## 6 Conclusions  
This study was the first to apply ultrasonic pulse measurement to investigate the thermal-induced damage characteristics of concrete by conducting the uniaxial compressive test after concrete was subjected to heating under different thermal conditions (the rate of heating, maximum temperature, exposure time, as well as cooling condition). During the uniaxial compressive test process, a circumferential extensometer was used to prevent unstable crack growth. A complete stress-strain curve was then obtained. The experimental results show that the stiffness, strength, and pre-peak toughness decrease with an increase in maximum temperature, whereas the post-peak toughness increased with an increase in maximum temperature at a maximum temperature ranging from 200 to 500 \({}^{\circ}\)C. In addition, the wave velocity ratios in relation to the maximum temperature, stiffness, strength, and pre-peak toughness were obtained. The obtained experimental data was then analyzed using artificial intelligence.  
The thermal conditions in the experiment were used as input variables. The experimental stiffness, strength, toughness, and wave velocity ratio results were used as output variables. The obtained correlation of the input and output variables using artificial intelligence showed that the wave velocity ratio has a high relation with the maximum temperature, stiffness, strength, and pre-peak toughness. These results indicate that the wave velocity ratio can be used to identify the thermal-induced damage characteristics. Ultrasonic pulse measurement coupled with the uniaxial compressive test can be employed to investigate the degree of damage with respect to the maximum temperature of concrete subject to heating.  
Conceptualization, L.-H.C. and Y.-C.C.; Methodology, L.-H.C.; Software, K.-W.H.; Visualization, W.-C.C. and H.-J.L.; Formal Analysis, W.-C.C., H.-J.L., and K.-W.H.; Validation, M.-Y.L. and T.-C.W.; Resources, C.-F.C.; Writing-Original Draft Preparation, W.-C.C.; Writing-Review & Editing, W.-C.C.; Supervision, L.-H.C.; Project Administration, H.-J.L.  
This research was funded by Architecture and Building Research Institute, Ministry of the Interior, ROC (Taiwan) grant number 105301070000G0032.  
This research is supported by the Architecture and Building Research Institute, Ministry of the Interior, ROC (Taiwan).  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Input Variables**} & \multicolumn{5}{c}{**Output Variables**} \\ \cline{2-6}  & **Wave Velocity Ratio** & **Stiffness** & **Strength** & **Pre-Peak Toughness** & **Post-Peak Toughness** \\ \hline designed strength & \(-0.14\) & \(0.23\) & \(0.49\) & \(0.37\) & \(0.24\) \\ rate of heating & - & - & \(0.19\) & - & - \\ maximum temperature & \(0.78\) & \(-0.87\) & \(-0.65\) & \(-0.7\) & \(-0.73\) \\ exposure time & \(0.17\) & \(-0.42\) & \(-0.41\) & \(-0.4\) & \(-0.22\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Correlation coefficient between input and output variables.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Output Variables** & **Stiffness** & **Strength** & **Pre-Peak Toughness** & **Post-Peak Toughness** \\ \hline wave velocity ratio & \(-0.91\) & \(-0.89\) & \(-0.84\) & \(-0.67\) \\ stiffness & & \(0.99\) & \(0.94\) & \(0.8\) \\ strength & & \(0.97\) & \(0.84\) \\ pre-peak toughness & & & \(0.99\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Correlation coefficient between output variables.