## 3 Results and Discussion  
The root mean square error (RMSE) from the regression models was utilized to compare the performance of the CNN and regression model combinations. Table 6 presents the RMSE (mean \(\pm\) standard deviation) of predicted crack lengths (unit: mm) by the combinations of three CNNs and three regression models utilized, whereas in Table 7, the RMSE (mean \(\pm\) standard deviation) of the predicted crack width (unit: \(\upmu\)m) by these combinations is reported. The results show that among the CNN models utilized, the features extracted by VGG16 perform the best in the identification and quantification of the crack, because it provides the least RMSE values for the predicted crack length (RMSE: 0.63 \(\pm\) 0.03) and width (6.2 \(\pm\) 0.48). However, on occasion, GoogleNet performs well especially when combined with the linear regression model (RMSE: 0.91 \(\pm\) 0.07 for crack length estimation). Additionally, random forest regression is the best model to estimate the crack length and width with a lesser RMSE (mean \(\pm\) standard deviation: 0.63 \(\pm\) 0.03) as compared with the linear regression and support vector regression models. Figure 9 shows the simulation results for the acoustic responses of multiple geometries at specific time instances. Figure 9 shows the details related to the acoustic wave propagation and its interaction with different crack fronts that come in its path. The division of the principal wave in the transmitted and reflected parts can also be seen in Figure 9. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **GoogleNet** & **ResNet50** & **VGG16** \\ \hline Linear regression & 0.91 \(\pm\) 0.07 & 0.97 \(\pm\) 0.06 & 0.93 \(\pm\) 0.05 \\ Support vector regression & 0.81 \(\pm\) 0.06 & 0.75 \(\pm\) 0.05 & 0.69 \(\pm\) 0.05 \\ Random forest regression & 0.79 \(\pm\) 0.05 & 0.71 \(\pm\) 0.04 & 0.63 \(\pm\) 0.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: RMSE means and standard deviations in the predicted crack lengths (unit: mm) by the CNN model and regression model combinations utilized. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Comp \#**} & **Geometries Involved** & **Purpose (to Show if Statistically Significant** \\  & **(Shown in Figure 6)** & **Differences Are Present in Acoustic Responses of)** \\ \hline \multirow{2}{*}{1} & \multirow{2}{*}{6a, 6b, 6c} &When the incident acoustic wave comes in contact with a defect, a part of it is reflected back depending upon the interaction area. The reflections here are found to be directly proportional to the surface area/interaction area of the crack and the propagating wave. Figure 10 presents the snapshot of the pressure profile of the propagating acoustic wave on the specific time instances for various geometries. An acoustic wave is a longitudinal wave that travels in the form of compressions (high-pressure regions) and rarefactions (low-pressure regions). The red color shows the pressure peaks (compressions), whereas the blue color shows the troughs (rarefactions) of the acoustic wave during propagation. Figure 11 displays the results of a one-way test performed between the acoustic responses of the three samples shown in the Figure 6a-c. The bars show the average acoustic response intervals for the three geometries compared. The blue bar shows the  
Figure 10: Simulation snapshot for acoustic pressure of the propagating acoustic wave for all the simulated geometries, showing the reflection and transmission phenomena at the interaction points with internal defects. The red color shows the pressure peaks (compressions), whereas the blue color shows the troughs (rarefactions) of the acoustic wave during propagation. Figure 9: Simulation snapshot for the propagation of an acoustic wave within samples with internal cracks and without any defect, showing the acoustic wave interaction with internal defects at different locations for all the simulated geometries.