## 6 Conclusions  
In order to diagnose the fault of the rolling element bearings in strong noise conditions, the spectrum segmentation strategy of EWT is improved and a novel fault feature extraction and enhancement method is proposed by the combination of MCKD and EWT. The non-impact components are de-noised by MCKD at first, and then the signal is decomposed by improved EWT. Both simulations and experiments are performed to validate the effectiveness of the proposed method by comparison with the FK and OWPT methods. Several useful conclusions are listed as follows.  
Firstly, the improved EWT can adaptively segment the spectrum of the rolling element bearing in strong noise conditions. The modes number and frequency boundaries of each EWT mode can be easily determined, while the conventional EWT cannot segment the Fourier spectrum properly. In the proposed method, the influence induced by the single accidental impact and non-impact components is restrained after the de-noising process by the MCKD method, and then reasonable signal components can be obtained with the improved EWT method. This method can easily diagnose faults by choosing the best component with maximum kurtosis values and analyzing this signal component in the squared envelope spectrum and teager energy spectrum.  
Secondly, compared with the FK and OWPT methods, the MCKD-EWT method is more effective in weak fault feature extraction and enhancement. When the fault is large enough, FK, OPWT, and MCKD-EWT methods can find the resonant frequency band and realize fault diagnosis. However, when the fault is small, FK and OWPT methods cannot find the resonant frequency band and result in a failure of fault diagnosis, while the MCKD-EWT method can realize the fault diagnosis by combining the advantages of MCKD and EWT. Therefore, the MCKD-EWT procedure is more powerful in engineering applications.  
However, the detailed parameters of the MCKD-EWT procedure in this paper may not always be the best choice for the special bearing fault signal. When there is a large rotational speed fluctuation, the proposed method may be useless because the MCKD method needs to ensure the periodicity of the spacing of the pulses. The cost time of building the filters banks is too long, so it cannot be used in on-line fault diagnosis. Further investigation should be performed on choosing the optimal parameters of MCKD-EWT and finding an enhanced method for rotational speed fluctuations condition and finding a faster method.  
[PERSON] and [PERSON] conceived and designed the experiments. [PERSON], [PERSON] and [PERSON] performed the experiments. [PERSON] and [PERSON] analyzed the data; [PERSON] and [PERSON] provided guidance and recommendations for research. [PERSON] contributed to the contents and writing of the manuscript. All authors have read and approved the final manuscript.  
Funding was provided by the National Natural Science Foundation of China (Grant Nos. 51075224 and 51505486), Tsinghua University Initiative Scientific Research Program under Grant no. 2011Z08137, the State Key Laboratory of Tribology Initiative Research Program under Grant no. SKLT11A02, Shaanxi Natural Science Foundation under Grant no.2016 JQ5009, and Young Talent fund of University Association for Science and Technology in Shaanxi under Grant no. 20170511.  
The authors would like to gratefully acknowledge the Natural Science Foundation of China under Grant no.51075224 and 51505486, Tsinghua University Initiative Scientific Research Program under Grant no. 2011Z08137, the State Key Laboratory of Tribology Initiative Research Program under Grant no. SKLT11A02, Shaanxi Natural Science Foundation under Grant no.2016 JQ5009, Young Talent fund of University Association for Science and Technology in Shaanxi under Grant no. 20170511, and the Machine Fault Diagnostics Laboratory at Tsinghua University for their support. Finally, the authors would like to thank the editors and reviewers for their valuable comments and constructive suggestions.  
The authors declare no conflict of interest.