## 5 Conclusions  
This paper focuses on flexible PV support structures, conducting field modal testing and proposing a modal property identification method based on multi-source data fusion. The high-order modal properties of the actual flexible PV structures were obtained through field measurements. Based on the measured modal properties, response surface-based FE model updating of the flexible PV support structure was accomplished. The following conclusions can be drawn from this study:  
1. The effectiveness of the field modal testing method was verified. The results indicate that computer vision-based measurement enables high-precision identification of the first two order vibration modes of the PV support structure. For high-order modes, due to weaker vibration energy, ambient excitation combined with velocity sensors are more suitable.
2. The first four modal properties of the flexible PV support structure were identified. The first four modal frequencies are 1.49 Hz, 1.79 Hz, 2.98 Hz, and 3.53 Hz, and the first four damping ratios are 1.7%, 0.7%, 1.3%, and 0.4%. It is noteworthy that the damping ratios of the first- and second-order torsional modes are only 0.7% and 0.4%, respectively, indicating that the low-damping characteristics of the flexible PV structure should be given particular attention in the design practice.
3. A response surface-based finite element model updating method for flexible PV support structures was proposed. Based on the FE model updating results, the modeling of flexible photovoltaic support structures should consider a cable tension reduction factor of 0.866, a 2 kg metal frame mass, and the modeling of the columns. Validation against field-measured modal frequencies demonstrates significant error reduction: relative discrepancies in the first four modes decreased from 13.61%, 23.92%, 3.36%, and 21.11% to 0.5%, 1.39%, 8.72%, and 0.54%. The high fitting accuracy of the response surface surrogate model demonstrates its feasibility as an alternative to full finite element analyses.  
Figure 18: Convergence curve of the objective function.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Response Feature** & **Field-Measured** & **Initial Value** & **Updated Value** & **Initial Error** & **Updated Error** \\ \hline \(f_{1}\) (Hz) & 1.488 & 1.693 & 1.481 & 13.78\% & 0.47\% \\ \hline \(f_{2}\) (Hz) & 1.775 & 2.205 & 1.802 & 24.22\% & 1.52\% \\ \hline \(f_{3}\) (Hz) & 2.980 & 3.081 & 2.728 & 3.38\% & 8.46\% \\ \hline \(f_{4}\) (Hz) & 3.526 & 4.242 & 3.516 & 20.31\% & 0.28\% \\ \hline \hline \end{tabular}
\end{table}
Table 9: Comparison of modal frequencies before and after the update.  
**Author Contributions:** Conceptualization, C.Y. and M.H.; methodology, C.Y. and K.C.; formal analysis C.Y. and K.C.; investigation, M.H. and C.Y.; data curation C.Y. and X.L.; writing--original draft preparation, C.Y.; writing--review and editing, all authors; supervision, M.H. All authors have read and agreed to the published version of the manuscript.  
This research was partially supported by Ningbo Key R&D Program (Project No. 2023Z221 and 2024Z287), the National Natural Science Foundation of China (Project No. 52478564), and Research Grants Council of Hong Kong Theme-based Research Scheme (Grant No. T22-501/23-R).  
Not applicable.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
The authors would like to acknowledge Jiangsu Evershine Energy Technology Co., Ltd., for providing organization and coordination assistance during field testing.  
The authors declare no conflicts of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} PV & Photovoltaic \\ FE & Finite element \\ PSO & Particle swarm optimization \\ VMD & Variational mode decomposition \\ NExT & Natural excitation technique \\ SDESA & Smoothed discrete energy separation algorithm \\ HCEO & Half-cycle energy operator \\ MIC & Mutually independent component \\ \end{tabular}