## 6 Discussion
### Comparison with Other Models  
This section compares the proposed model's RUL prediction performance on the CMAPSS dataset with other state-of-the-art models from the literature. Since there are no similar complete frameworks for unsupervised engine clustering and RUL prediction validated with real-life turbofan engine operational data, the comparison focuses on the CMAPSS dataset, which is a common benchmark. As for the unsupervised clustering, the proposed GMM methodology was compared to other types of algorithms, such as spectral clustering. The results were presented in Chapter 6.3. Spectral clustering silhouette performance was equal to 0.05 for the real-life engine operational data and 0.18 for the CMAPPS data. These were 60% and 54% lower than for the GMM clustering, which proved GMM selection legitimacy. For the K-means clustering, the average silhouette was equal to 0.16 for the CMAPPS and 0.13 for the real-life engine operational data. The results achieved were 58% lower for the CMAPPS dataset, but, for the real-life data, about 7% higher. Still, engine RUL prediction accuracy was presented for the GMM and spectral clustering methods. The comparison is presented in Table 3.  
Figure 9: Examples of the selected engines’ RUL predictions for various engine health states: (**a**) real-life engine operational data; (**b**) CMAPPS dataset. Comparing K-means to spectral clustering, it might be deduced that although the first one is a very popular clustering method, RUL prediction performance measured by RMSE, R\({}^{2}\), Score, and Loss metrics achieved with spectral clustering is still better for both CMAPPS and real-life engine operational datasets, and all the metrics. In addition to this, it was decided to compare the proposed model to the other engine RUL prediction methods described in the literature. Since there are no publications in which the proposed ML models are validated with the real-life turbofan engine operational data, it was decided to compare the proposed model to other existing RUL prediction models on the CMAPSS dataset. Table 4 summarizes the results of RUL prediction performance comparison between the designed model and 12 existing deep neural networks specifically designed for aero-engine RUL prediction on the CMAPSS dataset. The bolded results highlight performance results for the proposed model and engine health states. As far as the RMSE is concerned, the prediction error result is the lowest among the NN architectures compared. The difference ranges from 29-58%. As for the Score performance metric, the proposed model achieved the best result in all cases. The proposed model outperformed the others by up to an order of magnitude or even greater. It proves that the proposed model has a competitive advantage in RUL prediction performance on the CMAPSS dataset compared to other models. This fact confirms that the proposed NN architecture can comprehensively extract the hidden information from the data as well as detect the most trendable engine operational data features. This results in a better engine health status estimation and more accurate RUL prediction. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**RUL Prediction Model**} & \multicolumn{2}{c}{**FD001 \(\div\) FD004 Mean**} \\ \cline{2-3}  & **RMSE** & **Score** \\ \hline LSTM-CNN [56] & 18.26 & 2629.75 \\ \hline MHN [57] & 16.76 & N/A \\ \hline DABA [58] & 15.65 & 951.00 \\ \hline BiGRU-TSAM [59] & 12.56 & 2.13 \\ \hline AttnPINN [60] & 17.21 & 1313.75 \\ \hline AE-MSEN [61] & 15.58 & 12.31 \\ \hline CNN-Wiener [62] & 17.47 & 1606.00 \\ \hline CBHRL [63] & 12.75 & 2.51 \\ \hline Double Attention [58] & 12.25 & 272.17 \\ \hline KGHM [58] & 13.18 & 250.99 \\ \hline TCN [64] & 14.99 & 330.54 \\ \hline IDMFFN [65] & 16.24 & 1392.12 \\ \hline
**AE-GMM-LSTM-SA** & **5.05 \(\div\) 12.94** & **-0.14 \(\div\) \(-\)0.04** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of RUL prediction performance between the proposed AE-GMM-LSTM-SA (in bold) and other models on the CMAPSS dataset.