Self-focusing Lamb waves based on the decomposition of the time-reversal operator using time–frequency representation

Active ultrasonic arrays are very useful for structural health monitoring (SHM) of large plate-like structures. Large areas of a plate can be monitored from a fixed position but it normally requires precise information on material properties. Self-focusing methods can perform well without the exact knowledge of a medium and array parameters. In this paper a method for selective focusing of Lamb waves will be presented. The algorithm is an extension of the DORT method (French acronym for decomposition of time-reversal operator) where the continuous wavelet transform (CWT) is used for the time–frequency representation (TFR) of nonstationary signals instead of the discrete Fourier transform. The performance of the methods is compared and verified in the paper using both simulated and experimental data. It is shown that the extension of the DORT method with the use of TFR considerably improved its resolving ability. To experimentally evaluate the performance of the proposed method, a linear array of small piezoelectric transducers attached to an aluminum plate was used to obtain interelement responses, required for beam self-focusing on targets present in the plate. The array was used for the transmission of signals calculated with the DORT-CWT algorithm. To verify the self-focusing effect the backpropagated field generated in the experiment was sensed using laser scanning vibrometer.