Faults in rolling element bearings often cause the breakdown of rotating machinery. Not only the fault type identification but also the fault severity assessment is important. So this paper emphasizes the fault severity assessment. The method proposed in this paper contains two steps: first, identify the fault type based on the combination of empirical mode decomposition (EMD) and fast kurtogram; Second, assess the fault severity. In the first step, the original signal is firstly decomposed

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... some intrinsic mode functions (IMFs) and the representative IMFs are selected based on correlation analysis, and then the reconstruction signal (RS) is generated; Secondly, the fast kurtogram method is applied to the RS, and the optimum band width and center frequency is obtained. The fault type can be identified based on the fault characteristic frequency marked in the envelope demodulation spectrum. In the second step, the energy percentage of the most fault-related IMF is chosen as an indicator of the fault severity assessment. Experimental data of rolling element bearings inner raceway fault (IRF) with three severities at four running speeds were analyzed. The results show that the IRF identification and fault severity assessment is realized. The breakthrough attempt provides the great potential in the application of condition monitoring of bearings. 3669 resonance demodulation to diagnose the fault of rolling element bearings in the 1970s. The SPM Company later developed an instrument to detect rolling element bearings faults based on the measurement of resonant responses of an accelerometer excited by the faults [8] . However, the effectiveness of this method depends on how well the vibration signal is pre-processed, and what de-noising method is adopted. On the one hand, it is usually difficult to gain a clear envelope spectrum when the background noise can't be properly separated from the original signal. On the other hand, the resonance frequency, chosen as center frequency, is not always optimal [9]. With the tireless efforts of many researchers, many advanced signal processing techniques were introduced to deal with such impacting signals in the past few decades. These include, wavelet transform [10, 11] , multiwavelet [12], empirical mode decomposition (EMD) [13] [14] [15] [16] , Hilbert-Huang transform (HHT) [17] , and Local mean decomposition [18, 19] . Thanks to the advantages of these, such as high capability of nonlinearity identifications, high immunity to additive Gaussian noise, spectral kurtosis (SK) was developed. Antoni and Randall made a significant promotion to SK technique [20] [21] [22] . In particular, Antoni [23] proposed a fast algorithm for computing the kurtogram and provided a good application in rolling element bearings faults diagnosis. This was achieved by providing the optimal center frequency and band width. However, high frequency noises may not be separated correctly or some important information may be left out [24] , especially when the fault is relatively serious. Therefore, it is necessary to adopt effective methods to improve the signal-to-noise ratio (SNR) before using SK. EMD proposed by Huang et al [25] can decompose a signal into a sum of intrinsic mode functions (IMFs) which reflect the local characteristic of the signal. The frequency band for each IMF ranges from high to low and changes with the original signal itself. The characteristic information of the original signal can be extracted more accurately and effectively based on each IMF, which will contribute to a high SNR. However, many researchers focus on fault type instead of fault severity when using EMD method. So this paper attempts to assess the fault severity by EMD after identifying the fault type. According to the discussions above, in this paper, a new method combining EMD and Fast Kurtogram is applied to rolling element bearings inner raceway fault diagnosis. Firstly, the raw acceleration vibration signal measured from detective bearings is decomposed by EMD and some IMF components are obtained. Secondly, the representative IMFs containing fault information are selected based on the correlation analysis, and the reconstruction signal (RS) is generated by the addition of the representative IMFs. Thirdly, the optimum bandwidth and center frequency of the RS is provided by Fast Kurtogram. The fault characteristic frequency is then marked in the envelope spectrum and the fault type is identified. Finally, the energy percentage of the most fault-related IMF from the representative IMFs is chosen as the indicator for fault severity assessment. Experimental data of rolling element bearings inner raceway fault (IRF) with three severities at four running speeds were analyzed. The results showed that the diagnosis approach combining EMD and Fast Kurtogram had good effectiveness in IRF identification and severity assessment. The paper is organized as follows. Section 2 is dedicated to the related work, including the brief introduction of EMD and its numerical simulation; the correlation analysis; the IMF energy percentage; and the definition and algorithm of Fast Kurtogram method. In Section 3, the fault signatures of rolling element bearings are introduced. In Section 4, the experimental rigs and data records are described. In Section 5, the fault diagnosis method for rolling element bearings based on EMD and Fast Kurtogram is proposed. Section 6 gives the application of the proposed method. Finally, the conclusions of this paper are given in Section 7. Yonggang Xu received Ph.D. degree in Mechanical Engineering from Xi'an Jiaotong University, Xi'an, Shanxi, China, in 2003. Now he is an Associate Professor at Beijing University of Technology. His current research interests include condition monitoring and fault diagnosis of large-scale electro-mechanical equipment, modern signals processing, and artificial intelligence.