Ellipse of uncertainty based algorithm for quantitative evaluation of defect localization using Lamb waves

Measurement deviation of time of flight (ToF) is inevitable in nondestructive testing based on the sparse array and ultrasonic Lamb waves. It affects the influence zone of temporal-spatial mapping trajectories (TSMTs) of signal parameters in the imaging zone, and further limits the quantitative evaluation of defect localization. In the paper, the ellipse of uncertainty (EOU) of TSMTs was derived from multiple parameters, including the group velocity, ToFs and their measurement deviations, distances between actuators and receivers. Then, an EOU-based algorithm was developed for quantitative evaluation of defect localization. The defects were localized by searching the individual scatterers at the intersection of multiple TSMTs. Based on the eccentricity of the uncertainty ellipse, a fuzzy scaling factor was introduced. It was combined with a fuzzy control parameter to tune the influence zone of TSMTs. Based on the acoustic reciprocity theorem and the fuzzy control parameter, the ToFs of scattering waves were fused to establish the one-to-one relation between individual scatterers and inspection pairs. Experimental results showed that the EOU-based algorithm can reduce the interferences of EOU in the detection; and the quantitative evaluation of defect localization was realized by analyzing the distribution of individuals and their ToF difference to inspection pairs.