Experimentally Derived Weight Distribution Function for Probabilistic Damage Imaging Using Guided Waves

Abstract

The reconstruction algorithm for probabilistic inspection of defects (RAPID) is widely employed to localize damage in thin-walled structures using guided waves. This method constructs probabilistic damage maps using damage indices (DIs) of the sensing paths in a sensor network and associated weight distribution functions (WDFs). Accurate weight distribution function (WDF) estimation is crucial for determining the probability of dam- age at a given point. Several WDFs have been proposed, including linear, Gaussian, and inverse power law functions, but they rely on assumptions without any experimental validation. We experimentally determine the WDF as the ratio of the DIs of a sensing path due to damage at a given point to its value when the damage is situated on the sensing path orthogonal to that point. Results reveal that the experimentally obtained variation of the damage index ratio does not conform to any of the existing WDF models for either baseline-based or baseline-free methods. Based on experimental data, we propose a simple exponential decay-type WDF, which is shown to be applicable for baseline-based methods and baseline-free refined time reversal method (RTRM) (developed by the second authors group). Thus, the newly proposed WDF provides an accurate estimate of damage probability for both baseline-based methods and the baseline-free RTRM.