## 3 Results and Discussion
Out of the 15 features, the uniformly most important feature to RUS prediction is the RMS (root mean square), which is defined as:  
\[\text{RMS}=\sqrt{\frac{1}{T_{RMS}}\int\limits_{t_{0}}^{t_{0}+T}U(t)^{2}} \tag{5}\] \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Method** & **Tube \#1** & **Tube 2** & **Tube \#3** & **Tube \#4** & **Tube \#5** & **Tube \#6** & **Tube \#7** & **Tube \#8** & **Tube \#9** & **Average** \\ \hline RF & 0.72 & 0.81 & 0.79 & 0.8 & **0.82** & 0.84 & 0.79 & **0.93** & 0.70 & 0.80 \\ CNN-basic & 0.82 & 0.87 & 0.85 & **0.83** & 0.76 & 0.83 & 0.79 & 0.86 & 0.81 & 0.82 \\ CNN-squeeze & **0.84** & **0.9** & **0.88** & 0.79 & 0.79 & **0.86** & 0.79 & 0.87 & **0.83** & **0.85** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Pearson correlation (R) as evaluated by 9-fold CV. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Method** & **Tube \#1** & **Tube \#2** & **Tube \#3** & **Tube \#4** & **Tube \#5** & **Tube \#6** & **Tube \#7** & **Tube \#8** & **Tube \#9** & **Average** \\ \hline RF & 3.3 & **4.03** & 3.21 & **3.26** & **4.99** & 4.60 & **2.98** & **2.33** & 4.63 & 3.70 \\ CNN-basic & 2.23 & 4.08 & 3.3 & 3.37 & 5.2 & **4.07** & 3.01 & 2.94 & 4.15 & 3.60 \\ CNN-squeeze & **2.13** & 4.09 & **2.81** & 3.56 & 5.51 & 4.1 & 3.07 & 2.64 & **4.02** & **3.55** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Root mean square error (RMSE) of the remaining useful strength (RUS) values as evaluated by 9-fold cross-validation (CV). where \(U(t)\) is the acoustic signal. The average impurity for RMS was 0.61 with a standard deviation of 0.06. Given that RMS is the most representative feature for an AE signal, we inspected how the AE signals from different strain stages differed across various tubes. In Figure 12, we illustrated that the strain distribution undergone by each tube, with respect to strain intensity (stages), was different for all tubes. For example, Tube #4 broke after applying a strain up to stage 4 while Tube #9 shows a much higher strength by holding up to the stage 9 strain before it broke. Additionally, Table 5 displays the average RMS values for each tube within each stage of strain. It can be found that AE signals from different tubes show high dissimilarity despite the fact that they occurred at similar stages of the degradation. The average RMS of AE signals displayed by the SiC\({}_{\text{f}}\)-SiC\({}_{\text{m}}\) tubes were considerably different and they did not present any apparent correlation pattern with the degradation stage. High and low average RMS values were seen throughout the entire testing. With respect to that difference among AE events from different tubes, we could validate the variation in performance of the models across the tubes. For AE events in a testing set, our models will more accurately predict their RUS the less unique these signals were because the models would have already learned their mapping to the degradation space from similar samples. Since the experiments were done in a controlled setting, we attributed the variation of the prediction output from different AEs to the fact that the tested SiC\({}_{\text{f}}\)-SiC\({}_{\text{m}}\) assembled tubes were also manufactured with a certain degree of variation. Lastly, there was no apparent correlation between our model performances on RUS prediction and the tubes experimental degradation process of the tubes. Figure 11: Description of the 10 stages of a tube’s degradation. Figure 12: Bar plot of strain by each tube. Each bar displays the categorization of the 10 strain phases described in Table 4.  
In Figure 13, the predicted and experimental RUS values were plotted against the true pressure values for each testing-set represented by a tube. A mere visualization inspection provided support for our earlier findings. Supporting our results in Table 3, the Squeezenet CNN models generally outperformed other methods.