Issue 45

S. Harzallah et al, Frattura ed Integrità Strutturale, 45 (2018) 147-155; DOI: 10.3221/IGF-ESIS.45.12 148 The (ECT) technique works on the principle of electromagnetic induction, and it consists on the detection of the magnetic field due to the eddy current induced on the tested specimen. The presence of the defect modifies the eddy currents pattern and hence gives rise to field perturbation closely related to the position and shape of the defects. The excitation field is carried out by using a coil fed by an alternating current and the changed impedance coil can be computed to account the defect influence on the induced currents. The modeling of a practical configuration of (EC) sensor is generally complex and requires extended analytical or numerical developments. The Finite Element method (FEM) is more general, numerically superior, primarily used for its versatility modeling of material properties, simulations of boundary conditions, modeling arbitrary domain space, and reduces substantially the experimental work [3]. The inverse Eddy current problem can be described as the task of reconstructing the electrical conductivity profile of an inspected specimen in order to estimate its material properties. This is accomplished by inverting Eddy current probe impedance measurements which are recorded as a function of probe position, excitation frequency or both. In eddy current nondestructive evaluation this is widely recognized as a complex theoretical problem whose solution is likely to have a significant impact on the characterization of conductive materials [4]. The Neurons are the fundamental elements in each layer, and every neuron in one layer is associated and interacts with other layers. The outputs of every neuron in the hidden and output layers are determined by the previous output ( ij j   Σ w x , j x is the input signals), activation function (   ij j  f Σ w x ), and weighting coefficients ( ij w ) [4]. The MLP network is processed as follows: the information flow is input into the input layer and passes through the hidden and output layers to achieve the output information. The Tan-sigmoid activation function is used in the neurons of hidden and output layers in this work [5]. ANN is composed of highly interconnected processing elements called neurons. These latest can perform arbitrary mappings between sets of input-output pairs. This is achieved by adjustment of the weights of interconnections after training through the presentation of examples. Neural network performance has been proven robustness when faced incomplete, fuzzy or novel data. Previous work has shown that ANN can also be used as for solving electric and/or magnetic inverse problems. ANN is then a tool used to information processing systems which can recognize highly complex patterns within available data. It has recently been applied to solve the electromagnetic non-destructive testing inverse problem and has been proved to have a higher accuracy compared to classical methods [6-8]. FEM DISCRETIZATION OF 3-D EDDY CURRENT GOVERNING EQUATIONS he eddy current testing phenomenon can be treated as a quasi-static electromagnetic field problem which is expressed by the governing field equations in terms of electrical scalar and magnetic vector potentials. These equations can be solved by 3-D Finite Element Method. Application of the Coulomb gauge allows simultaneous solution of the coupled magnetic vector potential and the electric scalar potential equation in the inductor Ω i and the conducting region Ω c , the non-conducting region representing the air Ω a with a current density source. These equations can be written as [9, 10]           0                                      . .          a p S i a in A A J in J A in                     (1)   . . 0 J A        (2) where, p  the penalty term,  the electric conductivity,  is the magnetic reluctivity and V is the electrical potential, S J the current density source. The integral A - V formulation is obtained when applying Galerkin’s methods and the weighted residuals for Eqns. (1) and (2), using vector Ni and scalar α i weighted functions. Such a formulation leads to the following integral forms by [11];           .  A  .   . A  V i p i i i N N d J N A d                         (3) T