Table 1.

Proposed set of statistical time-domain features for the characterization of the dynamic behavior of a signal.

Statistical Time-Domain Feature	Mathematical Equation
Mean	$T_1=\frac{1}{N}·{{\displaystyle \sum }}_{i=1}^N\left|x_i\right|$	(4)
Maximum value	$T_2=max\left(x\right)$	(5)
Root mean square	$T_3=\sqrt{\frac{1}{N}·{{\displaystyle \sum }}_{i=1}^N{\left(x_i\right)}^2}$	(6)
Square root mean	$T_4={\left(\frac{1}{N}·{{\displaystyle \sum }}_{i=1}^N\sqrt{\left|x_i\right|}\right)}^2$	(7)
Standard deviation	$T_5=\sqrt{\frac{1}{N}·{{\displaystyle \sum }}_{i=1}^N{\left(x_i-T_1\right)}^2}$	(8)
Variance	$T_6=\frac{1}{N}·{{\displaystyle \sum }}_{i=1}^n{\left(x_i-T_1\right)}^2$	(9)
RMS Shape factor	$T_7=\frac{T_3}{\frac{1}{N}·{{\displaystyle \sum }}_{i=1}^N\left|x_i\right|}$	(10)
SRM Shape factor	$T_8=\frac{T_4}{\frac{1}{N}·{{\displaystyle \sum }}_{i=1}^N\left|x_i\right|}$	(11)
Crest factor	$T_9=\frac{T_2}{T_3}$	(12)
Latitude factor	$T_{10}=\frac{T_2}{T_4}$	(13)
Impulse factor	$T_{11}=\frac{T_2}{\frac{1}{N}·{{\displaystyle \sum }}_{i=1}^N\left|x_i\right|}$	(14)
Skewness	$T_{12}=\frac{\sum \left[{\left(x_i-T_1\right)}^3\right]}{T_5^3}$	(15)
Kurtosis	$T_{13}=\frac{\sum \left[{\left(x_i-T_1\right)}^4\right]}{T_5^4}$	(16)
Fifth moment	$T_{14}=\frac{\sum \left[{\left(x_i-T_1\right)}^5\right]}{T_5^5}$	(17)
Sixth moment	$T_{15}=\frac{\sum \left[{\left(x_i-T_1\right)}^6\right]}{T_5^6}$	(18)