Noise-robust method using sparsity for locating a crack in a steel rod based on the Fourier coefficients of the leakage magnetic flux

In the leakage magnetic flux (LMF) method for non-destructive inspection, locating a tiny crack with a depth of less than 100 µm is a challenge due to the low signal-to-noise ratio. This paper presents a noise-robust method for locating a tiny surface crack in a moving steel rod. For the time series data obtained with our two previously proposed sensors, which measure the circumferential Fourier cosine and sine coefficients of the LMF, we introduce a method that solves a linear inverse problem with sparsity regularization, enabling localization of a crack with a depth of 70 µm.