entropy method and the improved entropy methods, respectively. In the end, a summary and some research prospects are given.

This paper presents a novel signal processing scheme, bandwidth empirical mode decomposition, and adaptive multiscale morphological analysis (BEMD-AMMA) for early fault diagnosis of rolling bearings. In this scheme, we propose a bandwidth based method to select the best envelope interpolation method. First, multiple envelope algorithms are defined and separately subtracted from the original data to obtain the preintrinsic mode functions (PIMFs). Second, an IMF with the smallest frequency bandwidth is selected to be the optimal IMF (OIMF). Third, this OIMF is subtracted from the original signal, and then repeat the sifting process until the residual is a constant or monotonic. Since the OIMF has the smallest frequency bandwidth, the mode mixing phenomenon can be significantly weakened. After that the OIMFs with clear fault information are used to construct the main component of the original signal. Then, the AMMA is introduced to demodulate the constructed main component. Simulation and experimental vibration signals are employed to evaluate the effectiveness of the proposed method. Results show that the proposed method outperforms EMD-AMMA, ensemble empirical mode decomposition-AMMA, and generalized empirical mode decomposition-empirical envelope demodulation in detecting early inner race fault.