# Rolling Bearing Incipient Fault Detection Based on a Multi-Resolution Singular Value Decomposition
## 6 Conclusions  
In this study, a new technique based on MRSVD has been developed for the initial fault detection of a rolling bearing. With this method, the raw bearing vibration signal acquired at the incipient failure stage, which contains the background noise, the harmonic interference, and the periodic impulse characteristics, can be decomposed to a series of approximate signals and detailed signals with different resolutions. Thus, the background noise, the harmonic interference, and the periodic impulse characteristics will correspond to different signal components. Theoretical and experimental analyses show that the first detail signal is mainly composed of noise and the last approximate signal is mainly  
Figure 12: Time domain waveform and Hilbert envelope demodulation spectrum of the detail signal with the maximum kurtosis value. (**a**) The waveform of the detail signal with the maximum kurtosis value. (**b**) The Hilbert envelope demodulation spectrum of the detail signal with the maximum kurtosis value.  
Figure 13: Time domain waveform of the five detail signals with the maximum kurtosis value and their corresponding Hilbert envelope demodulation spectrum. (**d1–d5**) The five detail signals with maximum kurtosis values obtained using MRSVD decomposition. (**h1–h5**) The corresponding Hilbert envelope demodulation spectrums of the five detail signals in (**d1–d5**).  
composed of harmonic interference. Therefore, the periodic impulse characteristics that are related to the rolling bearing failure can be extracted from the detail signals (in addition to the first detail signal).  
The advantages of the introduced approach include the following: (a) in contrast to the resonant demodulation approaches, this approach extracts the periodic impulse characteristics for demodulation analysis in order to identify the fault without relying on prior knowledge of the fault-excited resonance frequency; (2) this approach is computationally efficient, as except for the singular value decomposition of a two-row matrix, the algorithm only involves addition and subtraction.  
The topic of this research is designed by [PERSON] and [PERSON]; Formal analysis is completed by [PERSON]; The first version of manuscript is prepared by [PERSON]; and this version of the manuscript is read, approved and substantially contributed by all authors.  
This work was supported by the Natural Science Foundation of China (grant no. 51605405, 51975121, 51605406), the Science and Technology Innovation Project of Fujian Province, China (grant no. 2016H2003), the Natural Science Foundation of Fujian Province (grant no. 2018J01531), and the program for Innovative Research Team in Science and Technology at the Fujian Province University. Their support is gratefully acknowledged.  
The authors wish to thank [PERSON] and [PERSON] for their experimental work carried out at the University of Ottawa lab. They also wish to thank the Board member and the reviewer for their valuable suggestions and comments that have helped improve this paper.  
The authors declare no conflict of interest.