A general probabilistic framework for impact localisation based on flexural wave propagation

Flexural wave propagation-based impact localisation methods for composite structures face challenges in accurately estimating the group velocity profile (GVP) and quantifying localisation uncertainties due to wave dispersion . This paper introduces a two-step probabilistic framework to address these challenges. In the first step, a probabilistic model for GVP estimation is developed using Bayesian inference, leveraging wave dispersion relations from classical laminate theory to define the GVP probability space. Three GVP estimation methods depending on structural complexity and available knowledge are explored: physics-based, data-driven, and hybrid physics-data method. The estimated GVP facilitates multi-frequency probabilistic impact localisation in the second step, wherein the maximum likelihood impact location is identified solely using fast gradient-based optimisation. Experimental impact testing on laminated composite flat, stiffened, and sandwich panels validates the framework, demonstrating its efficiency, accuracy, and scalability in GVP estimation, impact localisation, and uncertainty quantification across diverse composite structures. The data-driven method notably requires only sparse reference impacts and a limited sensor network (each with no more than four) to accurately estimate GVPs for these structures.