## 3 Results
### Numerical Simulation
The orthogonality index is defined as:  
\[OI=Average\frac{\left|\langle\text{mod}_{n}(t),\text{mod}_{w}(t)\rangle\right| }{\left\|\text{mod}_{n}(t)\right\|_{2}\left\|\text{mod}_{w}(t)\right\|_{2}},n \
eq w, \tag{39}\]  
where \(\text{mod}_{n}(t)\) represents the \(i\)-th mode component that is decomposed. The root mean square error (RMSE) is the square root of the ratio of the sum of squares of the deviation between the observed value and the true value to the number of observations m. It is used to measure the deviation between observed values and true values and judge the standard error between the decomposed signal and the original signal; also, it is used to represent dependency or decoupling. The run time parameter can be  
Figure 3: Comparison chart of the decomposition results of three methods: Complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), improved complete ensemble intrinsic time-scale with adaptive noise (ICEITDAN), and intrinsic time decomposition (ITD). (**a**) CEEMDAN, (**b**) ICEITDAN, and (**c**) ITD. used to judge arithmetic efficiency. Therefore, the closer these three indicators are to 0, the higher their performance in signal processing. According to Table 1, the root mean square error and orthogonality index are the smallest and the closest to zero for the method that is proposed in this paper. In terms of run time, the method that is proposed in this paper requires less time than CEEMDAN but more than ITD. However, in contrast to the other two parameters and the signal reconstruction error of the ITD algorithm, the method that is proposed in this paper has a longer run time, but a higher precision. During practical use, the efficiency of the calculation will not be affected. The reason for the shorter computing time of ITD compared with the CEEMDAN method is that the core of the CEEMDAN method is the EMD algorithm. Compared with the EMD method, the ITD method avoids laborious and inefficient screening and spline interpolation processes and can decompose the original signal into A series of rotating components with a reliable instantaneous frequency and amplitude and residual monotonic trend signals, so the ITD method has the advantage of high computational efficiency. At the same time, the CEEMDAN method adds a group of white noise to the EMD method for decomposition. The CEEMDAN method calculates that the time was further extended. Compared with the ICEITDAN method, the ITD method performs a process of adding white noise in groups to improve the modal aliasing. Therefore, the ICEITDAN operation time is extended. Therefore, the method that is proposed in this paper is more suitable for practical engineering applications according to this comprehensive evaluation. In addition, according to the reconstruction error in Figure 4, the reconstruction error of the method that is proposed in this paper is the smallest among those of the three methods, and the peak value is less than \(8\times 10^{-16}\), which can be regarded as the calculation error of the computer. Since signal decomposition is only used for noise reduction before fault feature extraction, it is necessary to select pattern components in the decomposition results for the extraction of the fault feature frequency. Kurtosis is a time domain parameter that is sensitive to faults, but kurtosis index pulse faults are sensitive, especially early faults, but not stable. Due to the use of the kurtosis as the component of the selected sensitive mode, it was found through the experiment that there was a deviation in the selected sensitive mode because non-Gaussian noise and a low signal-to-noise ratio more strongly influence the time domain kurtosis. With the objective of solving the problems of the signal selection and identification of fault-related sensitive mode components after processing, [PERSON] and [PERSON] (2019) proposed an improved standard that was based on the periodic modulation intensity (PMI) that was proposed by [PERSON] and [PERSON] (2019).