## 5 Conclusions  
An adaptive OMA method using a hybrid neural network is proposed and applied to extract modes from the acceleration response signals under non-white excitation. In this work, the proposed method has fewer layers and greatly fewer characteristic parameters, which simplifies the model and reduces the time cost of training and testing. The small sample dataset makes it possible to achieve the highest accuracy in the shortest possible time. The output function proposed in this paper is only related to the peak point of the singular value curve, which greatly reduces the computational cost, and can be used for non-white noise excitation.  
1. According to the comparison of the training and test results of the same dataset with different network structures, it shows that the hybrid neural network is optimal.
2. A total of 11 beams with different qualities are numerically simulated. The training time and convergence speed of the response data with different SNRs are the same, and the test results of the first beam are the same, showing that the anti-noise ability of the proposed method is strong. In addition, the effectiveness of the method is proved by comparing with the finite element solution, analytical solution, and the test results of the first beam.
3. The conventional OMA methods are used to identify the modal parameters of the beam. There are false modes and mode leakage when identifying the modal parameters of the response under non-white noise excitation (excitation spectrum 2 and excitation spectrum 3). Taking the analysis results as a reference, the results of different methods for identifying the response under non-white noise excitation are compared. It is found that the proposed method has no modal leakage and the highest identification accuracy. Therefore, the proposed method is not limited by the excitation type and is more suitable for the actual ambient excitation.
4. The results of the proposed method for identifying the rudder surface under different noise excitations are consistent, which shows that the anti-noise ability of the method is strong. Compared with the analysis results, the identification errors of the first four modal frequencies are all less than 0.2%, so the identification accuracy of the proposed method is high.  
Conceptualization, M.Q. and H.C.; methodology, M.Q., H.C. and R.Z.; software, M.Q.; validation, M.Q., H.C. and R.Z.; formal analysis, M.Q., H.C. and X.H.; investigation, M.Q. and S.R.; resources, H.C., R.Z. and X.H.; data curation, M.Q. and S.R.; writing--original draft preparation, M.Q.; writing--review and editing, H.C., R.Z. and X.H.; visualization, M.Q.; supervision, H.C., R.Z. and X.H.; project administration, H.C.; funding acquisition, H.C. All authors have read and agreed to the published version of the manuscript.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Excitations**} & \multicolumn{4}{c}{**The Proposed Method**} \\ \cline{2-5}  & **1 st** & **2 nd** & **3 rd** & **4 th** \\ \hline Excitation spectrum 1 (\%) & 0.19 & 0.04 & 0.049 & \(-\)0.049 \\ Excitation spectra & 0.19 & 0.04 & 0.049 & \(-\)0.049 \\
2 and 3 (\%) & 0.19 & 0.04 & 0.049 & \(-\)0.049 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The relative error of the proposed method for identifying the rudder surface.  
**Funding:** This work was supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).  
**Conflicts of Interest:** The authors declare no conflict of interest.