## 2 The Proposed Method  
### Original Features Extraction  
Data preprocessing, such as moving out the abnormal data form the original signal dataset, is an essential procedure before feature extraction, and more precise outcomes require more meticulous preprocessing. Since the original signal doped with a lot of messy interference information is unsuitable for analyzing directly, it is a good choice to extract the features of the signal data for further analysis. To retain the original useful information as much as possible, both classical and contemporary methods for feature extraction were employed in this paper.  
Time and frequency domain feature analysis is one of the dominant ways for state evaluation and fault diagnosis of mechanical equipment. Among which, time domain signal possessing the characteristics of containing large information, intuitive and easy to understand is the original basis for health evaluation and diagnosis of machines. The frequency domain characteristic parameters describe signal through the change of frequency band in signal spectrum and the dispersion of spectrum energy. Accompanied by the occurrences and developments of rotating machinery's faults, the frequency components of vibration signal would change as well, hence the running status of the equipment can be evaluated according to the composition and size of these frequency components.  
In this paper, 11 characteristic parameters in time domain and 13 characteristic parameters in time domain are adopted, which are displayed in Tables 1 and 2, respectively. In our research, these features are the most effective and the most widely used signal features.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Features** & **Names** & **Equations** & **Features** & **Names** & **Equations** \\ \hline \(p_{1}\) & Mean & \(\frac{\sum_{n=1}^{N}x(n)}{N}\) & \(p_{2}\) & Kurtosis index & \(\frac{1}{N}\sum_{i=1}^{N-1}(x(n)-p_{1})\) \\ \(p_{2}\) & variance & \(\sqrt{\frac{\sum_{n=1}^{N}\left(\frac{1}{N}(x(n)-p_{1})\right)^{2}}{N-1}}\) & \(p_{8}\) & Peak factor & \(\frac{1}{N}\sum_{i=1}^{N-1}(x(n)-p_{1})\) \\ \(p_{3}\) & Square root amplitude & \(\left(\frac{\sum_{n=1}^{N}\sqrt{\frac{1}{N}(n)}}{N}\right)\) & \(p_{9}\) & Margin indicator & \(\frac{p_{9}}{P4}\) \\ \(p_{4}\) & Valid value & \(\sqrt{\frac{\sum_{n=1}^{N}\left(\frac{1}{N}(\frac{1}{N})\right)^{2}}{N}}\) & \(p_{10}\) & Waveform indicator & \(\frac{p_{9}}{P3}\) \\ \(p_{5}\) & Peak & \(\max\left|x(n)\right|\) & \(p_{11}\) & Pulse indicator & \(\frac{p_{5}}{N}\sum_{i=1}^{N}\left|x(n)\right|\) \\ \(p_{6}\) & Skewness index & \(\frac{1}{N}\sum_{i=1}^{N}\left(\frac{1}{N}\right)\) & & \\ \hline \end{tabular} Note: \(x(n)\) is the sequence of time domain signal, \(n=1,2,\ldots,N\), \(N\) is the total number of samples.  
\end{table}
Table 1: Features in Time domain.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Features** & **Names** & **Equations** & **Features** & **Names** & **Equations** \\ \hline \(p_{12}\) & Mean,frequency & \(\frac{\sum_{n=1}^{N}s(a)}{A}\) & \(p_{19}\) & None & \(\sqrt{\frac{\sum_{n=1}^{N}f_{n}^{4}s(a)}{\sum_{n=1}^{N}f_{n}^{2}s(a)}}\) \\ \(p_{13}\) & Standard deviation frequency & \(\sqrt{\frac{\sum_{n=1}^{N}\left(s(a)-p_{12}\right)}{A-1}}\) & \(p_{20}\) & None & \(\frac{\sum_{n=1}^{N}f_{n}^{2}s(a)}{\sqrt{\sum_{n=1}^{N}s(a)\sum_{n=1}^{N}f_{n} ^