# An Improved Empirical Wavelet Transform and Its Applications in Rolling Bearing Fault Diagnosis
## 1 Introduction
This includes removing noise and combining empirical modes by calculating relevant indicators. Empirical modes reduce their own noise through the selection of mutual information; the reconstructed signals are used to combine the ambiguity function and correlation coefficients for ambiguity correlation classification (ACC). Finally, new signals are input into the ACC for testing and training [16]. [PERSON] [18] and [PERSON] [19] calculated the [PERSON]'s correlation coefficient of the envelope spectrum of each empirical mode. By comparing the coefficients of these modes and combining the empirical modes below the standard, a slightly smaller empirical mode can be obtained. This process combines noise modes and reduces the number of empirical modes. [PERSON] [20; 21] calculated root mean square, kurtosis, and skewness of each empirical mode and combined them into feature vectors; kernel density estimation (KDE) and mutual information (MI) are combined to estimate classification feature vectors to diagnose faults. Correlation coefficients among empirical modes are calculated to extract more valuable components; the instantaneous amplitude was extracted by HT and STFT and the damage was characterized [22]. In view of the inconvenience of EWT spectrum segmentation caused by noise, Fourier-Bessel series expansion (FBSE) is mentioned to enhance spectrum and reduce noise; the scale-space method is used to split the FBSE spectrum [23]. This method suppresses the noise to some extent, but does not solve the problems of mode aliasing and invalid components caused by the scale-space method in EWT. Similarly, [PERSON] [24] used the autoregressive power spectrum instead of the Fourier spectrum to divide boundaries; then, the boundaries were computed by the Burg algorithm to correct EWT. This approach also enhances the spectrum and reduces noise, but does not explain how to divide the boundaries in signals containing modulation components. This category adds more work on the premise that EWT takes more time. It takes a lot of time not only to set the initial parameters of EWT, but also to set the merge criteria. This will only make the algorithm more complicated. Although the noise is reduced to some extent, or the number of empirical modes is reduced, it does not change the defect of the EWT method itself. Therefore, it is necessary to improve the algorithm. The second category is optimizing the adaptability of EWT. Due to the disturbance of too many initial parameters, [PERSON] [15] proposed an adaptive parameterless empirical wavelet transform method. This method uses Otsu and K-means to segment the spectrum and establishes a set of adaptive bandpass filters to decompose the signal into mono-components with a compactly supported spectrum. Another adaptive method uses sparsity functions, first prewhitening the signal by using an autoregressive model, then automatically determining Fourier segments to conduct EWT and square envelope analysis [25]. Otsu and K-means methods have poor effects on spectrum segmentation; sparsity guide EWT needs to change parameters according to fault characteristics while optimizing parameters. The third category is optimizing spectrum segmentation. [PERSON] [17; 26] proposed a new method of spectrum segmentation, which uses an order statistical filter (OSF) to estimate the upper envelope function of the spectrum; by selecting the useful flat top in the upper envelope, the boundaries are determined to construct the filter and reconstruct the empirical modes. OSF is very effective in estimating envelope function, but the author did not point out how to get the best envelope function. Therefore, the method is not self-adaptive. [PERSON] [27] used multiple signal classification to calculate the spectrum, which zeroes the part considered as noise and enlarges the part deemed useful.