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This research demonstrates an alternative deep learning-based approach for predictive modeling of wave propagation signals within damaged structural elements. Our goal is to evaluate the wave propagation spatio-temporal solution matrix for a given crack depth and crack location within the structural element. To achieve this purpose, we first collected the wave propagation time histories in a cracked rod for various crack depths and locations by solving governing differential equations via the spectral element method. Then we applied the Fourier neural operator (FNO) based autoencoder to learn the wavefield representation. The encoder part of the autoencoder maps the high dimensional parametric solution to a low dimensional space (latent space) and a feed-forward neural network is trained to learn this latent space by feeding corresponding parameters. For a new parameter set (crack depth and location), trained feed-forward neural network predicts the encoded solution, and the decoder part of the trained autoencoder decodes it to the corresponding high dimensional solution. The FNO based autoencoder together with feed-forward neural network achieved accurate reconstructions/predictions with minimal mean square error. Compared to time-domain spectral element approach, our deep learning-based model produces comparable results with a narrow margin of error. This deep learning-based wave propagation predictive model can be a valuable resource for generating data for a given crack depth and location, which can be used for inverse formulations and various structural health monitoring applications.
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