# An Improved ABC Algorithm and Its Application in Bearing Fault Diagnosis with EEMD
## 1 Introduction  
A bearing is an essential part in a rotating machine, which can be easily damaged. At present, the scholars' research on bearing fault diagnosis can be roughly divided into the following: signal analysis based on vibration [1; 2; 3; 4], monitoring based on temperature [5], and analysis based on acoustic emission [6; 7], etc. Among them, the analysis based on vibration signal is the main method for bearing fault diagnosis. In the processing of vibration signals, the commonly used methods are time domain, frequency domain, and time-frequency domain diagnostic methods [8]. The time domain method extracts the time domain characteristics by calculating the time domain parameters of the vibration signal. This method can directly reflect the characteristic information, and the calculation is simple [9]. It can make a preliminary diagnosis on whether the equipment fails, but the fault type and fault location cannot be determined. And a specific judgment on the severity of the failure also cannot be made. The frequency domain diagnosis method analyzes the fault by identifying the difference in the frequency characteristics of the vibration signal between the fault and the normal state. It is based on the theory of Fourier transform [10], which is a global transformation, and unable to perform local analysis for non-stationary and nonlinear signals, moreover it is a pure frequency domain analysis method. There is no resolution in the time domain. Therefore, the frequency domain diagnosis method based on Fourier transform has certain limitations. The time-frequency domain diagnosis method combines the time domain and the frequency domain in two dimensions, so that the signal can be localized simultaneously in the time-frequency domain, which better reflects the local characteristics of the vibration signal [9]. The time-frequency domain diagnosis methods mainly include wavelettransform, wavelet packet transform, Wigner-Vile distribution and empirical mode decomposition (EMD); etc. Their advantages and disadvantages are shown in Table 1[11]. In Table 1, EMD is a non-stationary signal processing method proposed by [PERSON] et al., which can adaptively decompose the local time-varying signals into several intrinsic mode functions (IMF), and reduce the coupling information between signals [7]. Using EMD method to decompose the signal can accurately and effectively grasp the characteristic information of the original data, which is very beneficial to the deeper information mining. However, EMD also has inherent shortcomings, such as endpoint effect problems, mode mixing problems, and decomposition limitations. Therefore, many improved algorithms have been proposed. Ensemble Empirical Mode Decomposition (EEMD) is a major improvement on EMD, which solves the mode mixing problems of EMD [12]. In EEMD algorithm, the Gaussian white noise amplitude coefficient \(e\) and the number of EMD decomposition times \(N\) should be selected. After adding Gaussian white noise to the original signal \(x(t)\), and then starting the EMD decomposition for \(N\) times. Average the corresponding EMD decomposition results to get the final IMF [12]. Although EEMD algorithm has achieved good results in improving the mode mixing phenomenon, there are still some shortcomings to be solved. The most serious problem lies in the key parameters setting of the EEMD algorithm, the Gaussian white noise amplitude coefficient \(e\) need to be adjusted by experience, and cannot be adaptively gotten according to the characteristics of the signal. Therefore, the processing effect of this method is inevitable different for different signals. The existence of this problem seriously affects the versatility and scope of the EEMD application. In order to solve the problems of the EEMD method, a large number of researchers have contributed to the selection of the parameters.