A Machine Learning Framework for Reduced Order Modeling of Guided Waves Propagation

In structural health monitoring, it is critical to quantify the uncertainty in the knowledge of the internal parameters, which influence the response of a mechanical system to external loading. In thin structures, the variation of the mechanical properties, influences significantly the guided wave propagation taking place when dynamical loads are applied. Computational structural mechanics is a powerful tool to accurately evaluate the impact of the uncertainty in the material properties, to the mechanical behavior of thin structures. To reduce the computational cost and provide numerical solutions in a limited amount of time, the high fidelity computational models are replaced by reduced-order models (ROMs). This paper utilizes a state-of-the-art, machine learning (ML)-based ROM methodology combined with a singular value decomposition (SVD) update algorithm to reduce the simulation time. The developed framework, mentioned as FastSVD-ML-ROM, includes both linear and non-liner dimensionality reduction techniques by using SVD and convolutional autoencoders to extract latent variables. Fully connected neural networks are utilised to map the input parameter sets to the latent variables and long-short term memory networks, to predict the temporal scales. To evaluate the performance of FastSVD-ML-ROM the guided wave propagation taking place in a lightweight aluminum plate is examined. The numerical data needed to train and test FastSVD-ML-ROM, is obtained with simulations performed with the finite element method by varying the young modulus, poisson ratio, and the density of the plate. The accuracy of the predicted solutions showcases the robustness of the FastSVD-ML-ROM and demonstrates the ability to quantify the uncertainties introduced in the material properties of the propagating medium by significantly reducing the computational cost.