# Simulation of Full Wavefield Data with Deep Learning Approach for Delamination Identification
## 4 The Proposed DL Model for Supervised Learning  
In this research work, we developed a novel deep ConvLSTM autoencoder-based surrogate model utilising full wavefield frames of Lamb wave propagation for the purpose of data generation for delamination identification in thin plates made of composite materials. The developed DL model takes as an input of 32 frames without delamination (reference frames) representing the full wavefield and the delamination information of the respective delamination case in the form of binary images for the purpose of producing the full wavefield propagation of Lamb waves through space and time (3D matrix). The most important aspect of the DL model is the prediction of the interaction of Lamb waves with the delamination so that the delamination location, shape, and size can be estimated. The complete flowchart of the proposed DL model is presented in Figure 4. The training and evaluation process of the proposed model can be summarised in the following three steps:  
1. **Feature extraction:** As we have no labels for the dataset, the dataset is composed of delamination cases. So, the first task is to extract features from all of the delamination cases and then use these features as labels in the second step during model training. Therefore, in this step, the encoder and decoder parts of the proposed model are trained jointly, so the decoder part can be used separately for full wavefield predictions. During this step, the features are extracted with very minimal reconstruction error in a compressed form, which matches the dimensions of the latent space. 2. **Model training:** In this step, the actual model training is carried out. The full wavefield frames in a plate without delamination, along with the binary image of the respective delamination case, are fed into the DL model for training. The features extracted from encoder part of the first step are used as labels in this step, as shown in Figure 4.
3. **Evaluation of the proposed DL model on unseen data:** At this stage, both of the pretrained models (pretrained decoder from step 1 and pretrained encoder from step 2) are utilised for the prediction of the full wavefield frames on unseen data. During this step, the model just takes reference frames with the delamination information and produces the output as the full wavefield frames containing the interaction of Lamb waves with delamination. The proposed ConvLSTM autoencoder model takes 32 frames as input concatenated with a binary image, which is replicated 32 times (see Figure 4). The DL model consists of six ConvLSTM layers (see Figure 5). The first ConvLSTM layer has 32 filters, the second and third layers have 192 filters, the fourth layer has 32 filters, and the last two ConvLSTM layers have 192 filters. The kernel size of the ConvLSTM layers was set to \((3\times 3)\) with a stride of \((1)\). The padding was set to \"same\", which makes the output the same as the input in the case of stride \(1\). Furthermore, a tanh (the hyperbolic tangent) activation function was used within the ConvLSTM layers that output values in a range between \((-1\) and \(1)\). Maxpooling and upsampling were applied at each ConvLSTM layer for reducing the size of the features and the reconstruction purposes, respectively. Moreover, a batch normalisationtechnique [34] was applied at each of the ConvLSTM layers. At the final output layer, a 2D convolutional layer followed by a sigmoid activation function were applied. To alleviate the overfitting, we used an early-stopping mechanism that monitors the validation loss during the training of the model and stops the training of the model after 30 epochs if there is no improvement. The Adam optimiser was employed for backpropagation, and the MSE was used as a loss function for both training steps. The peak signal-to-noise ratio (PSNR) metric values as a function of the epoch is shown in Figure 6. During both training and validation, these metrics converged. Moreover, the  
Figure 4: The flowchart of the proposed DL model.