## 3 Proposed Method  
### Sensitive IMF Selection  
According to the principles of EEMD, a series of IMFs can be obtained when using it to deal with the complex signal. Simultaneously, the so-called useful information regarding mechanical faults is assigned to various IMF components. Therefore, how to select the sensitive decomposed composition is important for constructing a precise fault diagnosis method. Up to now, two common ways have been kurtosis analysis [40] and correlation analysis [41]. For the former, the first IMF has the biggest kurtosis because of the interference of noise and the high frequency component. For the latter, only the correlations of IMFs between observational vibration signal of are use, but the correlations of IMFs between the vibration signal of normal are not considered. Here, we combine above two types of correlations to select sensitive IMFs, and the main steps are shown below.  
(1) Set \(x_{nor}(t)\) and \(x(t)\) as the vibration signals of normal bearing and investigated bearing conditions, respectively. Then, compute the correlation coefficient of the \(i\)th IMF and \(x(t)\) by  
\[r_{c_{i},x}=|\frac{\sum_{t=1}^{n}(x(t)-\overline{x})(c_{i}(t)-\overline{c_{i}}) }{\sigma_{c_{i}}\sigma_{x}}|, \tag{12}\]  
where \(c_{i}(t)\) is the \(i\)th decomposed IMF of EEMD; \(\sigma_{c_{i}}\) and \(\sigma_{x}\) are the deviations of \(c_{i}(t)\) and \(x(t)\), respectively; \(\overline{c}_{i}(t)\) and \(\overline{x}(t)\) are the means of \(c_{i}(t)\) and \(x(t)\).  
(2) Compute the correlation coefficient (\(r_{c_{i},x_{nor}}\)) between the vibration signal under normal conditions and the \(i\)th IMF with Equation (12).  
(3) Calculate the ratio between \(r_{c_{i},x}\) and \(r_{c_{i},x_{nor}}\) using  
\[\gamma_{i}=r_{c_{i},x}\frac{r_{c_{i},x}}{r_{c_{i},x_{nor}}}, \tag{13}\]  
where \(\gamma_{i}\) is defined as the correlation coefficient ratio factor (CCRF) that is used to select sensitive IMFs.  
(4) Rank these CCRF values as a new sequence from biggest to smallest, i.e., \(\lambda_{1}\geq\lambda_{2}\geq\cdots\geq\lambda_{M}\), and \(M\) represents the total number of CCRFs.  
(5) Select \(K\) IMFs with the larger CCRF values and assign the weight, \(w_{k}\), to the \(k\)th selected sensitive IMF. Then, a new reconstructed signal is obtained by \[\begin{cases}x_{new}(t)=\sum_{k=1}^{K}w_{k}c_{k}(t)\\ w_{k}=\frac{\gamma_{k}}{\sum_{k=1}^{K}\gamma_{k}}\end{cases}. \tag{14}\]  
The two correlation coefficients calculated in steps (1) and (2) reflect the correlation degrees of these decomposed IMFs with their original vibration signals \(x(t)\) and \(x_{nor}(t)\). In accordance with the similarity theory, \(r_{c_{i},x}\) and \(r_{c_{i},x_{nor}}\) are between zero and one. If the correlation coefficient is equal to zero, these two signals are completely uncorrelated. If the correlation coefficient is equal to one, these two signals are completely correlated. That is, the larger \(r_{c_{i},x}\) is, the more related the \(i\)th IMF and \(x(t)\) will be; the smaller \(r_{c_{i},x_{nor}}\) is, the less related the \(i\)th IMF and \(x_{nor}(t)\) will be. From Equation (13), it can be observed that \(\gamma_{i}\) considers not only the value of \(r_{c_{i},x}\) but also the ratios of \(r_{c_{i},x}\) and \(r_{c_{i},x_{nor}}\). Therefore, we can select the components with the greatest CCRF values as the sensitive IMFs. In this paper, three sensitive IMFs were obtained for further feature extraction analysis.