Table 1.

Mathematical definitions of features.

Feature	Mathematical Definition	Feature	Mathematical Definition
Mean Value (MV)	$\frac{1}{N}{\displaystyle \sum _{i=1}^N}{x}_i$	Standard Deviation (SD)	$\sqrt{\frac{1}{N-1}{\displaystyle \sum _{i=1}^N}{\left(x_i-\overline{x}\right)}^2}$
Variance (VAR)	$\frac{1}{N-1}{\displaystyle \sum _{i=1}^N}{x}_i{}^2$	Root Mean Square (RMS)	$\sqrt{\frac{1}{N}{\displaystyle \sum _{i=1}^N}{x}_i{}^2}$
Skewness (SKE)	$\frac{1}{N{\sigma }^3}{\displaystyle \sum _{i=1}^N}{\left(x_i-\overline{x}\right)}^3$	Kurtosis (KUR)	$\frac{1}{N{\sigma }^4}{\displaystyle \sum _{i=1}^N}{\left(x_i-\overline{x}\right)}^4$
Interquartile Range (IQR)	$Q_3-Q_1$	Peak to Peak(P2P)	$x_{max}-x_{min}$
Mean Absolute Value (MAV)	$\frac{1}{N}{\displaystyle \sum _{i=1}^N}\left|x_i\right|$	Waveform Length (WL)	${\displaystyle \sum _{i=1}^{N-1}}\left|x_{i+1}-x_i\right|$
Zero Crossing (ZC)	$\{\begin{array}{c}ZC={\displaystyle \sum _{i=1}^N}{z}_i\times z{c}_i\\ z{c}_i=sgn\left(-x_i{x}_{i+1}\right)\\ z_i=\{\begin{array}{l}1, \left|x_i-x_{i+1}\right|>{\delta }_z\\ 0, else\end{array}\end{array}$	Slope Sign Change (SSC)	$\{\begin{array}{c}SSC={\displaystyle \sum _{i=2}^{N-1}}{s}_i\times ss{c}_i\\ ss{c}_i=sgn\left[\left(x_i-x_{i-1}\right)\left(x_i-x_{i+1}\right)\right]\\ s_i=\{\begin{array}{l}1, \left|x_i-x_{i+1}\right|>{\delta }_s \cap \left|x_i-x_{i-1}\right|>{\delta }_s\\ 0, else\end{array}\end{array}$
Wilson Amplitude (WAMP)	${\displaystyle \sum _{i=1}^{N-1}}sgn\left(\left|x_{i+1}-x_i\right|-{\delta }_{\mathrm{w}}\right)$	Log Detector (LD)	$\exp \left(\frac{1}{N}{\displaystyle \sum _{i=1}^N}log\left(\left|x_i\right|\right)\right)$
Auto Regressive Coefficient (ARC)	$x_k={\displaystyle \sum _{i=1}^4}{a}_i{x}_{k-i}+e_k$	Energy	$\frac{1}{N}{\displaystyle \sum _{i=1}^N}{\left|x_i\right|}^2$
Modified Mean Absolute Value (MMAV)	$\{\begin{array}{c}\frac{1}{N}{\displaystyle \sum _{i=1}^N}{\omega }_i\left|x_i\right|\\ {\omega }_i=\{\begin{array}{l}1, 0.25N\le i\le 0.75N\\ 0, else\end{array}\end{array}$	Correlation Coefficient (CC)	$\frac{{{\displaystyle \sum }}_{i=1}^N\left(cc{a}_i-\overline{cca}\right)\left(cc{b}_i-\overline{ccb}\right)}{\sqrt{{{\displaystyle \sum }}_{i=1}^N{\left(cc{a}_i-\overline{cca}\right)}^2{{\displaystyle \sum }}_{i=1}^N{\left(cc{b}_i-\overline{ccb}\right)}^2}}$
Jerk	$\frac{1}{2}{\displaystyle \sum _{i=2}^N}{\displaystyle \sum _{j=1}^3}{\left(AC{C}_j\left(i\right)-AC{C}_j\left(i-1\right)\right)}^2$	Signal Magnitude Area (SMA)	$\frac{1}{N}{\displaystyle \sum _{i=1}^N}\left(\left|sma{x}_i\right|+\left|sma{y}_i\right|+\left|sma{z}_i\right|\right)$
Mean Power Frequency (MPF)	$\frac{{{\displaystyle \sum }}_{i=1}^n{p}_i{f}_i}{{{\displaystyle \sum }}_{i=1}^n{p}_i}$	Entropy	$-{\displaystyle \sum _{i=1}^n}\left(\frac{p_i}{{{\displaystyle \sum }}_{i=1}^n{p}_i}ln\left(\frac{p_i}{{{\displaystyle \sum }}_{i=1}^n{p}_i}\right)\right)$
Median Frequency (MDF)	${\displaystyle \sum _{i=f_{min}}^{MDF}}{p}_i={\displaystyle \sum _{i=MDF}^{f_{max}}}{p}_i$	One Quarter of Frequency (F25)	$3{\displaystyle \sum _{i=f_{min}}^{F25}}{p}_i={\displaystyle \sum _{i=F25}^{f_{max}}}{p}_i$
Three Quarters of Frequency (F75)	${\displaystyle \sum _{i=f_{min}}^{F75}}{p}_i=3{\displaystyle \sum _{i=F75}^{f_{max}}}{p}_i$