Lamb wave-based subwavelength damage imaging using the DORT-MUSIC technique in metallic plates

A Lamb wave-based, subwavelength imaging algorithm is developed for damage imaging in a metallic plate based on a decomposition of the time-reversal operator method together with a multiple signal classification imaging condition in the space-frequency domain. In this study, a hybrid non-contact inspection system was proposed to image damage in an aluminum plate using a piezoelectric linear array for actuation and a laser Doppler vibrometer line-scan perpendicular to the piezoelectric array for sensing. The physics of incident waves, reflection, and reflected waves that underlie the transfer matrix in the decomposition of the time-reversal operator method is mathematically formulated in the context of guided waves based on the first-order Born approximation. Singular value decomposition is then employed to decompose the experimentally measured transfer matrix into three matrices, detailing the incident wave propagation from the linear actuator array, reflection from the damage, and followed by reflected waves toward the linear sensing array for each small damage. The singular value decomposition and multiple signal classification imaging condition enable providing insight on both the damage "reflectivity'' and detecting damage smaller than a wavelength (subwavelength). With the flexibility of this inspection system, a considerably large area can be imaged using lower frequency Lamb waves with rapid line-scans. The experimental results showed that the hardware system with a signal processing tools such as the decomposition of the time-reversal operator with multiple signal classification (time-reversal with multiple signal classification) imaging technique can provide robust, highly accurate imaging results as well as providing damage reflectivity estimation with unknown material properties.