## 4 Results and Discussion
### SDL Model Implementation on Datasets Type-2: Reflection Wave Propagation Simulation
#### 4.2.2 SDL Model Simulation for Reflected Wave Propagation with Varying Frequencies and Cycles
The SDL models developed in this work are applicable for  
Figure 10: Reflected wave propagation with a varying number of cycles: A qualitative comparison between the FE and SDL simulations modeled in the rectangular domain, with the varying number of cycles with a 5 MHz central frequency with a single-point excitation source on the top edge. (**a**) represents the simulation of two cycles, and (**b**) illustrates the simulation of three cycles, at identical time instances. Figure 9: Line scans of reflected wave propagation with varying frequency: The FE- and SDL-model-generated simulations are compared, quantitatively, by extracting the displacement values, which are extracted at x = 15 mm and y = 0 to 40 mm for different time instances, from Figure 8. (**a**) Represents the line scans that are extracted from Figure 8 for 4 MHz, and (**b**) illustrates the line scans that are extracted from Figure 8, for 7 MHz in the rectangular domain. Figure 11: Line scans of reflected wave propagation with a varying number of cycles: The SDL model predicted simulation with FE simulation to examine quantitatively; the displacement values are extracted at x = 15 mm and y = 0 to 40 mm for different time instances from Figure 10. **(a)** Represents the line scans are extracted from Figure 10 for two cycles, and **(b)** illustrates the line scans are extracted from Figure 10, for three cycles in the rectangular domain. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Datasets of**} & \multicolumn{4}{c}{**MAE**} & \multicolumn{4}{c}{**RMSE**} & \multicolumn{4}{c}{**MAPE (\%)**} \\ \cline{3-14}
**Line Scan** & \multirow{2}{*}{**Varying Frequencies**} & \multicolumn{4}{c}{**Sequence of Images at**} & \multicolumn{4}{c}{**Sequence of Images at**} & \multicolumn{4}{c}{**Sequence of Images at**} \\ \cline{3-14}  & & \multirow{2}{*}{**and Cycles**} & \multirow{2}{*}{**T-1**} & \multicolumn{1}{c}{**T-2**} & \multicolumn{1}{c}{**T-3**} & \multicolumn{1}{c}{**T-4**} & \multicolumn{1}{c}{**T-5**} & \multicolumn{1}{c}{**T-1**} & \multicolumn{1}{c}{**T-2**} & \multicolumn{1}{c}{**T-3**} & \multicolumn{1}{c}{**T-4**} & \multicolumn{1}{c}{**T-5**} & \multicolumn{1}{c}{**T-1**} & \multicolumn{1}{c}{**T-2**} & \multicolumn{1}{c}{**T-3**} & \multicolumn{1}{c}{**T-4**} & \multicolumn{1}{c}{**T-5**} \\ \hline \multirow{4}{*}{Amplitude} & 5 MHz with 2 cycles & 0.00 & 0.00 & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.19 & 0.00 & 0.00 & 0.00 & 0.00 & 50.1 \\  & 5 MHz with 3 cycles & 0.01 & 0.00 & 0.02 & 0.01 & 0.01 & 0.23 & 0.22 & 0.21 & 0.05 & 0.21 & 118 & 477 & 108 & 99.2 & 111 \\ \cline{2-14}  & 4 MHz with 2 cycles & 0.00 & 0.00 & 0.01 & 0.02 & 0.01 & 0.24 & 0.12 & 0.07 & 0.13 & 0.28 & 132 & 221 & 24.8 & 44.7 & 54.0 \\  & 7 MHz with 2 cycles & 0.00 & 0.01 & 0.01 & 0.01 & 0.09 & 0.15 & 0.09 & 0.12 & 0.11 & 203 & 111 & 87.7 & 116 & 135 \\ \hline \multirow{4}{*}{Time of Flight} & 5 MHz with 2 cycles & 0.00 & 0.00 & 0.00 & 0.00 & 0.56 & 0.00 & 0.00 & 0.00 & 0.00 & 0.88 & 0.00 & 0.00 & 0.00 & 0.00 & 1.9 \\  & 5 MHz with 3 cycles & 1.14 & 1.00 & 2.86 & 0.86 & 1.59 & 2.03 & 1.68 & 5.05 & 2.72 & 2.38 & 3.03 & 2.39 & 5.44 & 2.72 & 2.95 \\ \cline{1-1} \cline{2-14}  & 4 MHz with 2 cycles & 0.36 & 1.50 & 0.21 & 0.57 & 0.79 & 0.71 & 2.87 & 0.46 & 0.93 & 1.16 & 1.51 & 2.60 & 0.78 & 1.19 & 2.03 \\ \cline{1-1}  & 7 MHz with 2 cycles & 0.36 & 0.64 & 0.43 & 0.50 & 1.14 & 0.71 & 0.96 & 0.65 & 0.71 & 2.45 & 0.81 & 1.37 & 0.93 & 0.94 & 5.21 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Reflection wave propagation on the rectangular domain with varying frequencies and cycles: The SDL model line scan amplitude and time of flight (TOF) are compared with FE using MAE, RMSE, and MAPE methods at different time instances, as shown in Figures 9 and 11.