## 3 Results and Discussion  
To evaluate the performance of our models, we used metrics of RMSE (Equation (3)) and the Pearson correlation coefficient (R; Equation (4)). The latter describes the linear relationship between two continuous variables in Equation (4) as:  
\[R(y,\hat{y})=\frac{\sum_{i=1}^{n}(y_{i}-\overline{y})\big{(}\hat{y}_{i}- \overline{\hat{y}}\big{)}}{\sqrt{\sum_{i=1}^{n}(y_{i}-\overline{y})^{2}}\; \sqrt{\sum_{i=1}^{n}\big{(}\hat{y}_{i}-\overline{\hat{y}}\big{)}^{2}}} \tag{4}\]  
where \(y\) defines the experimental value and \(\hat{y}\) the predicted RUS value. Overall, the two metrics differ in that the RMSE scores the model's ability to correctly identify the range in which the predicted RUS resides while R measures the model's ability to linearly rank the RUS of different AE signals. We used 9-fold cross-validation to evaluate three prediction models in terms of their RUS prediction performance based on AE signals of SiC\({}_{\text{f}}\)-SiC\({}_{\text{m}}\) materials:  
Figure 10: Workflow Schema of our CNN models. (**a**) Normalized Input is a 1-dimensional array of 3072 values. (**b**) Kernels of 1D-CNN layers convolve over input x. (**c**) Outputs of 1D-CNN layers are fed to a pooling layer. (**d**) Subsampled outputs are provided to fully connected layers, which then output a remaining useful strength (RUS) value. * Method-1: random-forest model trained with the 15 expert-selected features;
* Method-2: simple standard CNN model trained with the AE signals;
* Method-3: SqueezeNet based model trained with the AE signals. The RMSE and Pearson correlation coefficient results for each model are reported in Tables 3 and 4. As expected, there was a clear performance difference between these two types of models when predicting RUS on a given set of AE signals. In regards to the average scores of RMSE and Pearson correlation coefficient R, the CNN models achieved better performance for RUS prediction with their lower average RMSEs of 3.60 and 3.55 compared to 3.70 of RF (last column in Table 3). The CNN models also achieved higher average Pearson correlation coefficient R values of 0.82 and 0.85 compared to 0.80 of RF (last column in Table 4), which means that the predicted remaining stress values to break by the CNN models aligned better with the true values compared to the random forest models. Particularly, between the two types of CNN models, the SqueezeNet model outperformed the standard deep CNN model given that it had the lowest RMSE of 3.55 ksi units and highest R of 0.85. More interestingly, even though the RF algorithm achieved better RMSE results for five out of the nine tubes (tubes numbered 2, 4, 5, 7 and 8), only of three were significantly better (4, 5, 8). On the other hand, the Pearson correlation coefficient results from the convolutional neural network models were higher in nearly all tubes except three tubes (tubes numbered 1, 2, 3, 4, 6 and 9). Other than the variation by the model architecture, the RUS prediction results also varied amongst the tubes. For tubes numbered 1, 3, 6 and 9, CNN models output RMSE scores that were consistent with the corresponding R values: the highest R values corresponded to the lowest RMSE scores. In contrast, RF outputted consistent results of RMSE and R only in tube 5 and 8. Hence, it was apparent that the models had a challenge at properly mapping AE events distinct to particular tubes to their correct degradation phase. With the knowledge that all of the tubes exhibited different experimental patterns while undergoing the degradation process, we made the assumption that AE signals belonging to different tubes must also differ despite the fact they may have occurred at similar stages of degradation. To verify the assumption, we first categorized a tube's degradation, with respect to the undergone strain, into 10 stages as defined in Figure 11 and then show the strain stage distribution for all tubes before they broke as shown in Figure 12.  
From the RF model outputs, we verified the importance of the features from the model's training.