Fast Magnetic Flux Leakage Signal Inversion for the Reconstruction of Arbitrary Defect Profiles in Steel Using Finite Elements

This paper proposes a fast and effective method for reconstructing arbitrary defect profiles in steel plates from magnetic flux leakage (MFL) measurements widely used in nondestructive testing (NDT) of oil storage tanks and pipelines. The inverse reconstruction problem is formulated based on a nonlinear forward model using the finite element method (FEM) and is implemented in 2-D. A Gauss-Newton optimization is applied to reconstruct the defect geometry, using efficiently calculated Jacobian information directly derived from the FEM system matrix. The algorithm's effectiveness is tested on a simulated and complex-shaped reference defect under various conditions. For a realistic MFL sensor distance to the plate surface and noise level on the signals, the algorithm is capable of reconstructing the defect profile from the MFL signals using 49 surface degrees of freedom with high accuracy in less than 15 s on an Intel Core i7 2.6-GHz laptop. The presented technique exhibits high inversion speed while maintaining the high prediction accuracy of the MFL signals by using a full-scale and flexible nonlinear FEM model. Our technique also exhibits a good convergence behavior and is stable and robust. These properties, together with its easy extension to 3-D, make our technique an extremely promising and novel approach for the practical application of surface profile reconstruction for NDT.