Model-based Probe State Estimation and Crack Inverse Methods Addressing Eddy Current Probe Variability

Recent work on model-based inverse methods with eddy current inspections of surface breaking discontinuities has shown some sizing error due to variability in probes with the same design specifications [1]. This is an important challenge for model-based inversion crack sizing techniques, to be robust to the varying characteristics of eddy current probes found in the field [1-2]. In this paper, a model-based calibration process is introduced that estimates the state of the probe. First, a carefully designed surrogate model was built using VIC-3D® simulations covering the critical range of probe rotation angles, tilt in two directions, and probe offset (liftoff) for both tangential and longitudinal flaw orientations. Some approximations and numerical compromises in the model were made to represent tilt in two directions and reduce simulation time; however, this surrogate model was found to represent the key trends in the eddy current response for each of the four probe properties in experimental verification studies well. Next, this model was incorporated into an iterative inversion scheme during the calibration process, to estimate the probe state while also addressing the gain/phase fit and centering the calibration notch indication. Results are presented showing several examples of the blind estimation of tilt and rotation angle for known experimental cases with good agreement within +/- 2.5 degrees. The RMS error was found to be significantly reduced by fitting the probe state and, in many instances, probe state estimation addresses the previously un-modelled characteristics (model error) with real probe inversion studies. Additional studies are presented comparing the size of the calibration notch and the quality of the calibration fit, where calibrating with too small or too large a notch can produce poorer inversion results. Once the probe state is estimated, the final step is to transform the base crack inversion surrogate model and apply it for crack characterization. Because of the dimensionality of this problem, simulations were made at a limited set of select flaw sizes with varying length, depth and width, and an interpolation scheme was used to address the effect of the probe state at intermediate solution points. Using this process, results are presented demonstrating improved crack inversion performance for extreme probe states