Table 1 Predictive features and their calculations

Time domain

Mean slope (MS)

\( \frac{f_s}{N-1}{\displaystyle \sum_{i=2}^N\left|{x}_i-{x}_{i-1}\right|} \)

Median slope (MdS)

median(x_i − x_{i − 1})f_s

Amplitude range (AR)

max(x_i) − min(x_i)

Signal integral (SignInt)

\( {\displaystyle \sum_{i=1}^N\left|{x}_i\right|} \)

Average peak-to-peak amplitude (PPA)

\( \frac{1}{L}{\displaystyle \sum_{i=1}^L\left( \max \left({x}_{i,L}\right)- \min \left({x}_{i,L}\right)\right)} \)

Root mean square (RMS)

\( \sqrt{\frac{1}{N}{\displaystyle \sum_{i=1}^N{\left({x}_i-\overline{x}\right)}^2}} \)

Frequency domain

Amplitude spectral area (AMSA)

\( {\displaystyle \sum_{j=1}^M{A}_j{f}_j} \)

Power spectrum analysis (PSA)

\( {\displaystyle \sum_j{P}_x\left({f}_j\right)\cdot {f}_j} \)

Max power (MP)

\( \underset{j}{ \max}\left({P}_x\left({f}_j\right)\right) \)

Peak frequency (PF) or dominant frequency

\( \underset{j}{ \arg \max}\left({P}_x\left({f}_j\right)\right) \)

Centroid frequency (CF)

\( \frac{{\displaystyle \sum_j{f}_j\cdot {P}_x\left({f}_j\right)}}{{\displaystyle \sum_j{P}_x\left({f}_j\right)}} \)

Energy (EG)

\( {\displaystyle \sum_j{P}_x\left({f}_j\right)} \)

Others

Spectral flatness measure (SFM)

\( \frac{ \exp \left(\frac{1}{M}{\displaystyle \sum_j \ln \left({P}_x\left({f}_j\right)\right)}\right)}{\frac{1}{M}{\displaystyle \sum_j{P}_x\left({f}_j\right)}} \)

Wavelet energy (WE)

\( {\displaystyle \sum_j\left|{W}_x\left({c}_j\right)\right|} \)

Spectrum entropy (SPE)

\( \hbox{-} {\displaystyle \sum_{i=1}^L\left[\left(\frac{{\displaystyle \sum_{f_{j,L}}{P}_x\left({f}_{j,L}\right)}}{{\displaystyle \sum_j{P}_x\left({f}_j\right)}}\right)\cdot { \log}_2\left(\frac{{\displaystyle \sum_{f_{j,L}}{P}_x\left({f}_{j,L}\right)}}{{\displaystyle \sum_j{P}_x\left({f}_j\right)}}\right)\right]} \)

Hurst index (Hu)

\( \frac{ \log \left[R(i)/S(i)\right]}{ \log (i)} \)