## 4 Conclusions  
Unlike conventional dual-sphere tags, this work pioneers hull-integrated acoustic tags through scalable cylindrical geometry, where the acoustic encoding scheme based on multilayered elastic cylindrical shells outperforms existing methods (e.g., dual-sphere configurations and multilayered hemispherical shells) in coding capacity, environmental robustness, and noise tolerance. This study addresses the high-density identification requirements for autonomous underwater vehicles (AUVs) by proposing a passive acoustic identification tag (AID) design based on multilayered elastic cylindrical shell structures. Through theoretical modeling using the normal series method, finite element numerical validation, and large-scale material combination simulations, we elucidate the regulatory mechanisms of material layering strategies on far-field acoustic scattering characteristics and establish a time-frequency domain fusion encoding system with high robustness.  
Figure 10: Detection error rate variation with matrix dimensionality (boxplot, the grey dotted line represents the average value, the black solid line within the box is the median line, and the black dots are the outliers).  
The results demonstrate that the proposed scheme achieves competitive performance in encoding capacity and noise resistance, offering an innovative solution for underwater collaborative navigation. Key findings include the following.  
By adjusting the material stacking sequence and impedance matching in multilayered elastic cylindrical shells, distinctive time-domain multi-peak echo features can be engineered. These features enable high-information-density encoding via peak interval sequences, while optimized impedance differences effectively suppress encoding distortion.  
Under 3 dB SNR conditions, Jaccard similarity analysis and Bootstrap resampling quantify the influence of layering strategies on encoding uniqueness. Combined with rapid matching algorithms (single recognition cycle <1.5 s) and noise-resistant processing, the system achieves a 99% recognition success rate in complex acoustic environments.  
Increasing the number of material layers significantly expands encoding combinations: three-, four-, and five-layer structures generate 210, 840, and 2520 unique codes, respectively (Table 4). This represents a substantial improvement over traditional dual-sphere tags, which offer only a limited number of combinations.  
Conceptualization, Z.P.; methodology, Z.D., S.X. and Z.P.; software, Z.D.; validation, Z.D.; formal analysis, Z.D.; investigation, Z.D. and S.X.; resources, Z.D. and Z.P.; data curation, Z.D.; writing--original draft preparation, Z.D.; writing--review and editing, Z.D., Z.P. and S.X.; visualization, Z.D. and Z.P.; supervision, Z.P. and S.X.; project administration, Z.P. and S.X.; funding acquisition, Z.P. All authors have read and agreed to the published version of the manuscript.  
National Natural Science Foundation of China (52201397); Laboratory of Science and technology on integrated Logistics Support, National University of Defense Technology (WDZC20235250311); Open Fund of Ship Vibration and Noise Key Laboratory (6142204230709, 6142204240202), Natural Science Foundation of Hunan Provincial (2023)[J60544).  
Not applicable.  
All evaluated data are presented in this paper in graphical form. Original data of this study are available upon request from the corresponding author.  
The authors declare no conflicts of interest.