Fast damage imaging using the time-reversal technique in the frequency-wavenumber domain

The time-reversal technique has been successfully used in structural health monitoring (SHM) for quantitative imaging of damage. However, the technique is very time-consuming when it is implemented in the time domain. In this paper, we study the technique in the frequency-wavenumber (f-k) domain for fast real-time imaging of multiple damage sites in plates using scattered flexural plate waves. Based on Mindlin plate theory, the time reversibility of dispersive flexural waves in an isotropic plate is theoretically investigated in the f-k domain. A fast damage imaging technique is developed by using the cross-correlation between the back-propagated scattered wavefield and the incident wavefield in the frequency domain. Numerical simulations demonstrate that the proposed technique cannot only localize multiple damage sites but also potentially identify their sizes. Moreover, the time-reversal technique in the f-k domain is about two orders of magnitude faster than the method in the time domain. Finally, experimental testing of an on-line SHM system with a sparse piezoelectric sensor array is conducted for fast multiple damage identification using the proposed technique.