Imaging defects with reduced space inversion of magnetic flux leakage fields

Magnetic flux leakage technique is being used for detection of defects inside a magnetically permeable bar by measuring the leakage fields outside the bar. Defects in magnetically permeable bar have been modeled as localized anti-dipoles whose moments and locations have to be determined. Generalized inverse or pseudo-inverse technique has been used to image the defects using least-square minimum-norm solution. An initial estimate of the defects is obtained by utilizing the generalized inverse of the lead matrix over the entire region of the sample space using the measured magnetic field data including random noise. By defining a suitable threshold, and ignoring the defect locations where the moment inferred in the initial estimate was below the chosen threshold, the image of the defect is again obtained by repeating the calculation in this reduced space for the lead matrix. The leakage fields from both a line defect and a deeply buried defect were simulated and utilized for inversion using this approach. It has been possible to image the defects and quantify the strengths of the moments with the correlation coefficient approaching unity for low-noise case and attain significant improvement in the correlation coefficient for data with reasonable levels of noise.