Issue 28

B. Ye et alii, Frattura ed Integrità Strutturale, 28 (2014) 32-41; DOI: 10.3221/IGF-ESIS.28.04 38 In ECNDT, the problem of quantifying defect size from probe signals is formulated as an optimization problem, which seeks a set of defect size by minimizing an objective function, representing the difference between the models predicted signal and the measured signal. The inversion process iteratively attempts to estimate a set of defect size so that the correspondingmodel predicted signal matches themeasured signal. Suchmethod presented by this paper is based on the underlying physical process. A time-varying current flowing into an exciting coil placed near to the specimen induces eddy current in the specimen under testing. The induced eddy current, depending on the spatial values of the resistivity andmagnetic permeability, affects the signal detected by the surrounding pick-up coils ormagnetic sensors. Then, changes in impedance of the coil are used as a basis for detecting the presence of discontinuities in the specimenby inversionof themeasured data. The inversionprocess is shown inFig. 4. Figure 4: The flowchart of quantitative estimating size of deep defects inmulti-layered structures fromECNDT signals using IACA. The measured signal at the position of the defect is assumed the target signal. A set of randomly generated initial defect parameters are given to the finite element model to predict the eddy current coil responses associated with these defects. Then, the model predicted signals are compared with the measured signal and the corresponding value of the objective function is evaluated. If the value of the objective function is less than a predefined threshold, the iterative process is terminated. Otherwise the IACA correct the defect parameters. Then the process is iterated until the error becomes less than the predefined threshold. N UMERICALANDEXPERIMENTALRESULTS o use IACA in optimization, it is essential to settle the configurationofmany parameters. Parameter equal division number ( N ), ant number ( m ) andmaximummoving times ( t max ) are heuristically determined and dependent on the optimizationproblem. In themethod with the help of IACA applied to determinate the parameters of the defect, the length, the height and the depthof the defect are expressed as: X =[ l , h , d ] (17) where, l is the lengthof the defect, h is the height of the defect; d is the depthof the defect. The object function is: 2 1 1 1 ' g i i i f a z z      (18) where, a is a constant, z i is the model predicted coil impedance at scanning position i , and z i ’ is the corresponding probe impedance from actual measurement. g is the number of scanning positions. The object function is calculated by comparing the signals of themeasurement with those of the prediction by FEM forwardmodel. Updating the pheromone and deterministically moving are operated based on the object function value. After a lot of iteration, the ant with the highest object function value is expected to indicate the defect size. The other features of IACA which are used in this paper are shown inTab. 1. The structure parameters are shown inTab. 2 and the coil parameters are shown inTab. 3. T N Predicted signal Stop Initial defect parameters Numerical simulate FEM forwardmodel Δ Z ≤ε ? Stop criterion? Y Measured signal Modified defect parameters