Table 4 Features of different methods
Feature name | Features of optimized VMD+BALW method | Optimized VMD + Conventional features method | Formula | Prompt |
|---|---|---|---|---|
Angle of shock initiation | √ | × | \(a{\text{ = ang}}\left( {\frac{{\sqrt {1 - \xi_{2}^{2} } \ln 0.01}}{{2{\uppi }f\xi_{2} }} + \tau } \right)\) | \({\text{ang}}\left( \cdot \right)\) converts time into angles |
Peak value | √ | √ | \(p = \max \left\{ {\left| x \right|} \right\}\) | |
Shock frequency | √ | × | \(\omega = \mathop {\arg \max }\limits_{\omega } \left\{ {\left| {\hat{x}} \right|} \right\}\) | \(\hat{x}\) is the Fourier transform of the signal x |
Root mean square | √ | √ | \(x_{{{\text{rms}}}} = \sqrt {\frac{1}{n}\sum\nolimits_{i = 1}^{n} {x_{i}^{2} } }\) | |
Standard deviation | √ | √ | \(\sigma = \sqrt {\frac{1}{n}\sum\nolimits_{i = 1}^{n} {\left( {x_{i} - \overline{x}} \right)^{2} } }\) | |
Kurtosis | √ | √ | \(ku = \frac{1}{n}\sum\limits_{i = 1}^{n} {\left( {\frac{{x_{i} - \overline{x}}}{\sigma }} \right)^{4} }\) | |
Crest factor | √ | √ | \(c = p/x_{{{\text{rms}}}}\) | |
Skewness | √ | √ | \(s = \frac{1}{n}\sum\limits_{i = 1}^{n} {\left( {\frac{{x_{i} - \overline{x}}}{\sigma }} \right)^{3} }\) |