Model-Driven Optimization of In-Pipe Magnetic Flux Leakage Detectors

Background self-leakage in magnetic flux leakage (MFL) magnetizers can reduce the flux available for pipe wall magnetization. This study develops a geometry-dependent equivalent magnetic circuit (EMC) model for a permanent-magnet, yoke, and steel-brush assembly and couples it with NSGA-II to minimize the background self-leakage ratio and magnetic component volume. Pipe wall magnetic flux density and background leakage were evaluated for different geometric parameters and brush–wall clearances. The design variables were yoke length, magnet length, magnet height, and brush height. For an 8 mm-thick pipe wall, the selected compromise design had a yoke length of 65.93 mm, magnet length of 12.77 mm, magnet height of 8.02 mm, and brush height of 12.00 mm. It achieved an EMC-predicted leakage ratio of 0.24% and a combined yoke–magnet volume of 43.21 cm3. Across optimized configurations with wall thicknesses of 7–10 mm, nonlinear finite element (FE) simulations predicted average pipe wall magnetic flux densities of 1.94–1.98 T. EMC–FE errors were 0.00–1.52% for pipe wall flux density and 11.29–16.00% for background leakage. The method supports preliminary magnetic circuit design; experimental verification and defect-signal assessment remain necessary.