# Continuous Wavelet Transform and CNN for Fault Detection in a Helical Gearbox
## 5 Experiments and Discussions
### Experiments with the Proposed Defect Detection Models
The information acquired by the triaxial accelerometer on the _Z_-axis favors the detection of the structural defects D3 and D4, with the Mcwt_z model achieving very high F1 scores (>99.5%) for these classes and only 98.73% for D1 and D2. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Model**} & \multicolumn{4}{c}{**Predicted class**} \\ \cline{3-7}  & **Mcwt\_xyz** & **D1** & **D2** & **D3** & **D4** & **Recall (\%)** \\ \hline \multirow{3}{*}{**True class**} & **D1** & 3889 & 1 & 0 & 0 & 99.97 \\ \cline{2-7}  & **D2** & 2 & 3658 & 0 & 0 & 99.95 \\ \cline{2-7}  & **D3** & 0 & 0 & 3657 & 3 & 99.92 \\ \cline{2-7}  & **D4** & 1 & 0 & 7 & 3652 & 99.78 \\ \hline \multirow{3}{*}{**Precision (\%)**} & **Precision (\%)** & 99.92 & 99.97 & 99.81 & 99.92 & **CI accuracy (\%)** \\ \cline{2-7}  & **F1 score (\%)** & 99.95 & 99.96 & 99.86 & 99.85 & **99.91 \(\pm\) 0.03** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Model Mcwt_xyz: global confusion matrix and the performance metrics for 10 runs. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Model**} & \multicolumn{4}{c}{**Predicted class**} \\ \cline{3-6}  & **Mcwt\_z** & **D1** & **D2** & **D3** & **D4** & **Recall (\%)** \\ \hline \multirow{3}{*}{**True class**} & **D1** & 3838 & 45 & 4 & 3 & 98.66 \\ \cline{2-6}  & **D2** & 35 & 3616 & 7 & 2 & 98.80 \\ \cline{2-6}  & **D3** & 5 & 3 & 3648 & 4 & 99.67 \\ \cline{2-6}  & **D4** & 7 & 1 & 11 & 3641 & 99.48 \\ \hline \multirow{3}{*}{**Precision (\%)**} & **Precision (\%)** & 98.79 & 98.66 & 99.40 & 99.75 & **CI accuracy (\%)** \\ \cline{2-6}  & **F1 score (\%)** & 98.73 & 98.73 & 99.54 & 99.62 & **99.15 \(\pm\) 0.13** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Model Mcwt_z: confusion matrix and the performance metrics for 10 runs. In general, the efficiency of the accelerometer axes in the classification quality can be influenced by particular aspects regarding the geometry and positioning of the defect on the flanks of the gear, the type of gear and bearing, the working conditions, and the dynamics of the entire structure that affect the vibration transmission path from the fault to the sensor. The D3-D4 slight confusion in prediction of the model Mcwt_xyz can be explained by observing similarities and dissimilarities of the two states (defects). Among similarities, one can mention that both defects are structural, located in two similar pinions (P1), and on the pinions' active flanks. In the following lines, we present some dissimilarities. The extent of the two defects is different, the wear zone being larger than the pitting area. The position of each defect on the pinion's flank differs: the wear zone has an edge position and the associated effect manifests itself when the flanks come into contact, while the pitting defect is at a distance from the edge. Another dissimilarity is the position on the height of the tooth flank: pitting is about the pitch point, while the wear zone is at the addendum of the unhealthy tooth (with the effect of shortening the contact line). The helical gear pair has an increased length of the contact line, associated with the number of tooth pairs found in contact (contact ratios) as opposed to a spur gear. On the other hand, the position effect is diminished by the contact line length, which is larger in the helical gear pairs.