Enhancement of crack reconstruction through inversion of eddy current testing signals with a new crack model and a deterministic optimization method

Abstract

This paper proposes a new crack model to parameterize profile of a natural crack in order to improve the inversion precision of crack profile with eddy current testing (ECT) signals. In this novel crack model, the edge profile of a planar crack is parametrized with 6 feature parameters of three curves, i.e., two quarter-elliptic curves and a straight line. Compared with the conventional rectangular and semi-elliptical crack model, the new model gives better profile fitting of actual cracks such as a fatigue crack or a stress corrosion crack. In addition, the reconstruction procedure with the new crack model is more stable than using the arbitrary-shaped crack model outlined by a piecewise line as the unknown parameters to be reconstructed is significantly reduced. To apply the new crack model for crack inversion with the conventional conjugate gradient method, the formulae for calculating the gradient vector regarding to the feature parameters of the new crack model are deduced. To investigate the performance of the new model for crack sizing, cracks of different sizes and complex shapes were reconstructed using the new crack model and the fast forward ECT signal simulator using unflawed field database and the multimedia finite element scheme. Meanwhile, inverse analyses for sizing cracks of complicated shapes were also carried out based on ECT signals containing random noise to clarify the robustness of the new inversion scheme. The numerical results show that reconstructed crack parameters are identical with the true ones in acceptable accuracy, which proved the validity and efficiency of the new method.

An Efficient Phenomenological Inversion Method for Reconstruction of Crack Depth Profile in a Metal From ACFM Probe Output Signals

“…The gradient-based optimization methods are preferred to their stochastic rivals that suffer from slow convergence speed due to their intrinsic time-consuming searching mechanisms [20]. In these methods, the gradient of the objective function is used to update the solution in each iteration [21][22][23][24][25]. The convergence speed and the avoidance of trapping in local minimums depend strongly on the number of equations and unknowns, the initial choice of solution, and how to calculate the gradient of the objective function.…”