Generalized virtual wave reconstruction for vibrothermography: Overcoming the wavefront-free behavior and quantification challenges in the diffusion-wave field

Abstract

Wavefront-free behavior and the resulting quantification difficulties are intrinsic limitations of vibrothermography due to the diffusive nature of thermal fields. This work proposes a generalized virtual wave reconstruction framework to address the absence of propagation features in thermal diffusion-wave fields and its impact on quantitative defect characterization. Unlike conventional virtual wave formulations restricted to Dirac-type excitations, the proposed approach establishes a rigorous spatiotemporal mapping between diffusion-wave fields and virtual wave fields under arbitrary heat-generation conditions without simplifying assumptions on thermo-mechanical coupling. The resulting ill-posed inversion problem is solved using truncated singular value decomposition (T-SVD) and the alternating direction method of multipliers (ADMM) to enhance numerical stability and suppress noise amplification. Numerical simulations demonstrate that the reconstructed virtual wave fields recover propagation characteristics absent in temperature distributions, leading to improved defect boundary definition, contrast enhancement, and depth-resolved analysis. Experiments on CFRP laminates validate the robustness of the approach and show significantly improved signal-to-noise ratio, spatial clarity, and defect size estimation compared with conventional thermographic processing methods.