Physics-based reduced order modeling for uncertainty quantification of guided wave propagation using Bayesian optimization

Abstract

Guided wave propagation (GWP) is commonly employed for the design of SHM systems. However, GWP is sensitive to variations in the material properties, often leading to false alarms. To address this issue, uncertainty quantification (UQ) is employed to improve the reliability of the predictions. Computational structural mechanics is a useful tool for the simulation of GWP. Even so, the application of UQ methods requires numerous solutions, while large-scale, transient GWP simulations increase the computational cost. In this paper, we propose a machine learning (ML)-based reduced order model (ROM), annotated as BO-ML-ROM, to decrease the computational time of the GWP simulation. The ROM is integrated with a Bayesian optimization (BO) framework to adaptively sample the data for the ROM training. The results showed that BO outperforms one-shot sampling methods, both in terms of accuracy and speed. The developed ROM, which is orders of magnitude faster than the original solver, is then applied for forward uncertainty quantification of the GWP in an aluminum plate and a composite panel under varying material properties. The UQ analysis reveals the higher impact of the uncertainties in the wave reflections. Furthermore, to compute the influence of the material properties on the predictions, a sensitivity analysis (SA) is performed using the variance-based Sobol’ indices and the Shapley additive explanations, where it is shown that the uncertainties in the elastic properties have a varying influence across time. The predicted results reveal the efficiency of BO-ML-ROM for the simulation of the GWP and demonstrate its utility for UQ and SA.