# An Improved ABC Algorithm and Its Application in Bearing Fault Diagnosis with EEMD
## 1 Introduction
For example, in literature [13; 14], the added white noise was calculated by the high frequency component after EMD decomposition of the original signal, but often due to noise effects and mode mixing, the first IMF cannot accurately reflect the high frequency information. In literature [15], the method of literature [13] was improved by introducing white noise to suppress low-frequency signals and get accurate extraction of high-frequency information. In literature [16], the parameters of the EEMD were determined using signal-to-noise (SNR). In literature [17], the singular value difference spectrum theory is used to extract the composite signal \begin{table}
\begin{tabular}{c c c} \hline \hline
**Methods** & **Advantages** & **Shortcomings** \\ \hline \multirow{6}{*}{Wavelet Transform} & It has the characteristics of time domain & The limited length of the wavelet basis function \\  & localization and multi resolution. & leads to the energy leakage, which makes the \\  & The analysis precision can be adjusted, & quantitative analysis of the \\  & so that it can accurately locate the short & energy-frequency-time distribution become \\  & time high frequency and the low frequency & difficult; It does not have adaptive ability, once \\  & component of the signal. & the basic wavelet is selected, it must be used to \\ \hline \multirow{2}{*}{Wavelet Packet Transform} & It can decompose not only the low & \multirow{2}{*}{The wavelet packet energy, the time-frequency} \\  & frequency portion of the signal, but also the & information are not intuitive. \\  & high frequency part of the signal, with no & \\  & redundancy, nor omissions. & \\ \hline \multirow{6}{*}{Wiger–Ville} & It belongs to bilinear time frequency & \multirow{2}{*}{Energy density is not guaranteed to be non \\  & distribution and has many excellent & negative in all time and frequency ranges, \\  & characteristics, such as high time frequency & and serious cross term interference exists. \\  & resolution, energy concentration and time & \\  & frequency edge characteristics. & \\ \hline \multirow{6}{*}{EMD} & It is especially suitable to analyze nonlinear & \multirow{2}{*}{The end effect problem, the mode mixing} \\  & and non-stationary signal. It breaks through & \\ \cline{1-1}  & the limitation of the Fourier transform, not & \\ \cline{1-1}  & only has the characteristics of self & \multirow{2}{*}{problem exist.} \\ \cline{1-1}  & adaptation, orthogonality and & \\ \cline{1-1}  & completeness, but also has the & \\ \cline{1-1}  & advantages of high efficiency. & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of different time-frequency domain methods. composed of the impact signal and the noise signal, and the probability distribution of the normal distribution function is used to determine the standard deviation of the white noise. In literature [18], white noise with different amplitudes were selected in the interval to perform EEMD decomposition, \(e_{1}\) that minimize the standard deviation of the longitudinal and lateral distributions of the maximum value and \(e_{2}\) that minimize the standard deviation of the longitudinal and the lateral distribution of the minimum value are averaged to get the best \(e\). Based on the predecessors, this paper proposes a new idea of using an improved ABC optimization method to select the EEMD parameter \(e\), which reduces the blindness of selecting \(e\) when extracting the fault features and improves the applicability of EEMD. The experimental example shows the superiority of the proposed algorithm.