Amplitude Dispersion Compensation in Time-Reversed Lamb Waves for Enhanced Sensitivity in Damage Detection

Abstract

In Lamb wave-based baseline-free damage detection employing the time-reversal method (TRM), the damage index (DI) is computed from the similarity between the main mode of the reconstructed signal obtained after the time-reversal process (TRP) and the input signal, both normalized. However, a perfect similarity with a zero DI value cannot be achieved for undamaged structures due to the amplitude dispersion of Lamb waves, which is not compensated in the TRP. Thus, a nonzero DI does not necessarily indicate the presence of damage. Even worse is the fact that the similarity and, therefore, the DI for the pristine structure depend on the probing frequency, making it difficult to estimate a unique threshold value of DI for damage identification. The imperfect reconstruction also significantly reduces the relative sensitivity of the DI to the presence of damage. In this article, we propose a method to compensate the amplitude dispersion in the main mode of the reconstructed signal for undamaged metallic plates to achieve a zero threshold of DI. First, the transfer function of the main mode of the reconstructed signal for an undamaged path (the path with the least DI for a network of sensing paths) is obtained by exciting the actuator with a broadband excitation and extracting the S0 and A0 modes from the forward response measured at the sensor. To compensate the amplitude dispersion in the TRP-generated main mode, the transfer function of the recorded signal of a path is divided by the transfer function of the main mode obtained for the undamaged path. A comprehensive numerical study shows that the DI computed with the compensated reconstructed signal has much higher sensitivity to damage than that without applying the proposed compensation at all frequencies, providing the flexibility to choose the probing frequency according to the desired damage size to be detected.