Multi-mode dispersion compensation in Lamb wave time-reversal method for high damage sensitivity across frequencies

The time-reversal method (TRM) for Lamb wave-based damage detection faces challenges due to amplitude dispersion, which prevents achieving a zero damage index (DI) for undamaged structures. Additionally, the healthy state DI varies with input excitation frequency, which complicates establishing a consistent DI threshold, and a high threshold diminishes its sensitivity to damage. This article proposes a novel technique that eliminates amplitude dispersion in the main mode of the reconstructed signal after the time-reversal process, enabling a near-zero DI threshold. The method involves dividing the transfer function of the reconstructed signal by the main mode transfer function (MTF) of a path with the least DI, representing the healthy state. The MTF is determined directly from the forward response measured under a broadband excitation. The unique property of this function's independence from sensing path length allows for application in networks of multiple sensing paths with varying lengths for damage localization in isotropic structures. The DI is calculated using an extended signal length that captures the extra modes induced by damage, further enhancing sensitivity. Numerical and experimental studies demonstrate the effectiveness of the proposed dispersion-compensated TRM in detecting and sizing different damage types, such as notch-type and block-mass damage, both on and away from the sensing path. Results show a significant improvement in damage sensitivity across all excitation frequencies, eliminating a major limitation of TRM in structural health monitoring.