# Continuous Wavelet Transform and CNN for Fault Detection in a Helical Gearbox
## 5 Experiments and Discussions
### Comparison of Defect Detection Performance Achieved by Several Models on the Same Dataset  
This section is dedicated to the last research goal (RG3). In the first comparison, we want to emphasize the positive impact of CWT applied to raw data in order to obtain graphical representations of vibration signals that better distinguish the four states of the gearbox. Paper [10] provides performance results in terms of the accuracy of four CNN  
Figure 11: F1 scores for classes (defects) in each of the four models.  
Figure 10: Comparison of the defect detection performance in all four models, at the level of classes.  
based detection models that were built and tested on the raw data of the same dataset of observations. Three models correspond to the information acquired on individual accelerometer axes and are 1D-CNN-based models, and the fourth is a 2D-CNN-based model built on the signals from all three axes. From the bar chart in Figure 12, we draw the following conclusions:  
* In both cases, using raw data or CWT-processed data, the lowest accuracies are achieved by the models that use as input the vibration signals measured on the X or Z axes, and the best-performing model is built on the signals acquired on all three axes.
* Of all three axes, the information measured on the \(Y\)-axis (parallel to the helical reducer input shaft) is the most relevant one in detecting the four states, and by using CWT processing, the accuracy increases by 0.63%.
* When CWT-processed data are used instead of raw data, a significant 2% improvement in accuracy is observed for the models built on the vibration signals measured on the X and Z axes, and only a 0.28% increase is observed for the model built for all three axes.  
In Figure 13, the F1 scores at the level of classes and for individual accelerometer axes achieved by the CNN-based models using raw data [10] are compared with the corresponding scores of the 2D-CNN-based models built on CWT-processed data, showing the better performance of the second group of models. We notice similar trends for each axis with respect to defect identification. A uniform improvement of about 2% in F1 scores for all classes is observed in the model built for the \(X\)-axis when using CWT-processed data compared to raw data. For the \(Y\)-axis, small increases (from 0.37% to 0.9%) in F1 scores can be seen. The relevance of the CWT processing of the vibration signals is better observed in a high increase (about 3%) in the F1 scores for the classes D1 and D2, reached by the model built on the information measured on the \(Z\)-axis.  
For the second comparison, we present in Table 7 the classification performances achieved by three defect detection models that are built and tested on the same dataset of observations measured on all three accelerometer axes. With an accuracy of 99.73%, the model developed in [PERSON] et al. [4] showed that the band powers of six regular GMF harmonics and the first two sideband pairs for each harmonic are relevant features in solving the proposed defect detection task. The model proposed in the current paper, Mcwt_xyz, with a very high accuracy of 99.91%, highlights the importance of the CWT processing of the initial signals, outperforming the similar 2D-CNN-based model [10] built on raw data.  
Figure 12: Comparison of accuracies of the CNN-based models using raw data versus CWT-processed data for each axis and for all three axes.  
It is not appropriate to directly compare the results of the proposed models with those of other models in the literature due to the different datasets used. However, our best-performing model outperforms or equals the performance of other deep learning-based models (presented in Introduction) that detect gearbox faults on public and/or private datasets.