## 3 Markov Chain Monte Carlo Algorithms
### Transitional Markov Chain Monte Carlo (TMCMC)
#### 3.2.3 Implementation and Algorithmic Steps
Future research will focus on advancing LFI methods and integrating machine learning techniques to overcome the limitations of traditional Bayesian model updating, thereby improving structural damage detection and model updating in complex, large-scale systems. Conceptualization, J.Z. ; Methodology, L.L., H.C. and J.Z. ; Software, H.C. and J.Z. ; Validation, H.C. and S.W. ; Formal analysis, L.L. and J.Z. ; Writing--original draft, L.L. and J.Z. ; Writing--review & editing, H.C., S.W. and J.Z. ; Funding acquisition, L.L. All authors have read and agreed to the published version of the manuscript. Funding Funding for this work was provided by the Scientific Research Project of the Hubei Provincial Department of Education (No. B2022490 and No. B2022491). The support is gratefully acknowledged. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data and codes used in this study are publicly available and can be accessed at [[https://github.com/Jice1991](https://github.com/Jice1991)]([https://github.com/Jice1991](https://github.com/Jice1991)) (accessed on 19 September 2024). The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ## References

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