# An Improved Empirical Wavelet Transform and Its Applications in Rolling Bearing Fault Diagnosis
## 1 Introduction
On the one hand, using multiple signal classification to calculate the spectrum of signals can reduce noise; on the other hand, it can amplify useful information while weakening the irrelevant information, so as to facilitate the division. In Reference [28], the natural frequencies are used as useful frequencies to calculate the support boundaries and decompose the signal into multiple components; kurtosis is used to automatically filter defect-related components and envelopes to extract characteristic frequency. However, the above three methods have certain limitations: the noise interference is very obvious when calculating the signal spectrum, and how to distinguish the strong noise from the signal needs to be further explored. Calculating the cutoff frequency and initializing the boundary with the type of fault needs to be performed; the final boundaries are determined by an iterative backward forward search algorithm, and MFMindex-aided adaptive Fourier spectrum segmentation is realized [29]. The multilevel EWT method proposed by [PERSON] [30] simplifies the rules for splitting the spectrum. A multilevel boundary array is constructed based on the rotational frequency, outer race fault characteristic frequency, inner race fault characteristic frequency, roller fault characteristic frequency, and cage fault characteristic frequency and used for filtering and reconstruction. This method provides a complete framework for splitting the spectrum without depending on the characteristics of the spectrum. However, because of the difference between roller fault and inner ring fault characteristic frequencies, the decomposition level will be different. Self-adaptability is improved, while computing time is wasted. More invalid modes are extracted from each level. Therefore, optimizing the core of the EWT algorithm--segmentation of the spectrum--has become the focus of this research. In this paper, a fast empirical wavelet transform is proposed. Based on the waveform characteristics of the spectrum, the problem of spectrum segmentation in EWT is improved. The trend of the spectrum is reconstructed from the Fourier function of the spectrum, and the minimum points of the trend are calculated as the boundaries. Different frequency components in the key function can reconstruct different trend components. By comparing the success rate and error rate of separation, it is proved that the boundaries of the fast empirical wavelet transform (FEWT)method are more reasonable. The experimental results show that the method is effective in the analysis of rolling bearing fault diagnosis. The method of dividing boundaries based on the Fourier transform function of the spectrum is not only fast but also self-adaptive, and can be effectively applied to online fault diagnosis systems. The structure of this paper is as follows: Section 2 briefly introduces EWT and its shortcomings; Section 3 elaborates the proposed FEWT method in detail and introduces the trend estimation method based on key function and threshold denoising; Section 4 uses three kinds of simulation signals to prove that the trend estimation method can obtain more reasonable boundariesand extract useful information effectively; and Section 5 combines kurtosis and fast kurtogram to verify the validity of the method through the fault of outer and inner rings of rolling bearings.