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Table 3 Details of the extracted features

From: Multi-Scale Convolutional Gated Recurrent Unit Networks for Tool Wear Prediction in Smart Manufacturing

Index

Features

Expressions

Statistical

Root mean square

\(\sqrt {\frac{1}{n}\sum\nolimits_{i = 1}^{n} {x_{i}^{2} } }\)

Variance

\(\frac{1}{n}\sum\nolimits_{i = 1}^{n} {\left( {x_{i} - \overline{x}} \right)^{2} }\)

Maximum

\(\max \left( x \right)\)

Skewness

\(E\left[ {\left( {\frac{x - \mu }{\sigma }} \right)^{3} } \right]\)

Kurtosis

\(E\left[ {\left( {\frac{x - \mu }{\sigma }} \right)^{4} } \right]\)

Peak-to-peak

\(\max \left( x \right) - \min \left( x \right)\)

Frequency

Spectral Skewness

\(\sum\nolimits_{i = 1} {k\left( {\frac{{f_{i} - \overline{f}}}{\sigma }} \right)^{3} S\left( {f_{i} } \right)}\)

Spectral Kurtosis

\(\sum\nolimits_{i = 1} {k\left( {\frac{{f_{i} - \overline{f}}}{\sigma }} \right)^{4} S\left( {f_{i} } \right)}\)

Spectral power

\(\sum\nolimits_{i = 1}^{k} {\left( {f_{i} } \right)^{3} S\left( {f_{i} } \right)}\)

Time-frequency

Wavelet energy

\(\sum\nolimits_{i = 1}^{N} \omega t_{\phi }^{2} \left( i \right)/N\)