Physics-based Reduced Order Modeling for Uncertainty Quantification of
  Guided Wave Propagation using Bayesian Optimization
G. I. Drakoulas T. V. Gortsas D. Polyzos
In the context of digital twins, structural health monitoring (SHM)
constitutes the backbone of condition-based maintenance, facilitating the
interconnection between virtual and physical assets. Guided wave propagation
(GWP) is commonly employed for the inspection of structures in SHM. However,
GWP is sensitive to variations in the material properties of the structure,
leading to false alarms. In this direction, uncertainty quantification (UQ) is
regularly applied to improve the reliability of predictions. Computational
mechanics is a useful tool for the simulation of GWP, and is often applied for
UQ. Even so, the application of UQ methods requires numerous simulations, while
large-scale, transient numerical GWP solutions increase the computational cost.
Reduced order models (ROMs) are commonly employed to provide numerical results
in a limited amount of time. In this paper, we propose a machine learning
(ML)-based ROM, mentioned as BO-ML-ROM, to decrease the computational time
related to the simulation of the GWP. The ROM is integrated with a Bayesian
optimization (BO) framework, to adaptively sample the parameters for the ROM
training. The finite element method is used for the simulation of the
high-fidelity models. The formulated ROM is used for forward UQ of the GWP in
an aluminum plate with varying material properties. To determine the influence
of each parameter perturbation, a global, variance-based sensitivity analysis
is implemented based on Sobol' indices. It is shown that Bayesian optimization
outperforms one-shot sampling methods, both in terms of accuracy and speed-up.
The predicted results reveal the efficiency of BO-ML-ROM for GWP and
demonstrate its value for UQ.