# Simulation of Full Wavefield Data with Deep Learning Approach for Delamination Identification
## 7 Conclusions and Future Work  
In this research work, we presented a novel DL-based surrogate model. The developed model adopts the architecture of the autoencoder-decoder in conjunction with the ConvLSTM algorithm for the prediction of a full wavefield containing interacting Lamb waves with delamination. In the proposed model, the encoder and decoder parts were trained jointly on a synthetic dataset consisting of frames, which contain wave patterns of the delamination reflections and changes in the wavefront due to delamination. Then, the encoder was trained separately on reference data without delamination. The delamination information in the form of binary images has also been provided, along with the reference images to the encoder part for training the encoder and the final prediction of the frames propagating in the plate with delamination. In simple words, this DL-based surrogate model takes the full wavefield frames of propagating waves in a healthy plate as input and predicts full wavefields in a plate that contains single delamination.  
The proposed DL model performed well, as was proven by the results. The proposed DL model is helpful for the prediction of the full wavefield data from the time of excitation initiation to the desired simulation time. The predicted wavefield from the proposed architecture can be used for inverse problems in NDT (shown here) and SHM (possibly in the future). The wavefield prediction using the proposed DL model is ultrafast: therefore, objective functions, which require multiple evaluations, can be applied in the inverse methods. In contrast, such an approach is unfeasible using conventional forward solvers, e.g., based on p-FEM or SEM.  
It should be noted, however, that the generalisation capabilities of the applied DL model highly depend on the dataset provided for training. The method was tested only on one type of CFRP layup and on one type of excitation signal. For the real case scenario, the DL model should be trained considering the complexity of the inspected structure such as  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Case Number**} & \multicolumn{3}{c}{**IoU**} \\ \cline{2-4}  & & **Current** & **[11]** \\ \hline \multirow{2}{*}{1} & run 1 & 0.25 & \multirow{2}{*}{0.74} \\  & run 2 & 0.41 & & \\  & run 3 & 0.34 & & \\ \hline \multirow{2}{*}{2} & run 1 & 0.84 & \multirow{2}{*}{0.76} \\  & run 2 & 0.32 & & \\ \cline{1-1}  & run 3 & 0.34 & & \\ \hline \multirow{2}{*}{3} & run 1 & 0.78 & \multirow{2}{*}{0.88} \\  & run 2 & 0.60 & & \\ \cline{1-1}  & run 3 & 0.85 & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Damage identification evaluation metrics for three numerical cases.  
the stiffeners and material properties. Therefore, the initial computational effort is high in comparison to data-driven-only approaches.  
It is planned to test the proposed damage identification framework on experimental data in the future.  
Conceptualisation, S.U. and P.K.; methodology, S.U. and P.K.; software, S.U., P.K., and A.A.I.; validation, S.U. and A.A.I.; formal analysis, P.K.; investigation, S.U.; resources, P.K.; data curation, A.A.I.; writing--original draft preparation, S.U. and P.K.; writing--review and editing, E.C. and W.O.; visualisation, S.U. and P.K.; supervision, P.K.; project administration, W.O.; funding acquisition, W.O. and E.C. All authors have read and agreed to the published version of the manuscript.  
The research was funded by the Polish National Science Centre under grant agreements no 2019/01/Y/ST8/00060.  
Not applicable  
The dataset is made available online at [[https://doi.org/10.5281/zenodo.5414555](https://doi.org/10.5281/zenodo.5414555)]([https://doi.org/10.5281/zenodo.5414555](https://doi.org/10.5281/zenodo.5414555)) (accessed on 3 September 2021) so that the results can be easily replicated. See also reference [31].  
The authors declare no conflicts of interest.