## 4 Conclusions  
In this paper, we defined a new type of system prognostic problem, the remaining useful strength (RUS) prediction problem and proposed and developed three machine learning algorithms including random-forest and convolutional neural networks. We applied these algorithms to predict the RUS of the SiC\({}_{\text{f}}\)-SiC\({}_{\text{m}}\) tube of materials by employing the AE events from nine burst tubes collected during an internal pressure test. Namely, The RUS is defined as the residual amount of pressure left to rupture an assembled tube of SiC\({}_{\text{f}}\)-SiC\({}_{\text{m}}\). We conducted comprehensive 9-fold cross-validation experiments for training and evaluating our CNN and RF models using the full acoustic emissions signals and their features. We show that while the CNN models on average outperformed the RF model, they present the disadvantage with poor prediction performance in the early stages of the degradation. Additionally, due to the presence of rather unique AE signals in some tubes, the models' ability at predicting the RUS of an AE depended on the type of tube that an AE belonged to. Our results indicate that AE analysis using state-of-the-art machine learning methods is a reliable and efficient means for monitoring the degradation process of SiC\({}_{\text{f}}\)-SiC\({}_{\text{m}}\) materials. In general, using deep convolutional neural networks to extract features from acoustic emission signals is a more robust means to represent the audio samples for predicting their RUS and corresponding stages in the degradation process.  
Conceptualization, J.H. and X.H.; methodology, J.H., S.-Y.M.L. and A.N.; software, S.-Y.M.L. and A.N.; validation, S.-Y.M.L., Y.Z., A.N., and Y.C.; investigation, S.-Y.M.L., J.H., A.N., and X.H.; resources, J.H. and X.H.; data curation, J.B. and X.H.; writing--original draft preparation, S.-Y.M.L. and J.H.; writing--review and editing, S.-Y.M.L. and J.H.; visualization, S.-Y.M.L. and J.J.; supervision, J.H.; funding acquisition, J.H. and X.H. All authors have read and agreed to the published version of the manuscript.  
Research reported in this paper was supported in part by the NSF under grant numbers 1905775, OIA-1655740 and SC EPSCOR/IDeA under grant number GEAR CRP-GC03 and in part by DOE NEUP program (DE-NE0008792). The views, perspective, and content do not necessarily represent the official views of the SC EPSCoR/IDeA Program or those of the NSF. The authors would also like to acknowledge [PERSON] and the Advanced Materials laboratory at General Atomics for supplying of test specimens. Fabrication and testing of samples at GA and USC were supported by the U.S. Department of Energy, Office of Nuclear Energy Accident Tolerant Fuel program under contract DE-NE-0008222 (by way of Westinghouse Electric Company under subcontract 4500665245). At GA, method development was supported by General Atomics' Internal Research and Development Funding. The authors would like to acknowledge the work of [PERSON] and [PERSON] in the EM2 SiC Composite Laboratory at GA for their assistance with fabrication and testing of materials. This report was prepared as an account of work partially sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof nor any of their employees make any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process or service by trade name, trade mark, manufacturer or otherwise does not constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of the authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.  
The authors declare no conflict of interest.