## 3 Results
### Discussion  
This section describes the three primary outcomes of the present work.  
First, as shown in Table 8, the training accuracy obtained with GP-based feature construction is higher than the training accuracy obtained considering the feature selected through the Relieff and the feature extracted through the PCA. This result implies that the constructed features FC1 and FC2 well separate the two classes corresponding to the settings. On the contrary, using all the time-domain features provides a better training accuracy. However, the so-built models overfit the training data. Indeed, the testing accuracy is equal to 31% in the case of DT and 61% in the case of k-NN. Similar testing accuracies are obtained with PCA and Relieff as well. On the contrary, the testing accuracies obtained by using the GP features are higher than 67%. Therefore, the features FC1 and FC2 separate the two settings and allow the building of a more generalizable classification model.  
Second, as shown in Table 9, when GP features are used to train classification models with three classes, classification accuracy is higher than using the extracted feature through the Relieff. This result implies that FC is better than feature selection for novelty detection. Indeed, only selected features are used as input trained models in streaming diagnostics and prognostics. This means that if a feature does not reveal an unknown setting, the change cannot be detected.  
Finally, concerning the GP trained to extract a HI for the belt prognostics, results show that the constructed HIs have similar trends for failure occurred in the same operating condition. However, the trend is not strictly monotonic, which makes it hard to build a robust degradation model for RUL prediction. Indeed, no HI produces a mean RUL prediction error lower than 10%. However, the constructed HI is compared with the correlation coefficient between a nominal signal and the two fault signals collected during two different settings. This comparison shows that correlation coefficients have lower values of monotonicity, prognosability, and trendability than the constructed HI through the GP. Therefore, the constructed HIs are more suitable for component-level prognostics.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Setting** & **Metric** & **X-a1** & **Y-a1** & **Z-a1** & **X-a2** & **Y-a2** & **Z-a2** & **X-a3** & **Y-a3** & **Z-a3** \\ \hline \multirow{4}{*}{C1} & Monotonicity & 0.0045 & 0.0154 & 0.0036 & 0.0041 & 0.0035 & 0.0080 & 0.0138 & 0.0147 & 0.0160 \\  & Trendability & 0.0040 & 0.0077 & 0.0011 & 0.0311 & 0.0241 & 0.0262 & 0.0074 & 0.0083 & 0.0173 \\  & Prognosability & 0.1997 & 0.8400 & 0.8152 & 0.8247 & 0.9104 & 0.3104 & 0.6745 & 0.8328 & 0.4767 \\  & Monotonicity & 0.0133 & 0.0060 & 0.0301 & 0.0093 & 0.0031 & 0.0071 & 0.0041 & 0.0072 & 0.0033 \\ \multirow{4}{*}{C2} & Trendability & 0.0503 & 0.0222 & 0.1513 & 0.0090 & 0.0414 & 0.0589 & 0.0242 & 0.0313 & 0.0150 \\  & Prognosability & 0.2828 & 0.3350 & 0.2577 & 0.2569 & 0.0632 & 0.3011 & 0.2316 & 0.8701 & 0.3361 \\ \hline \hline \end{tabular}
\end{table}
Table 13: Length of nominal and fault signals considered for the correlation coefficient computation.