A graph-aware meta network for domain generalization in cross-condition bearing RUL prediction | International Journal of Metrology and Quality Engineering (IJMQE)

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Table 3

Definitions of the extracted features.

Feature	Formula	Feature	Formula
Standard deviation	$ρ = \sqrt{\frac{1}{N} \sum_{i = 1}^{N} {(x_{i} - \bar{X})}^{2}}$	Kurtosis	$X_{K} = \frac{1}{N} \sum_{i = 1}^{N} \frac{{(x_{i} - \bar{X})}^{4}}{ρ^{4}}$
Mean	$\bar{X} = \frac{1}{N} \sum_{i = 1}^{N} x_{i}$	Median frequency	$F_{1} = f (\min {k \| \frac{\sum_{j = 0}^{k} p_{s} [j]}{\sum_{j = 0}^{K / / 2 - 1} p_{s} [j]} \geq 0.5})$
Maximum	$X_{M a x} = \max (x_{i})$	Average frequency	$F_{2} = \frac{\sum_{k = 1}^{K} s (k)}{K}$
Minimum	$X_{M i n} = \min (x_{i})$	Maximum amplitude	$F_{3} = \max (s (k))$
Skewness	$X_{S k e} = \frac{1}{N} \sum_{i = 1}^{N} \frac{{(x_{i} - \bar{X})}^{3}}{ρ^{3}}$	Frequency of maximum amplitude	$F_{4} = f (F_{3})$
Root mean square	$X_{R M S} = \sqrt{(\frac{1}{N} \sum_{i = 1}^{N} x_{i}^{2})}$	Band power	$F_{5} = \sum_{f \in [f_{\min}, f_{\max}]} p_{s}$
Peak-to-Peak	$X_{P} = X_{M a x} - X_{M i n}$	Maximum power Spectral density	$F_{6} = \max (p_{s})$

where x_i is sample i and N is the total number of samples, s(k) denotes the signal's spectrum at index k, f(k) indicates the frequency associated with bin k, and p_s represents the power spectral density estimated using Welch’s method.

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