## 2 Methods
### Signal Feature Extraction  
The Fourier transform can be used within the field of signal processing to not only analyze a signal in the time domain, but also to analyze signal spectrum, thereby allowing more convenient signal feature extraction. However, these features of the Fourier transform are only suitable for stationary signals over the entire time period. This limitation of the Fourier transform prevents it from being used to analyze a signal with local characteristics [27]. The short-time Fourier transform shows clear advantages over the Fourier transform for processing non-stationary signals. The theoretical premise of the short-time Fourier transform method is the construction of a short-time stationary period for non-stationary signals, similar to the windowing theory. However, since the size of the moving window is fixed, the short-time Fourier transform has a fixed resolution for signal analysis, which presents some challenges. The wavelet transform follows the same concept as the short-time Fourier transform and a moving window. However, there are some shortcomings within the application of wavelet theory multi-resolution analysis to high-frequency signal processing. Wavelet packet theory stipulates the construction of orthogonal wavelets based on multi-resolution analysis, which are further decomposed into low-frequency and then high-frequency wavelets. In addition, wavelet packet decomposition technology can be used to screen the decomposed frequency band according to the characteristics of the signal itself. This allows for the selection of the suitable frequency band or an analysis of the original signal, thereby improving the time-frequency resolution [28; 29].  
Figure 1b is the decomposed structure of a three-layer wavelet packet. The wavelet packet decomposition technology further simultaneously decomposed the high-frequency and low-frequency signals when decomposing the second and third layers, instead of only decomposing the low-frequency part. In addition, the frequency band suitable for the signal feature extraction is selected. This improves resolutions of the time and frequency domains of the signal. Since the studied fault signal is often non-stationary, wavelet packet decomposition technology is the most appropriate for analyzing the full frequency band to obtain effective fault feature information.  
Before performing the wavelet packet decomposition, the Daubechies (db3) wavelet packet basis function is used to decompose the degeneration signal of the HSV. The noise proportion in the HSV current signal is small, and there is no need for too many layers of decomposition. Therefore, choosing the three-layer wavelet packet decomposition of the signal can separate the noise on the premise of ensuring the authenticity of the signal reconstruction.  
The total energy of each frequency band signal is extracted and is regarded as a feature vector of state type, as shown in Equations (1) and (2) [30]. After the three-layer  
Figure 1: Scheme of the data-driven prognostic strategy.  
decomposition, the state signal is decomposed into eight different frequency bands, and the feature vector is converted, as shown in Equation (2).  
\[E_{3j}=\sum_{k=1}^{n}\left|x_{jk}\right|^{2} \tag{1}\]  
\[T=\left|E_{30}E_{31}E_{32}\ldots E_{37}\right| \tag{2}\]  
where \(x_{jk}\) (\(j=1\):\(7\), \(k=1\):\(n\)) represents the amplitude of the discrete point of the reconstructed signal.