## 5 Conclusions
As a preliminary study, the validation findings indicate that the transfer matrix-based damage localization method shows promise for practical application in real-world engineering settings. This innovative approach holds potential for being integrated into advanced online structural health monitoring systems, offering a robust solution for detecting and localizing damage in bridges under various operational conditions. It is important to acknowledge that while the proposed method offers the aforementioned benefits, its applicability is predicated on the assumption that the bridge system behaves linearly, even with local structural damage, and the reconstruction process is essentially framed as a multiple linear regression problem. For large-span bridges characterized by significant nonlinear behavior, the proposed method may not be appropriate. Instead, more sophisticated time-related models that leverage extensive databases with detailed time-varying traffic loading information may be required to accurately simulate the time-varying nonlinear transfer matrix. Furthermore, when selecting base cross-sections for analysis, it is crucial to choose locations that are less likely to be affected by damage or are situated far from regions prone to damage. This strategy helps to mitigate the risk of encountering nonlinear mechanical situations that could render the proposed method ineffective. In addition, the accuracy of the proposed method is inevitably affected by noise conditions, which is the primary reason this study opted for inclination measurements for damage localization. The other machine learning methods need to be tested and compared to achieve better reconstruction results. Additionally, since mode shape functions may remain almost constant even with overall material degradation, the proposed method might also be ineffective in detecting long-term bridge degradation. Also, this study indicates the influence of distance between sensors and the damage location, which is another important issue involving optimal sensor placement. These limitations are recognized, and these issues will be the focus of further investigation in future studies to enhance the method's robustness and applicability to a broader range of bridge monitoring scenarios. Conceptualization, methodology, software, validation, and writing--original draft preparation, X.L. ; investigation, writing--original draft preparation, C.W. ; writing--review and editing, supervision, and funding acquisition, L.S. ; resources, data curation, W.Z. All authors have read and agreed to the published version of the manuscript. The following cooperation Project of Shanghai Qi Zhi Institute (NO. SQZ202310); Fujian Provincial Department of Science and Technology, China (Optimization design and key technology research of urban bridge cluster monitoring; Grant NO. 2023Y0040). Not applicable. The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy. Author [PERSON] was employed by the company Fujian Provincial Construction Engineering Quality Testing Center Co., LTD, Fujian Academy of Building Research Co., LTD. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.