Inverse Problem in Nondestructive Testing Using Arrayed Eddy Current Sensors

Abstract

A fast crack profile reconstitution model in nondestructive testing is developed using an arrayed eddy current sensor. The inverse problem is based on an iterative solving of the direct problem using genetic algorithms. In the direct problem, assuming a current excitation, the incident field produced by all the coils of the arrayed sensor is obtained by the translation and superposition of the 2D axisymmetric finite element results obtained for one coil; the impedance variation of each coil, due to the crack, is obtained by the reciprocity principle involving the dyadic Green’s function. For the inverse problem, the surface of the crack is subdivided into rectangular cells, and the objective function is expressed only in terms of the depth of each cell. The evaluation of the dyadic Green’s function matrix is made independently of the iterative procedure, making the inversion very fast.

Electromagnetic Field Analysis and Modeling of a Relative Position Detection Sensor for High Speed Maglev Trains

“…The outside pole is set at O 2 , the centre of spherical surface Γ 2 . The solution to the Laplace Equation (6) in the valid domain is given as follows [4,7,8]: $\begin{array}{ll}leftW\hfill & =A+\sum _{l=1}^{N_l}{r}_i^{l}false(A_i^l{P}_{l}false(cos{\theta }_{i}false)+\sum _{m=1}^l{P}_l^m(cos{\theta }_i)(A_i^{\mathit{\text{lm}}}cosm{\alpha }_i+B_i^{\mathit{\text{lm}}}sinm{\alpha }_i)false)+\sum _{p=1}^{N_p}[\frac{A_{\mathit{\text{op}}}}{r_{\mathit{\text{op}}}}+\sum _{l=1}^{N_{\mathit{\text{op}}}}{r}_{\text{italicop}}^{-false(l+1false)}false(A_{\text{italicop}}^l{P}_{l}false(cos{\theta }_{\text{italicop}}false)+\sum _{m=1}^l{P}_l^m(cos{\theta }_i)(A_{\mathit{\text{op}}}^{\mathit{\text{lm}}}cosm{\alpha }_{\mathit{\text{op}}}+B_{\mathit{\text{op}}}^{\mathit{\text{lm}}}sinm{\alpha }_{\mathit{\text{op}}}))\hfill \\ left\hfill & =\sum _{k=1}^N{\alpha }_k{U}_k\hfill \end{array}$where $r_i=\left|\stackrel{true\to }{r}-\stackrel{true\to }{r_{i1}}\right|$, $\stackrel{true\to }{r_{i1}}$…”

Eddy Current Sensor Modeling for the Nondestructive Evaluation of Stress Intensity Factor

“…Stress Intensity Factor (SIF) is an important parameter in Linear Elastic Fracture Mechanics (LEFM) for the structural integrity assessment of structures containing cracks and singular stress fields [1]. SIF gives a measure of the intensity of the stress field in the crack tip region.…”

Eddy current modelling using multi-layer perceptron neural networks for detecting surface cracks

“…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 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 ( 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.…”