## 6 Discussion
### Performance Evaluation  
The evaluation of the proposed methodology on both real-life engine data and the CMAPPS dataset provided valuable comparative insights. The autoencoder reconstruction error for the real-life dataset was slightly higher than that for the CMAPPS dataset, which is expected, given the higher noise levels and variability in real-world data. Despite this, the GMM clustering approach maintained a clear separation of engine states, indicating the robustness of the methodology. The question might be raised as to why it was decided to select GMM clustering instead of any others. To confirm the performance of the GMM clustering, another method was used and compared to the GMM. In this case, it was a spectral clustering algorithm. This method bridges graph theory and machine learning, making it a powerful tool for complex clustering tasks where traditional methods fail. Spectral clustering silhouette performance was equal to 0.05 for the real-life engine operational data and 0.18 for the CMAPPS data. These are 60% and 54% lower than for the GMM clustering, which proved GMM selection legitimacy. Figure 7 presents spectral clustering results for real-life engine operational data (a) and the CMAPPS dataset (b). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Engine Health State**} & \multicolumn{2}{c}{**RMSE**} & \multicolumn{2}{c}{**R\({}^{2}\)**} & \multicolumn{2}{c}{**Score**} & \multicolumn{2}{c}{**Loss**} \\ \cline{2-9}  & **CMAPPS** & **Real** & **CMAPPS** & **Real** & **CMAPPS** & **Real** & **CMAPPS** & **Real** \\ \hline Healthy & 17.556 & 211.687 & 0.899 & 0.455 & 4.859 & 2.338 \(\times\) 10\({}^{25}\) & 0.138 & 0.031 \\ Middle & 55.830 & 340.864 & 0.678 & 0.191 & \(-\)0.841 & 4.992 \(\times\) 10\({}^{19}\) & 0.047 & 0.028 \\ Unhealthy & 17.587 & - & 0.928 & - & 5.090 & - & 0.137 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: RUL prediction accuracy comparison for the model without the self-attention mechanism. Figure 7 displays the engine health states clustering results obtained using spectral clustering for (a) the real-life engine data and (b) the CMAPSS engine dataset. Comparing these results with the GMM clustering results presented in Figure 5, it is evident that the GMM provides superior clustering performance. For the real-life engine data with spectral clustering (Figure 7a), it is significantly more difficult to distinguish between engine health states, indicating less clear cluster separation. This visual comparison, coupled with the quantitative silhouette performance metrics (0.05 for real-life data and 0.18 for CMAPSS with spectral clustering, significantly lower than the GMM's 0.12 and 0.39, respectively), strongly supports the legitimacy of selecting a GMM for this study. In Figure 8, plots presenting actual RULs (blue lines) and predicted RULs (red lines) were presented for two datasets: real-life engine operational data (a) and CMAPSS (b), for three various engine health states. Figure 8 presents plots comparing the actual RUL (blue lines) against the predicted RUL (red lines) for engines in three different health states across two datasets: (a) CMAPSS and (b) real-life engine operational data: Healthy: Slow decline (1000+ cycles); Unhealthy: Rapid drop (<200 cycles). CMAPSS (a) shows idealized degradation, while real data (b) exhibits stochastic fluctuations due to operational variability. Analyzing these RUL predictions, it can be concluded that the proposed neural network architecture and prediction algorithm perform better for the simulated CMAPSS dataset than for the real-life engine data. For CMAPSS, the RUL prediction lines, representing engine degradation, closely follow the actual engine life-cycle reduction, indicating high accuracy. While the predictions for real-life data show more variability, they still provide valuable prognostic information despite the inherent noise and complexity of the dataset. Figure 9 presents examples of the engines' RUL predictions for real-life engine operational data (a) and CMAPPS dataset (b).