## 4 Conclusions  
In this paper, a novel approach for dynamic load identification on aerospace structures based on a deep convolutional network in the transform domain is proposed. The proposed approach first applies wavelet transform to the vibration signals in time domain on aerospace structures. The decomposed components are input to the designed one-dimensional convolutional network to extract the transformed domain features of the vibration signals, and subsequently predict the representation of the load in the transform domain. The proposed method avoids the explicit modelling structural transfer functions while achieving higher identification accuracy than the conventional regularization-based method. Results from ablation studies indicate that using decomposed components in the transformed domain helps the network refine its learning of signal features in different frequency ranges, leading to excellent results in random load identification. Additionally, the proposed method demonstrates a certain level of robustness to measurement noise and unknown vibration disturbances.  
In our future work, we seek to further improve the robustness of the identification approach on various types of noises or disturbances, while exploring the optimal measurement position on aerospace structures for load identification. The architecture of the network can be further optimized for a lower amount of parameters using techniques like  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Sensor Distribution** & **Case** & **RMSE** & **CC** \\ \hline \multirow{2}{*}{Symmetric} & time-domain & 0.6247 & 0.9470 \\  & ours & 0.4824 & 0.9702 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Ablations on network input in different domain. The effectiveness of the usage of wavelet transform is evaluated using random load with symmetrical sensor distribution. For the case of “time-domain”, the acceleration measurements are directly input to the network, while in the case of “ours”, the proposed method is evaluated.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Sensor Distribution** & **Noise Strength** & **Run No.** & **RMSE** & **CC** \\ \hline \multirow{6}{*}{Symmetric} & & 1 & 0.9217 & 0.8798 \\  & & 2 & 0.9007 & 0.8873 \\  & 10\% & 3 & 0.9552 & 0.8743 \\  & & 4 & 0.8903 & 0.8925 \\  & & 5 & 0.9260 & 0.8836 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Quantitative evaluation results on extra runs of the experiment of additional sensor measurement noises.  
DSC [31; 32; 33]. Since the proposed method is a supervised data-driven method, there would be a domain gap problem when applying it to unknown structures, using the unsupervised learning method, which would reduce the dependence on training data; this is a direction worth exploring further.  
Conceptualization, X.Z.; data curation, T.B. and B.L.; formal analysis, X.Z. and Q.C.; investigation, X.Z. and W.H.; methodology, X.Z. and W.H.; project administration, X.L.; software, X.Z., T.B., B.L. and J.L.; supervision, Q.C., X.L.; visualization, T.B.; writing--original draft, X.Z.; writing--review and editing, W.H., Q.C. and X.L. All authors have read and agreed to the published version of the manuscript.  
This work is supported in part by the Natural Science Foundation of China under Grant 62201479, in part by the Natural Science Foundation of Sichuan Province under Grant 2023 NSFSC1388. in part by the Key Laboratory of Medicinal and Edible Plant Resources Development of Sichuan Education Department, Chengdu University under Grant 10Y202201.  
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.  
The authors declare no conflicts of interest.