## 3 Verifications and Results
### Effectiveness of AID Tags  
Time-domain echo signals and their corresponding AID tags for different material layer arrangements in a three-layer cylindrical shell (outer radius: 0.25 m, uniform layer thickness: 0.01 m) are shown in Table 3.  
The barcodes in Table 3, when decoded, exist as 0-1 binary sequences at the host terminal. For binary existence-based set data, target recognition can be performed using the Mean Jaccard Index (MJI) [26], as defined in Equation (16). To enhance recognition accuracy, multiple sampling analyses were conducted, with the aggregated results presented in Table 4.  
\[Sim(A,B)^{Jaccard}=\frac{\left|A\cap B\right|}{\left|A\cup B\right|} \tag{16}\]  
where  
\(A,B=\) Binary code sets from clean/noisy signals. \(\left|*\right|=\) Cardinality of set. AUVs typically employ aluminum alloys or high-strength steel for structural frames and pressure hulls [27]. To further analyze the impact of metallic backplates on AID tag feature recognition, an additional thin metal layer (0.002 m) was introduced under the same conditions as Table 4 for MJI detection comparison. The results are presented in Table 5.  
For cylindrical shells internally filled with air, the addition of rigid internal structures has minimal impact on target feature recognition, as demonstrated in Table 4, where the average recognition rate remains largely unchanged. To further investigate the diversity and effectiveness of AID tags, seven materials from Table 1 (excluding water, structural steel, and aluminum) were selected. The study systematically controls material permutation sequences and layer counts, with the specific combinatorial configurations quantified in Table 6.  
A Jaccard similarity coefficient comparison was conducted between a total of 3570 datasets and their corresponding counterparts with added Gaussian noise, with the results illustrated in Figure 5.  
As illustrated in the heatmap in Figure 5, the red points within the circled area represent recognition errors caused by the co-arrangement of materials with similar impedance. Statistical analysis reveals that these errors are most significantly influenced by the distinct layered combinations of Acrylic Acid (AA), PMMA, and PVC. The average power reflection coefficients for these three materials under varying combinations are shown in Figure 6.  
As shown in Figure 7, when materials with low acoustic impedance differences are employed, the average power reflection coefficient remains below 0.05 at a thickness of 0.01 m. This diminishes the characteristic features of the target echo, necessitating the avoidance of layered configurations using materials with closely matched acoustic impedance. \begin{table}
\begin{tabular}{l l} \hline
**Configuration Name** & **Environmental Parameter** \\ \hline RAM & 32 GB DDR4 (3200 MHz) \\ \hline COMSOL Multiphysics & 6.2 \\ \hline MATLAB & R2024b \\ \hline \end{tabular}
\end{table} 
Table 2: _Cont._ \begin{table}
\begin{tabular}{c c} PMMA-PTFE-LDPE & \\ LDPE & \\ PMMA-LDPE & \\ PTFE & \\ PTFE-PMMA-LDPE & \\ LDPE & \\ PTFE-LDPE-PMMA & \\ PMMA & \\ PMMA & \\ \end{tabular}
\end{table} 
Table 3: Time-domain echoes and corresponding AID tags for six three-layer polymer combinations (outer radius 0.25 m, layer thickness 0.01 m). Binary encoding based on peak intervals demonstrates unique signatures despite 3 dB Gaussian noise. As delineated in Figure 7, the intervals 1-210, 211-1050, and 1051-3570 correspond to three-, four-, and five-layered media, respectively. A 95% confidence interval Bootstrap resampling analysis [22] was applied to calculate the Jaccard similarity coefficients between noise-containing and noise-free echo signals from identical materials in the diagonal regions \begin{table}
\begin{tabular}{c c} \hline
**Comparison Data** & **MJI (\%)** \\ \hline PMMA-PTFE-LDPE & 99.02 \\ \hline PMMA-LDPE-PTFE & 98.24 \\ \hline PTFE-LDPE-PMMA & 98.71 \\ \hline PTFE-PMMA-LDPE & 98.27 \\ \hline LDPE-PMMA-PTFE & 97.58 \\ \hline LDPE-PTFE-PMMA & 97.40 \\ \hline Mean & 98.20 \\ \hline \end{tabular}
\end{table}