Second harmonic ultrasonic signal detection of mechanical structural defects using VMD combined with wavelet threshold

We propose a digital signal processing method based on variational mode decomposition (VMD) and wavelet thresholding, which is applied to time of flight (TOF) estimation in the detection of second-harmonic ultrasonic signals for internal material defects, aiming to achieve accurate condition assessment of the detected objects. This study is to address the key challenges: “noise masking of second-harmonic signals” and “difficulty in identifying echo onsets,” thereby enabling precise condition assessment of the detected mechanical structures. The hypothesis of this study is as follows: By adaptively decomposing echo signals and separating different frequency components via VMD, and combining wavelet thresholding to denoise and reconstruct the decomposed modal components, this method can effectively improve the signal-to-noise ratio (SNR) of the second-harmonic component in the echo and accurately locate the echo onset. Specifically, the echo signal is processed using the variational mode decomposition (VMD) method. The decomposed components denoised using a wavelet threshold technique, and the denoised components are subsequently reconstructed by summation to identify the echo’s starting point. The method’s efficacy is validated through experimental data obtained from a laser wire-cut aluminum plate with cracks, demonstrating its suitability for scenarios with unknown crack signal characteristics and low signal-to-noise ratios.