Nonlinear ultrasonic analysis inspired by phase-based motion magnification

Nonlinear ultrasonic modulation is favored for early-stage fatigue crack detection by inspecting the modulation components at the sum and difference of two distinct input frequencies. However, it is difficult to extract the modulation components using a conventional spectral density function considering the modulation components can be easily buried under noisy environments. In this study, we proposed a new nonlinear ultrasonic analysis method inspired by phase-based motion magnification. First, a one-dimensional time-domain ultrasonic signal is filtered to remove the large motions of the primary linear response components. Then, the filtered signal is used to construct a two-dimensional video and the phase-based motion magnification algorithm is applied to enhance the movements at the predetermined modulation frequencies inside the video. This step is achieved by phase denoising and phase magnification, which supports large magnification factors and is significantly insensitive to noise. Finally, an amplified one-dimensional signal is extracted from the two-dimensional video and can be used for further nonlinear ultrasonic analysis. The proposed method was successfully validated with a group of synthetic data at different noise levels. Additionally, we have also successfully applied the proposed method for fatigue crack detection in a steel padeye.