Ultrasonic guided wave damage imaging using the time difference coefficient between direct and scattered waves

To address the challenges of damage imaging under wave speed uncertainty and dispersion, this study proposes an ultrasonic guided wave (UGW) damage imaging method based on the time difference coefficient (TDC). The method integrates amplitude and instantaneous phase information to construct an amplitude-phase product signal, which enhances the characteristic information of the UGW. By analyzing the slope change of the peak values in the product signal, the TDC determines the arrival-time difference between the direct and scattered waves without requiring prior knowledge of wave speed. The TDC is combined with the reconstruction algorithm for probabilistic inspection of damage (RAPID) for imaging. Numerical simulations and experiments are conducted on aluminum plates with single and double through-hole damages, and the performance of the TDC method is compared with the conventional signal difference coefficient (SDC), the energy damage index (EDI), and the root mean square error (RMSE). The results show that the TDC method achieves a localization error of less than 3.54 mm, outperforming the SDC, EDI, and RMSE methods under the tested conditions. The proposed method demonstrates improved localization accuracy and tolerance to moderate dispersion and boundary reflections under the tested aluminum-plate conditions, providing a practical tool for guided-wave structural health monitoring.