József Pávó

Parallel Realization of the Element-by-Element FEM Technique by CUDA

The utilization of Graphical Processing Units (GPUs) for the element-by-element (EbE) finite element method (FEM) is demonstrated. EbE FEM is a long known technique, by which a conjugate gradient (CG) type iterative solution scheme can be entirely decomposed into computations on the element level, i.e., without assembling the global system matrix. In our implementation NVIDIAs parallel computing solution, the Compute Unified Device Architecture (CUDA) is used to perform the required element-wise computations in parallel. Since element matrices need not be stored, the memory requirement can be kept extremely low. It is shown that this low-storage but computation-intensive technique is better suited for GPUs than those requiring the massive manipulation of large data sets.

Fast flaw reconstruction from 3D eddy current data

An eddy current flaw reconstruction strategy based on the minimization of nonlinear least-squares error functionals is developed for problems with arbitrary specimen, probe and defect shapes. A fast 3D forward solver is created to rapidly predict eddy current signals in the inversion shell. The high speed of the signal evaluation comes by utilizing a reaction data set constructed before performing the inversion by a finite element electromagnetic field simulator. The same pre-calculated reaction data set supports the quick evaluation of sensitivity information, thereby ensuring the efficient implementation of an optimization algorithm. This optimization algorithm combines first-order and stochastic optimization strategies and improves the reliability of the reconstruction significantly if the observed data contain large noise components. Examples with tube specimens are presented for different 3D flaw shapes.

Calculation of eddy current testing probe signal with global approximation

Global approximating function sets applicable to the solution of the integral equation used to calculate an eddy current testing probe signal are proposed. Rectangularly-shaped cracks normal to the surface of plate specimens are considered. The approximating functions are orthogonal harmonic functions satisfying the boundary conditions at the edges of the crack. The calculations using the proposed approximating functions are fast, numerically stable and provide a robust alternative to other methods used in the literature. A number of numerical examples are shown for illustration and discussed

Numerical calculation method for pulsed eddy-current testing

A numerical method is presented for the calculation of the time-dependent response of the interaction of a stratified plate specimen of linear conductor containing a planar flaw and an eddy-current induction coil fed by a current pulse. The flaw might be located on any sides of the layers of the plate specimen. The calculations are done with the help of Fourier-transform (FT). The time-harmonic responses of the system are calculated at properly chosen frequencies, and the obtained results are weighted by the FT of the excitation to provide the FT of the response. The results of the presented method can be used for various pulsed eddy-current testing (ECT) applications.

Characterization of a 3D defect using the expected improvement algorithm

Purpose – The purpose of this paper is to provide a new methodology for the characterization of a defect by eddy‐current testing (ECT). The defect is embedded in a conductive non‐magnetic plate and the measured data are the impedance variation of an air‐cored probe coil scanning above the top of the plate.Design/methodology/approach – The inverse problem of defect characterization is solved by an iterative global optimization process. The strategy of the iterations is the kriging‐based expected improvement (EI) global optimization algorithm. The forward problem is solved numerically, using a volume integral approach.Findings – The proposed method seems to be efficient in the light of the presented numerical results. Further investigation and comparison to other methods are still needed.Originality/value – This is believed to be the first time when the EI algorithm has been used to solve an inverse problem related to the ECT.

Calculation of losses in laminated ferromagnetic materials

A numerical method for calculation of the power losses of nonlinear laminated ferromagnetic cores is presented. The calculation is made in two subsequent steps. In the first step, the approximate magnetic field distribution in the material is determined assuming a nonlaminated bulk nonlinear ferromagnetic material with anisotropic conductivity. In the second step, the nonlinear ferromagnetic material of the laminated core is replaced to linear material with spatially inhomogeneous permeability. The actual permeability distributions of the lamination are determined based on the magnetic field obtained from the first calculation and the nonlinear B-H curve of the material. In this paper, the outlined method is verified through calculations and measurements made on simple benchmark arrangements. Different methods for assigning the inhomogeneous permeability are also investigated.

Solution of Inverse Problems in Nondestructive Testing by a Kriging-Based Surrogate Model

The inverse problems of electromagnetic nondestructive testing are often solved via the solution of several forward problems. For the latter, precise numerical simulators are available in most of the cases, but the associated computational cost is usually high. Surrogate models (or metamodels)-which are getting more and more widespread in electromagnetics-might be promising alternatives to heavy simulations. Traditionally, such surrogates are used to replace the forward model. However, in this paper the direct use of surrogate models for the solution of inverse problems is studied and illustrated via eddy-current testing examples.

Numerical calibration of fluxset probe for quantitative eddy current testing

Fluxset type eddy current probes are used for detecting discontinuities in conducting materials. The measurements obtained by such probes can be used for the reconstruction of the parameters of the detected discontinuity if the output signal of the measurement is uniquely related to the measured field. In this paper a calibration method is presented for the establishment of the relation between the measured magnetic field and the output signal of the probe. The relation is obtained by the optimisation of the parameters of the mapping between the calculated magnetic field distribution and the measured output signal. The magnetic field distribution due to the interaction of the probe and an infinitesimally thin crack located in a conducting plate is calculated numerically by the solution of a boundary integral equation.

Modeling of Resonant Wireless Power Transfer With Integral Formulations in Heterogeneous Media

A full-wave integral formulation has recently been proposed for the simulation of magnetically coupled resonant wireless power transfer (WPT) arrangements in homogeneous medium. In this paper, the formulation is extended to the case where two different types of dielectrics are separated by a planar interface. This configuration has extensive practical interest nowadays, especially for modeling biomedical WPT applications. The new formulation is based on a stationary approximation, which is valid at the typical operating frequencies. The proposed scheme requires much less computational resources compared with standard finite-element simulations. The results are validated against alternative simulations and measured data as well.

Kriging for Eddy-Current Testing Problems

Accurate numerical simulation of Eddy-Current Testing (ECT) experiments usually requires large computational efforts. So, a natural idea is to build a cheap approximation of the expensive-to-run simulator. This paper presents an approximation method based on functional kriging. Kriging is widely used in other domains, but is still unused in the ECT community. Its main idea is to build a random process model of the simulator. The extension of kriging to the case of functional output data (which is the typical case in ECT) is a recent development of mathematics. The paper introduces functional kriging and illustrates its performance via numerical examples using an ECT simulator based on a surface integral method. A comparison with other classical data interpolation methods is also carried out.