## 6 Conclusions  
This study demonstrates the effectiveness of wave propagation analysis in understanding global structural behavior and local material integrity. By applying CWI to both ultrasonic waves and seismic interferometry of vibrational data, the advantages of wave propagation in damage detection were validated, surpassing the results of modal analysis. The sensitivity of wave propagation to environmental factors and prestress loss was thoroughly examined.  
While adjusting post-tensioning force was straightforward, controlling bridge temperature posed significant challenges due to outdoor fluctuations. This highlights the importance of addressing on-site measurement data, including temperature variations, for consistent comparisons. Long-term monitoring is essential to capture these effects, and our findings demonstrate the feasibility of compensating for temperature-induced changes in wave velocity through empirical relationships.  
In conclusion, this work re-evaluates the perceived limitations of vibration-based damage detection in prestressed structures. It shows that, when integrated with wave-based techniques, vibration measurements can provide valuable insights into structural health--especially in detecting subtle changes due to cracking and prestress loss. Additionally, irregularities observed in mode shapes suggest that span-specific differences in crack density may influence modal behavior, warranting further investigation.  
Future research should focus on the following. (1) Environmental compensation: enhancing the robustness of damage detection by refining the relationship between temperature and wave velocity. (2) Crack density effects: systematically studying discrepancies between modal analysis and CWI results under controlled variations in cracking density. High-resolution imaging or distributed sensing could be employed to monitor these variations, offering deeper insights into the complementary strengths and limitations of each method.  
Ultimately, this work supports the development of more comprehensive and resilient SHM strategies for PC infrastructure.  
Investigation and data curation, C.-M.L. and F.B.; writing--original draft preparation, C.-M.L.; writing--review and editing, C.-M.L., E.N. and H.I; project administration and funding acquisition, H.I., C.H. and E.N. All authors have read and agreed to the published version of the manuscript.  
This paper is part of the research conducted under the GIOTTO Project (GIOTTO: Gebaude-schwingungen: kombinierte Zustandsanalyse mit innovativem Sensorkonzept), which is financially supported by the Bundesministerium fur Bildung und Forschung (BMBF) as part of the \"Fruherkennung von Erdbeben und ihren Folgen\" program. The grant number is 03G0885D.  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
**Acknowledgments:** The authors extend their gratitude to colleagues from BAM division 8.2 for the ultrasonic testing and division 7.2 for their assistance with the post-tensioning system used in the experiment. The authors also extend their sincere thanks to the reviewers and academic editors for their insightful comments and suggestions, which have greatly contributed to enhancing the scientific rigor and clarity of this paper.  
**Conflicts of Interest:** The authors declare no conflicts of interest.