# Simulation of Full Wavefield Data with Deep Learning Approach for Delamination Identification
## 3 Dataset Computation and Preprocessing
### Dataset Computation  
A synthetic dataset of propagating waves in carbon fibre-reinforced composite plates was computed by using the parallel implementation of the time domain SEM [15]. The model is based on the Mindlin-Reissner theory of plates, which means that five degrees  
Figure 1: Flowchart of the proposed inverse method for damage identification. of freedom are available at each node, namely three translational displacements and two rotational displacements. The input signal was a five-cycle Hann window-modulated sinusoidal tone burst. The carrier frequency was assumed to be 50 kHz. The total wave propagation time was set to 0.75 ms. The number of time integration steps was 150,000, which was selected for the stability of the central difference scheme. It should be added that the PZT was not fully modelled. The excitation was applied in the form of equivalent piezoelectric forces. Additionally, the stiffness and mass were modified in plate elements corresponding to the PZT position. The material was a typical cross-ply CFRP laminate. The stacking sequence \([0/90]_{4}\) was used in the model. The delamination was modelled between the third and fourth lamina at 3/8 of the total thickness. The properties of a single ply were as follows [GPa]: \(C_{11}=52.55\), \(C_{12}=6.51\), \(C_{22}=51.83,C_{44}=2.93,C_{55}=2.92,C_{66}=3.81\). The assumed mass density was 1522.4 kg/m\({}^{3}\). These properties were selected so that the wavefields simulated numerically would match the wavefields measured by the SLDV on real CFRP specimens. The wavelength of the dominating A0 Lamb wave mode was 21.2 mm. This information was utilised for the automatic generation of unstructured meshes so that at least 10 nodes per wavelength were obtained. A total of 475 cases were simulated, thus representing Lamb waves propagation and interaction with single delamination for each case. The following random factors were used in the simulated delamination scenarios:  
* The coordinates of the centre of delamination;
* The delamination geometrical size determined by the ellipse minor and the major axis randomly selected from the range 10-40 mm;
* The delamination angle randomly selected from the range 0\({}^{\circ}\)-180\({}^{\circ}\). An embedded MATLAB function was used for randomisation. However, the coordinates of the centre of delamination very close to the PZT were excluded. It should be added that two types of delamination, as shown in Figure 2, were possible, namely fully embedded or opened at the edge. The delamination modelling was realised by writing custom geometry files, which were used to generate an unstructured mesh consisting of quadrilateral elements by using GMSH software [32] (one mesh per delamination scenario). An exemplary mesh of quadrilateral elements is shown in Figure 3 in which the green elements highlight the delamination, whereas the red elements represent the location of the piezoelectric actuator. Next, the mesh was modified by doubling elements and splitting nodes at the delamination region. This resulted in the so-called zero-volume delamination. Next, the quadrilateral elements were converted to 36-node spectral elements by using a custom MATLAB script. The wave propagation problem was solved using an in-house  
Figure 2: Numerical and experimental setup showing the types of possible delaminations (embedded and opened at the edge), piezoelectric transducer (PZT), and scanning laser Doppler vibrometer (SLDV). code of the time domain SEM, which was run on the GPU. The obtained animations of the propagating guided waves were converted to images (frames). The dataset contains 475 different delamination cases, with 512 frames per case, thus producing a total number of \(243,200\) frames with a frame size of \((500\times 500)\) pixels representing the geometry of the specimen surface of size \((500\times 500)\) mm\({}^{2}\). The frames in the dataset are 8-bit.png greyscale images. As was mentioned before, the dataset has been made available online [31].