## 5 Discussions and Future Directions  
The proposed robust DL-based method is essential and feasible due to the correlation patterns under the same loading field, the non-linearity of the correlation, and the DL-based implementation of missing data imputation and damage identification. Therefore, this method is suitable for monitoring data of various response types (such as displacement, strain, etc.) and structures.  
However, this method has some limitations. One limitation is the maximum length of the LSTM-structured model, which can be computationally complex for a recurrent neural network. Therefore, the correlation learned by this method is more suitable for short-term loading events such as vehicle loading. Another limitation lies in the difficulty of fusion with the hand-crafted features, such as the modal parameters, which may not be suitable for vibration data due to higher sampling frequencies and the developed hand-crafted modal features.  
Considering the above discussions and limitations, more advanced DL models such as CNN and transformer-based models can be developed to learn spectral features and longer correlations from time series data. Additionally, the explanation of self-learning features should be explored. Efficient fusion models of self-learning and hand-crafted features should also be valued to improve the effectiveness of this method.  
Conceptualization, S.W.; methodology, S.W.; software, S.W. and F.D.; validation, X.T. and P.W.; formal analysis, F.D., X.T. and P.W.; investigation, F.D., X.T. and P.W.; resources, F.D., X.T. and P.W.; data curation, F.D., X.T. and P.W.; writing--original draft preparation, S.W.; writing--review and editing, S.W.; visualization, S.W.; supervision, S.W.; project administration, S.W.; funding acquisition, S.W. All authors have read and agreed to the published version of the manuscript.  
Figure 9: Damage identification based on the reconstruction error.  
**Funding:** This work is financially supported by the National Natural Science Foundation of China (Grant Nos. 52208311, 51921006, and 52192661).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** [[http://www.schm.org.cn/#/IPC-SHM,2020/dataDownload](http://www.schm.org.cn/#/IPC-SHM,2020/dataDownload)]([http://www.schm.org.cn/#/IPC-SHM,2020/dataDownload](http://www.schm.org.cn/#/IPC-SHM,2020/dataDownload)).  
**Acknowledgments:** The authors would like to thank the organizations of the International Project Competition for SHM (IPC-SHM 2020), ANCRiSST, Harbin Institute of Technology (China), and the University of Illinois at Urbana-Champaign (USA) for their generosity in providing the invaluable data from actual structures.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
**Nomenclature**  
List of symbols  
\(\mathbf{x}\)Inputs of the model  
\(\mathbf{y}\)Targets of the model  
\(\mathbf{\alpha}(\cdot)\)Tanh-formed activation function  
\(\mathbf{y}\)Outputs of the model  
\(L\)Number of layers (Depth)  
\(L(\cdot)\)Loss function  
\(\mathbf{x}^{(t)}\)Inputs at step in LSTM  
\(\mathbf{W}^{t}\)Weights of the l-th layer  
\(\mathbf{h}^{(t)}\)Short memory state at t step in LSTM  
\(\mathbf{b}^{l}\)Bias of the l-th layer  
\(\mathbf{C}^{(t)}\)Long memory state at t step in LSTM  
\(\mathbf{W}_{t}\)\(\mathbf{W}_{i}\)\(\mathbf{W}_{o}\), \(\mathbf{W}_{c}\)Weights for states of forget/input/output gate and state update in LSTM  
\(\mathbf{U}_{t}\)\(\mathbf{U}_{t}\)\(\mathbf{U}_{t}\)\(\mathbf{U}_{t}\)Weights for inputs of forget/input/output gate and state update in LSTM  
\(\mathbf{b}_{b_{i}}\)\(\mathbf{b}_{b_{o}}\)\(\mathbf{b}_{b_{o}}\)Bias of forget/input/output gate and state update in LSTM  
\(f^{(t)},i^{(0)},o^{(t)}\)Forget gate, input gate, and output gate  
\(\mathbf{\theta}\)Parameter set of weights and bias for a neural network model  
\(f_{AE}(\cdot),f_{DE}(\cdot)\)Encoder and Decoder in the Autoencoder frame