# Gear Fault Detection Method Based on Convex Hull Clustering of Autoencoder's Latent Space
## 4 Results and Discussion  
To understand the nature of autoencoder and GAN behavior and evaluate the possibility of wear severity prediction, we present the labelled latent data of an autoencoder (Figure 23) and the discriminator output of the GAN (Figure 24).  
Figure 21: Discriminator output.  
Figure 22: Confusion matrix for convex hull classification of discriminator output.  
It can be seen that the latent data, mapped into three-dimensional space by adding the pitting wear coordinate (Figure 23b), allowed us to evaluate the pitting rate based on latent coordinates h1 h2. The plane was fitted with a 0.26 regression score. The prediction of wear based on linear regression was not accurate in this case, but it gave some idea of how the data points were spaced. A more sophisticated nonlinear regression should be applied like a decision tree or polynomial regressor, which would perform well in supervised learning within the latent space.  
The opposite situation might be observed within the output space of the discriminator (Figure 24). Data points formed nearly straight lines within the probability space. Mapping them into three-dimensional space by adding wear coordinates (Figure 24b) did not help, since wear took non-unique values for the same point on the probability plane. It can also be observed as an overlapping of clusters in Figure 24a.  
A comparison of the performance of the proposed models is given in Table 3.  
Recall was very high for both the autoencoder (AE) and autoencoder combined with convex hull classification of the latent data (AE+CH), while the lowest value was noted for GAN + convex hull. The best overall performance (highest precision, recall, and F1-score) was observed for the proposed AE+CH model. The conventional unsupervised machine learning approach based on principal component analysis (PCA) did not show a clear separation between normal and failure operations within a space of reduced dimensionality, making it difficult to generalize the model and provide proper classification of the fault. Reduced dimensionality by the autoencoder (AE+CH) provided an advantage over the PCA and GAN, that is, an almost linear separation between the two states of gearbox operation (Figures 15 and 16). This allows us, apart from failure detection, to monitor the condition of the gearbox in both normal and failure operations. It is worth mentioning that the proposed semi-supervised learning approach (AE+CH) achieved similar results to the supervised methods (AE + linear SVM and AE + nonlinear SVM).  
Figure 24: Labelled discriminator output for the GAN: (**a**) probability space; (**b**) percentage pitting wear.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Model** & **Precision** & **Recall** & **F1-Score** \\ \hline Autoencoder & 0.90 & 1.00 & 0.95 \\ Autoencoder + convex hull classification & 0.98 & 1.00 & 0.99 \\ Autoencoder + linear SVM & 1.00 & 0.99 & 0.99 \\ Autoencoder + nonlinear SVM & 1.00 & 1.00 & 1.00 \\ GAN + convex hull classification & 0.98 & 0.93 & 0.95 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of results.