The solution of magnetic inverse problems has been pursued for many years in numerous fields, from biomagnetism to nondestructive evaluation, and several different methods have been used to sovle them. One particular field of interest is the nondestructive evaluation of the integrity of oil and gas transmission pipelines performed by in-line magnetic inspection systems, known as pigs. This type of equipment has been proven to be indispensable in monitoring metal loss in transmission pipelines. The working principle of a typical in-line inspection system is the application of an axially oriented magnetic field to the ferromagnetic pipe wall by means of permanent magnets. Should there be a region of metal loss, usually due to corrosion, the applied magnetic field is perturbed, thus producing a characteristic flux leakage pattern. This magnetic flux leakage (MFL) pattern, characteristic of the flaw, is measured by magnetic field sensors. We propose in this work an inverse solution based in an least-squares optimizaiton procedure that uses a three-dimensional finite element model for the forward problem. The algorithm modifies iteratively the coordinates of the finite element mesh nodes in order to fit a magnetic field pattern that is related to a specific flaw geometry.
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