The Role of Boundary Control in Enhancing Damage Identification Using Eddy Current Sensors

Eddy current sensors provide an inexpensive means of detecting surface and embedded flaws in metallic structures due to fatigue, corrosion, and manufacturing defects. However, use of eddy current sensors for imaging flaws to determine their geometry is limited by sensitivity and mathematical uniqueness issues, as the magnetic flux distribution sensed at the boundary of a structure can be similar for dissimilar flaw geometries or flaw depths. This paper investigates the use of feedback control based on measured magnetic flux at a point on the boundary of the structure in order to address sensitivity and uniqueness issues for eddy current sensors and thus to enhance the ability to use these simple inexpensive sensors to determine flaw geometry. Using a parametrized two-dimensional flaw in which width and depth of the flaw are to be determined, scalar metrics are developed to relate the forward solution of the electromagnetic dynamics to the inverse problem of damage geometry reconstruction. Geometry is determined by interpolating metrics on a mesh and employing a systematic ranking process that is robust to weakly unique inverse problems. Finally, the concept of sensitivity enhancing feedback control (SEC) is applied to enrich the data set in order to improve damage geometry reconstruction. SEC feeds back measured magnetic flux at a single point along a scan line to affect the current density. Closed-loop compensation of eddy current dynamics is shown to improve uniqueness of scalar damage metrics to damage geometry parameters. Performance is demonstrated by simulation of geometry construction using finite-element models of two-dimensional flaws embedded in a material, both with and without feedback control and for noisy and noiseless simulated magnetic flux density measurement. For noiseless data, flaw depth and width are reconstructed within the resolution of the mesh (0.01 mm) using feedback control, while the relative accuracy of damage geometry identification for open-loop data is on the order of 0.1 mm in each dimension. Simulation of damage geometry identification with noisy data demonstrates lower relative error using closed-loop data, as measured by the mean and standard deviation in identified depth and width.