Parametric Damage Mechanics Empowering Structural Health Monitoring of 3D Woven Composites

Abstract

This paper presents a data-driven structural health monitoring (SHM) method by the use of so-called reduced-order models relying on an offline training/online use for unidirectional fiber and matrix failure detection in a 3D woven composite plate. During the offline phase (or learning) a dataset of possible damage localization, fiber and matrix failure ratios is generated through high-fidelity simulations (ABAQUS software). Then, a reduced model in a lower-dimensional approximation subspace based on the so-called sparse proper generalized decomposition (sPGD) is constructed. The parametrized approach of the sPGD method reduces the computational burden associated with a high-fidelity solver and allows a faster evaluation of all possible failure configurations. However, during the testing phase, it turns out that classical sPGD fails to capture the influence of the damage localization on the solution. To alleviate the just-referred difficulties, the present work proposes an adaptive sPGD. First, a change of variable is carried out to place all the damage areas on the same reference region, where an adapted interpolation can be done. During the online use, an optimization algorithm is employed with numerical experiments to evaluate the damage localization and damage ratio which allow us to define the health state of the structure.

Empowering optimal transport matching algorithm for the construction of surrogate parametric metamodel

“…The concept of interpolation between more than two distributions is relevant in various fields, including Machine Learning and Statistics. In these context, Euclidean distance is often used as a measure of dissimilarity or similarity between these distributions as is it applied in [16]. When interpolating between more than two distributions using the Wasserstein distance, the mathematical theory does not have a solid foundation.…”