Bayesian compressive sensing for recovering the time-frequency representation of undersampled Lamb wave signals

Abstract

The characteristic extraction of ultrasonic Lamb wave is the prerequisite for its efficient utilization in the structural health monitoring. In the situation of intentional signal compression or unexpected data missing, the accurate recovery of contained information is challenging. To address this problem, this work proposes the time-frequency representation (TFR) reconstruction scheme for undersampled Lamb wave signal. Unlike the conventional method, both the sparse prior and structural sparse prior in the two-dimensional plane are considered in the design of Bayesian compressive sensing. The simulated signal is adopted to validate the effectiveness of the proposed method. Furthermore, different ratios of available samples are investigated to analyze the recovery ratio of TFR. Even if the available samples are smaller than those from the Nyquist rate, the TFR recovery ratio can reach 70%. The experiments using array transducers in noisy environments are also conducted. The time-of-flight information extracted from the recovered TFR is accurate and the relative error is smaller than 3%. Besides, the comparisons with conventional schemes for compressive sensing are carried out to demonstrate its superiority.