Integration of multiple response signals into the probability of detection modelling in eddy current NDE of flaws

A new method of modelling the probability of detection (PoD) of a flaw parameter (flaw length) for the case of multiple correlated flaw response signals is proposed in this work. The PoD modelling is assisted by boundary element method in order to compute the required flaw features, the maximum change in the impedance of a coil, at two different frequencies. Experiments were performed using a LCR meter to verify the predictions of the boundary element model. The modelling was performed on a finite thickness aluminum-1050 plate with a narrow opening surface flaw. The features were computed for various flaw lengths and fit with a bi-variate Gaussian distribution, thus evading the problem of heteroscedasticity. On knowing the signal thresholds, the PoD of a flaw length can be computed from the Gaussian density. The obtained discrete PoD is then regressed by a generalized logistic function (GLF) in order to attain a continuous function for the PoD of the flaw length. The parameters of the GLF are estimated via non-linear least squares minimization by Levenberg-Marquardt algorithm.