## 5 Results and Analysis
### GMM Clustering Results
#### 5.2.2 Comparative Analysis  
Since the proposed model was one of the few in the literature trained and tested on real-life engine operational data, it was difficult to compare the results to other proposed models. To overcome this issue, it was decided to apply the proposed model to the most used literature engine data, the CMAPPS data.  
The reconstruction error for the CMAPPS engine dataset was equal to 1.34 \(\times\) 10\({}^{-2}\), while the loss function converged to 2.6 \(\times\) 10\({}^{-3}\).  
In Figure 4, GMM clustering results for the CMAPPS dataset are presented.  
Figure 4 presents the GMM clustering results for the CMAPSS dataset. In contrast to the real-life data, the CMAPSS data shows clearer distinctions in engine feature trends, particularly for Unhealthy engines. The feature values for Unhealthy engines exhibit a notably wider range (from \(-\)53 to +77) compared to the other two health states, making their trendability quite evident. This observation supports the conclusion that simulated engine datasets are generally easier to model and simulate than real-life engine datasets, which are collected over many years under diverse environmental conditions and contain more inherent noise and variability.  
To improve the visualization of the GMM clustering, the PCA analysis was applied to the CMAPPS and real-life engine data. The results were presented in Figure 5 for the CMAPPS data (a) and real-life engine data (b). PC1 (68% variance) captures overall degradation magnitude; PC2 (12% variance) isolates fault modes. Healthy engines cluster tightly (bottom-left), while Unhealthy engines disperse along PC1 (right) due to varied failure signatures. Middle states bridge this continuum.  
Figure 5 illustrates the GMM engine health state clustering results projected onto a 2D space using Principal Component Analysis (PCA). In this projection, each sample corresponds to an aggregated latent feature vector extracted by the autoencoder, representing an engine's overall health state averaged over time. Figure 5a displays the clustering for the CMAPSS engine dataset, which consists of 20,631 engine records from 100 engine serial numbers. For CMAPSS, 58 samples were assigned to the Healthy condition, 31 to Middle, and 11 to Unhealthy. Figure 5b shows the clustering for the real-life engine  
Figure 3: GMM cluster posterior probability distributions for three engine health states. Black circles indicate residual clustering probability.  
operational data, comprising 43,472 records from 53 separate engines. For the real-life data, 9 engines were classified as Healthy, 34 as Middle, and 10 as Unhealthy. The silhouette performance for CMAPSS GMM clustering was 0.39, which is approximately 70% better than the 0.12 achieved for the real-life engine operational dataset. This significant difference in silhouette scores visually confirms that the simulated data is considerably easier to model and process due to its clearer separation of health states compared to the more complex and noisy real-life data.  
Figure 4: GMM clustering results for the CMAPPS engine dataset. \(x\)-axis: Latent dimension index; \(y\)-axis: Standardized feature value.  
Figure 5: PCA projection of GMM clusters for (**a**) the CMAPPS engine dataset; (**b**) the real-life engine data.  
For the CMAPPS engine dataset and GMM clustering, the achieved silhouette performance was equal to 0.39. This result is about 70% better for the simulated data. This result confirms the assumption that the simulated data is much easier to model and process than the real-life one.