## 5 Conclusions  
The proposed optimized optical flow-based displacement sensor accurately detected MTS vibrations in laboratory experiments, achieving better accuracy of approximately 97% comparing with the existed optical flow-based displacement sensors. The proposed method maintained structural vibration detection accuracy exceeding 90% when utilizing UAV-recorded vibration videos. Effective compensation for six distinct UAV motions resulted in significant accuracy improvements.  
* The optimized optical flow displacement sensor proposed in this work obtains more accurate vibration detection results compared to the original optical flow method.  
Figure 21: Comparison of the Displacement Curves Computed by the Improved LK Method with the MTS Output Curves, Where the Displacement Curves are Derived from Data Collected by Fixed Cameras and UAV Cameras.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**ROI** & **Max Pt Region1** & **Min Pt Region1** & **Max Pt Region2** & **Min Pt Region2** \\ \hline Fixed Camera & 97.4\% & 94.5\% & 98.4\% & 98.9\% \\ UAV Camera & 92.4\% & 92.8\% & 96.1\% & 90.4\% \\ \hline \end{tabular}
\end{table}
Table 9: Accuracy Comparison of Region of Interest Calculation for Displacement Curves Derived from the Improved LK Method Based on Fixed and UAV Camera Data.  
* The proposed method effectively eliminated the motions of the UAV. In laboratory settings, when the UAV was employed along with the proposed method to measure vibrations, the resulting accuracy was satisfactory.
* The proposed method has successfully eliminated the motions of the UAV. In the field experiment, when using the UAV in conjunction with the proposed method to obtain vibration data, the achieved accuracy is satisfactory.
* In the field experiment, the accuracy of the measurement utilizing the UAV was approximately 93%, whereas the accuracy achieved with the fixed camera was 97%.Potential sources of error may be the lighting condition changes and the blurred image.
* When the proposed method is applied to eliminate the motions of the UAV, different fixed points selected in the background will give rise to varying degrees of errors. There are some ways to avoid these errors, such as fixing the reference point well, selecting reference targets with high contrast, and keeping the reference targets close to the structure.  
In summary, the angle-constrained optical flow algorithm proposed in this study realizes the measurement of the motion and structural response of the UAV platform, effectively eliminates the interference of UAV vibration artifacts, and significantly improves the vibration detection accuracy. It provides a new technical path for the application of visual displacement measurement in noisy environments. The limitations of traditional vision sensors are solved, and lightweight, non-contact structural vibration monitoring is realized.  
Conceptualization, X.B.; Funding acquisition, N.L. and Z.Z.; Methodology, X.B., R.X. and Z.Z.; Software, X.B. and R.X.; Supervision, X.B.; Validation, X.B.; Writing--original draft, R.X.; Writing--review and editing, X.B., N.L. and Z.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Key Laboratory of Architectural Cold Climate Energy Management, Ministry of Education, Jilin Jianzhu University (Grant No. IJZHDKF022024006); Department of Housing and Urban Rural Development of Jilin Province, China (Grant No. 2023-K-29); The Eighth Batch of Jilin Province's Youth Science and Technology Talent Support Program (Grant No. QT202412); International Science and Technology Cooperation Project of the Jilin Provincial Department of Science and Technology. (Grant No.20240402065 GH).  
Not applicable.  
Data Availability Statement: Data will be made available on request.  
The authors declare no conflicts of interest.