Table 1 Frequency-domain feature extraction.

From: A novel simultaneous monitoring method for surface roughness and tool wear in milling process

No.

Signal feature

Expression

1

Frequency center (fc)

\(\frac{\int _{0}^{+\infty } f P(f) df}{\int _{0}^{+\infty } P(f) df}\)

2

Mean square frequency (msf)

\(\frac{\int _{0}^{+\infty } f^{2} P(f) df}{\int _{0}^{+\infty } P(f) df}\)

3

Root mean square frequency (rmsf)

\(\sqrt{\frac{\int _{0}^{+\infty } f^{2} P(f) df}{\int _{0}^{+\infty } P(f) df}}\)

4

Frequency variance (fv)

\(\frac{\int _{0}^{+\infty } (f-fc)^{2} P(f) df}{\int _{0}^{+\infty } P(f) df}\)

5

Frequency standard deviation (fsd)

\(\sqrt{\frac{\int _{0}^{+\infty } (f-fc)^{2} P(f) df}{\int _{0}^{+\infty } P(f) df}}\)