## 3 Results and Discussion
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**CI Breaking** & **Weighing** & **CI Cracking** & **Weighing** & **CI Fitting** & **Weighing** & **CI Scuffing** & **Weighing** \\ \hline Mean & 27 & Skewness & 28 & TMHO & 25 & TMHO & 30 \\ Zero crossing & 26 & SSC & 25 & Mean & 24 & Mean & 27 \\ THHO & 26 & Mean & 20 & Energy operator & 19 & Skewness & 21 \\ Energy operator & 19 & TMHO & 19 & SSC & 19 & Zero crossing & 19 \\ SSC & 14 & Energy operator & 15 & Skewness & 15 & FSM & 17 \\ Kurtosis & 8 & FSM & 13 & Kur Kurtsts & 13 & Kurtsts & 8 \\ Light factor & 8 & Zero crossing & 11 & Energy operator & 6 \\ Shape factor & 7 & Clearance factor & 11 & SDIF & 9 & Impulse factor & 6 \\ SDIF & 6 & Kurtosis & 8 & Zero crossing & 7 & Clearance factor & 6 \\ Crest factor & 6 & SDIF & 5 & Clearance factor & 6 \\ Skewness & 5 & Shape factor & 3 & FSM & 5 & Shape factor & 5 \\ Waveform & 4 & Lattitrad factor & 3 & Lattitrad factor & 5 & Waveform & 5 \\ Impulse factor & 4 & NNNL & 2 & Waveform & 4 & SSC & 4 \\ Log-Log ratio & 3 & Impulse factor & 2 & Pulse index & 3 \\ Margin index & 2 & & Log-Log ratio & 1 & Wavelength & 1 \\  & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main CIs by failure and accelerometer. A complementary statistical analysis was incorporated based on the Bhattacharyya distance [36] to strengthen the validity of the final set of selected features, quantifying the separation of condition indicators (CIs) across class distributions. This metric was calculated for all 64 CIs, considering comparisons between the baseline class (P1) and the various fault severity levels. The results showed that the CIs selected through the proposed wrapper-based approach exhibited higher Bhattacharyya distance, confirming their discriminative capability. In contrast, multiple CIs with consistently low distances were identified and not selected during the feature selection phase, reinforcing the consistency between the statistical analysis and the multivariable classification performance. This comparison is detailed in Tables 5-8 and visually represented in Figure 7.  
Additionally, the methodological risk, widely discussed by [PERSON] [37], that some features with low individual informativeness could still provide value when combined with others, was taken into account. This risk was mitigated by employing a multivariable wrapper approach using Random Forest, which evaluates the performance of entire subsets of features and captures non-linear interactions. \begin{table}
\begin{tabular}{l l l} \hline \hline
**CI** & **Formula** \\ \hline Temporal moments higher order & \(\begin{array}{l}\left|\frac{1}{N}\sum_{i=1}^{N}x_{i}^{m}\right|\\ \text{m=3 as default}\end{array}\) \\ Mean & \(\begin{array}{l}\frac{1}{N}\sum_{i=1}^{N}x_{i}\\ \frac{N}{2},if\end{array}\) & \(\begin{array}{l}\frac{N\sum_{i=1}^{N}\left(x_{i}-T1\right)^{3}}{T3^{3}}\\ \\ \sum_{i=1}^{N}step[sign(-x_{i}*x_{i+1})]\\ step=\left\{\begin{array}{l}1,if\;\;\;x>0\\ 0,if\;\;\;x=0\\ -1,if\;\;\;x<0\end{array}\right.\end{array}\) \\ Zero crossing & \(\begin{array}{l}sign=\left\{\begin{array}{l}1,if\;\;\;x>0\\ \frac{1}{2},if\;\;\;x=0\\ 0,if\;\;\;x<0\end{array}\right.\end{array}\) \\ Slope sign change & \(\begin{array}{l}\sum_{i=2}^{N}f[(x_{i}-x_{i-1})*(x_{i}-x_{i+1})]\\ f=\left\{\begin{array}{l}1,if\;\;\;x\geq threshold\\ 0,\;\;\;otherwise\end{array}\right.\end{array}\) \\ Energy operator & \(\begin{array}{l}\frac{N^{2}\sum_{i=1}^{N}\left(\Delta y_{i}-\Delta y\right) ^{4}}{[\sum_{i=1}^{N}\left(\Delta y_{i}-\Delta y\right)^{2}]^{2}}\\ \\ \text{Kurtosis}\end{array}\) & \(\begin{array}{l}\frac{N\sum_{i=1}^{N}\left(x_{i}-T1\right)^{4}}{[\sum_{i=1} ^{N}\left(x_{i}-T1\right)^{2}]^{2}}\\ \end{array}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Main CIs formulas.