A stochastic finite element methodology for investigating the effects of material variability on ultrasonic guided wave propagation

Abstract

This study presents an uncertainty-aware methodological framework for analysing the propagation of ultrasonic guided waves (UGW) in aluminium panels using a Stochastic Finite Element Method (SFEM) approach. The work introduces three main contributions: (1) a literature-driven selection and assessment of multiple damage-sensitive signal features, also including a feature (f₆)—originally proposed in biomedical signal processing—which is here evaluated in UGW-based SHM and found to be highly damage-sensitive; (2) the identification, through sensitivity analysis, of robust DIs/features using a “stochastic survival” criterion to ensure reliability under intrinsic structural noise; (3) the development of a SFEM capable of assessing the combined effects of manufacturing and installation tolerances. Additionally, a systematic analysis of the variability of geometric and material parameters was performed to determine their influence on the SHM response: the less impactful parameters were considered constant in the stochastic framework to reduce computational cost without compromising accuracy. The SFEM methodology is based on a finite element (FE) model experimentally validated under pristine conditions, capable of accurately reproducing UGW propagation mechanisms. The results show that the most damage-sensitive DIs/features are also those most affected by model uncertainties, highlighting a trade-off between sensitivity and robustness. The generated numerical database serves as an important prerequisite for the development of uncertainty-aware predictive models, such as Physics-Informed Neural Networks, aimed at improving reliability in structural health monitoring systems.