Full Waveform Inversion for High-Resolution Imaging and Defect Detection in Composites: On the Choice of Misfit, Regularization, and Parameterization

Abstract

Detecting defects in materials and obtaining high-resolution images of the materials’ internal structures are essential for ensuring quality and structural integrity. Nondestructive testing (NDT) is favored for these purposes, thanks to its economic and environmental advantages. Among the various NDT techniques, ultrasound imaging shows great promise but entails several technical challenges, such as reliability and resolution. Full waveform inversion (FWI), an advanced optimization method, can generate high-resolution images of a material’s internal structure and identify defects. In principle, FWI minimizes the misfit between recorded ultrasonic signals and simulated ones, often through iterative optimization methods. However, the fact that FWI is highly nonlinear often hinders the reliability of the reconstructed images. This work explores different strategies to improve FWI for both high-resolution imaging and defect detection, focusing on defects such as delamination in composites. More specifically, it emphasizes the choice of misfit measures, regularization methods, and parameterization techniques; studies their impact on FWI improvements; and provides suggestions based on the resulting findings. Various misfit measures—including the L2- norm, L1-norm, cross-correlation (CC), and envelope measures—are compared in order to assess their effectiveness in improving FWI outcomes. Furthermore, different regularization methods were investigated for stabilizing FWI and enhancing its accuracy. Simple regularization methods (e.g., Tikhonov regularization) were compared with more advanced techniques (e.g., total variation regularization). Also, different parameterization strategies and their impacts on FWI performance were examined. By applying model constraints through reparameterization techniques, such as using Sigmoid transformations of model parameters and projecting them to expected ranges, this work aims to improve reconstruction accuracy and convergence. These findings suggest that CC functionals augmented with total variation regularization, while also applying Sigmoid transformation to the model parameters, is a particularly effective strategy for FWI in multilayered systems/materials with sharp-edged defects (e.g., delamination in composites.