Group sparse low-rank algorithm for ultrasonic guided wave defect feature extraction

Abstract Ultrasonic guided wave (UGW) is highly valued in the field of nondestructive testing due to their slow energy decay and extensive detection range, displaying unique advantages particularly in the inspection of long weld defects. However, the signal of defective echo is easily masked by strong noise interference, which makes feature extraction difficult. To address this issue, this paper proposes a Time-Frequency Analysis Overlapping Group Sparse Low-Rank (TFAOGSL) model. Firstly, the group sparsity and low-rankness of ultrasonic guided wave signals are revealed, and the TFAOGSL feature extraction is modelled on this basis. Secondly, the convexity condition of the TFAOGSL model is derived, and its optimal solution is deduced using the alternating direction method of multipliers (ADMM) algorithm in conjunction with the majorization–minimization (MM) algorithm. Additionally, optimal parameters for TFAOGSL were adaptively chosen using simulated signals. Finally, comparisons were made with some state-of-the-art methods, and the effectiveness of TFAOGSL was confirmed through ultrasonic guided wave detection experiments for welding defects. The results demonstrated that this method can accurately extract defect features and has significant advantages compared to other methods.