Table 1 List of signal features Index...

Table 1

List of signal features

Index	Feature name	Calculation formula
1	Maximum value	$x_{\max}$
2	Minimum value	$x_{\min}$
3	Mean value	$x_{m e a n} = \frac{1}{N} \sum_{i = 1}^{N} x_{i}$
4	Median value	$x_{m e d}$
5	Peak-to-peak	$x_{p - p} = x_{\max} - x_{\min}$
6	Average absolute value	$x_{a v} = \frac{1}{N} \sum_{i = 1}^{N} \| x_{i} \|$
7	Variance	$x_{v a r} = \frac{1}{N} \sum_{i = 1}^{N} (x_{i} - \bar{x})$
8	Standard deviation	$x_{s t d} = {(\frac{1}{N} \sum_{i = 1}^{N} (x_{i} - \bar{x}))}^{1 / 2}$
9	Root mean square	$x_{r m s} = {(\frac{1}{N} \sum_{i = 1}^{N} {x_{i}}^{2})}^{1 / 2}$
10	Mean square value	$x_{m s} = \frac{1}{N} \sum_{i = 1}^{N} {x_{i}}^{2}$
11	Root mean square amplitude	$x_{r m s a} = {(\frac{1}{N} \sum_{i - 1}^{N} \| x_{i} \|^{\frac{1}{2}})}^{2}$
12	Skewness	$x_{s k} = \frac{1}{n - 1} \frac{\sum_{i = 1}^{N} {(x_{i} - \bar{x})}^{3}}{{x_{s t d}}^{3}}$
13	Kurtosis	$x_{k u} = \frac{1}{n - 1} \frac{\sum_{i = 1}^{N} {(x_{i} - \bar{x})}^{4}}{{x_{s t d}}^{4}}$
14	Form factor	$S_{f} = \frac{x_{r m s}}{\frac{1}{N} \sum_{i = 1}^{N} \| x_{i} \|}$
15	Peak factor	$C = \frac{x_{p - p}}{x_{r m s}}$
16	Impulse factor	$S = \frac{x_{p - p}}{\frac{1}{N} \sum_{i = 1}^{N} \| x_{i} \|}$
17	Clearance factor	$L = \frac{x_{p - p}}{{(\frac{1}{N} \sum_{i - 1}^{N} \| x_{i} \|^{\frac{1}{2}})}^{2}}$
18	Center of gravity frequency	$f_{c} = \frac{\sum_{i = 1}^{N} f_{i} p_{i}}{\sum_{i = 1}^{N} p_{i}}$
19	Frequency variance	$v_{f} = \frac{\sum_{i - 1}^{N} {(f_{i} - f_{c})}^{2} p_{i}}{\sum_{i = 1}^{N} p_{i}}$
20	Frequency standard deviation	$v_{s} = \sqrt{v_{f}}$
21	Mean square frequency	$m s f = \frac{\sum_{i = 1}^{N} {f_{i}}^{2} p_{i}}{\sum_{i = 1}^{N} p_{i}}$
22	Root mean square frequency	$r m s f = \sqrt{m s f}$

Index	Feature name	Calculation formula
1	Maximum value	$x_{\max}$
2	Minimum value	$x_{\min}$
3	Mean value	$x_{m e a n} = \frac{1}{N} \sum_{i = 1}^{N} x_{i}$
4	Median value	$x_{m e d}$
5	Peak-to-peak	$x_{p - p} = x_{\max} - x_{\min}$
6	Average absolute value	$x_{a v} = \frac{1}{N} \sum_{i = 1}^{N} \| x_{i} \|$
7	Variance	$x_{v a r} = \frac{1}{N} \sum_{i = 1}^{N} (x_{i} - \bar{x})$
8	Standard deviation	$x_{s t d} = {(\frac{1}{N} \sum_{i = 1}^{N} (x_{i} - \bar{x}))}^{1 / 2}$
9	Root mean square	$x_{r m s} = {(\frac{1}{N} \sum_{i = 1}^{N} {x_{i}}^{2})}^{1 / 2}$
10	Mean square value	$x_{m s} = \frac{1}{N} \sum_{i = 1}^{N} {x_{i}}^{2}$
11	Root mean square amplitude	$x_{r m s a} = {(\frac{1}{N} \sum_{i - 1}^{N} \| x_{i} \|^{\frac{1}{2}})}^{2}$
12	Skewness	$x_{s k} = \frac{1}{n - 1} \frac{\sum_{i = 1}^{N} {(x_{i} - \bar{x})}^{3}}{{x_{s t d}}^{3}}$
13	Kurtosis	$x_{k u} = \frac{1}{n - 1} \frac{\sum_{i = 1}^{N} {(x_{i} - \bar{x})}^{4}}{{x_{s t d}}^{4}}$
14	Form factor	$S_{f} = \frac{x_{r m s}}{\frac{1}{N} \sum_{i = 1}^{N} \| x_{i} \|}$
15	Peak factor	$C = \frac{x_{p - p}}{x_{r m s}}$
16	Impulse factor	$S = \frac{x_{p - p}}{\frac{1}{N} \sum_{i = 1}^{N} \| x_{i} \|}$
17	Clearance factor	$L = \frac{x_{p - p}}{{(\frac{1}{N} \sum_{i - 1}^{N} \| x_{i} \|^{\frac{1}{2}})}^{2}}$
18	Center of gravity frequency	$f_{c} = \frac{\sum_{i = 1}^{N} f_{i} p_{i}}{\sum_{i = 1}^{N} p_{i}}$
19	Frequency variance	$v_{f} = \frac{\sum_{i - 1}^{N} {(f_{i} - f_{c})}^{2} p_{i}}{\sum_{i = 1}^{N} p_{i}}$
20	Frequency standard deviation	$v_{s} = \sqrt{v_{f}}$
21	Mean square frequency	$m s f = \frac{\sum_{i = 1}^{N} {f_{i}}^{2} p_{i}}{\sum_{i = 1}^{N} p_{i}}$
22	Root mean square frequency	$r m s f = \sqrt{m s f}$

Source(s): Authors' own work

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