# Simulation of Full Wavefield Data with Deep Learning Approach for Delamination Identification
###### Abstract  
In this work, a novel approach of guided wave-based damage identification in composite laminates is proposed. The novelty of this research lies in the implementation of ConvLSTM-based autoencoders for the generation of full wavefield data of propagating guided waves in composite structures. The developed surrogate deep learning model takes as input full wavefield frames of propagating waves in a healthy plate, along with a binary image representing delamination, and predicts the frames of propagating waves in a plate, which contains single delamination. The evaluation of the surrogate model is ultrafast (less than 1 s). Therefore, unlike traditional forward solvers, the surrogate model can be employed efficiently in the inverse framework of damage identification. In this work, particle swarm optimisation is applied as a suitable tool to this end. The proposed method was tested on a synthetic dataset, thus showing that it is capable of estimating the delamination location and size with good accuracy. The test involved full wavefield data in the objective function of the inverse method, but it should be underlined as well that partial data with measurements can be implemented. This is extremely important for practical applications in structural health monitoring where only signals at a finite number of locations are available. lamb waves; structural health monitoring; surrogate modeling; delamination identification; deep learning; autoencoders; ConvLSTM +
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In our previous works [8; 11], full wavefield data were directly processed to obtain damage maps. Here, full wavefield data are used to train a deep learning (DL) model for predicting guided wave interactions with defects. Such a DL model has wider potential application, including cases when sparse data are available. Full wavefield scans offer valuable insights into the interaction of guided waves with defects. However, acquiring the full wavefield of guided waves is a time-consuming process. Furthermore, the damage identification methods operating on the full wavefield cannot be directly extended to the cases when only spatially sparse data are available, e.g., an array of sensors is installed on the structure. In such a case, usually, an inverse procedure is employed in which efficient methods for solving wave equations are required. However, the numerical modelling of ultrasonic guided wave propagation in solid media exhibiting discontinuities, such as damage, is complex; it requires fine discretisation and is computationally intensive. Even though methods such as the p-version of the finite element method (p-FEM) [12], the isogeometric analysis (IGA) [13] approach, the spectral cell method (SCM) [14], and the time domain spectral element method (SEM) [15] are more efficient and accurate than the classical FEM with linear elements, they are not efficient enough to be used in inverse methods (about half the number of nodes is required to obtain the same accuracy according to [16]). In the end, calling the objective function for each damage case scenario in which the forward solver is used is unfeasible, because computations for even a simple plate can take up to 1 h.  
An alternative approach is to utilise a surrogate model for generating full wavefield data or time series-resembling signals registered at an array of sensors. A surrogate model imitates the behaviour of the simulation model while replacing time-consuming forward simulations with approximate solutions. It can be based on DL, as well as physics-informed, neural networks [17; 18]. DL has seen extensive research and successful implementation in the fields of NDT and SHM. The convolutional neural network (CNN) is among the most popular DL architectures. Initially introduced for image processing, the CNN has now been extended to various research domains, including NDT and SHM applications such as damage detection, localization, and characterisation [19; 20; 21].