Sandor Bilicz

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.

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.

Sparse Grid Surrogate Models for Electromagnetic Problems With Many Parameters

A sparse grid surrogate model (or metamodel) is proposed to reduce the computational time involved by accurate electromagnetic (EM) simulators. Sparse grids have already been used in many applications for interpolation and integration. The method can treat a high ber of independent parameters that are intractable for many other techniques due to the curse of dimensionality. Beyond the conventional method, adaptive sparse girds are also studied. The capabilities are illustrated through the examples drawn from the EM nondestructive evaluation.

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.

Finite-Element-Integral Equation Full-Wave Multisolver for Efficient Modeling of Resonant Wireless Power Transfer

With resonant wireless power transfer systems in operation, objects and/or humans having divers material properties come into the vicinity of the resonant coils. To model such systems efficiently, a novel full-wave multisolver is developed where the tangentially continuous vector finite element (FE) method is coupled with a method of moments (MoM) technique. The MoM technique is based on an electric field integral equation specifically designed to model the singular behavior of the thin coil wires, while the FE method is used to model the scattered field due to material inhomogeneities. A simplified sequential solver similar to the scattered field formulation is derived from the linear system of the multisolver in order to be applied as an efficient preconditioner, thereby speeding up the solution time significantly. The impedance change due to the material inhomogeneities can be calculated directly by applying the reaction concept. This ensures that the accuracy of the impedance change does not depend on the relative magnitude of the impedance change compared with the total impedance. The performance of the multisolver is illustrated by solving a test problem with a helical coil and a dielectric sphere with moderate conductivity, and comparing the multisolver results with the full FE solutions.

High-frequency modelling of coils by integral formulations

Purpose – The purpose of this paper is to discuss a numerically efficient simulation method for the study of the high-frequency behaviour of air-cored coils. The self-resonance phenomenon of coils can be studied which is important, e.g., in wireless power transfer (WPT). Design/methodology/approach – A full-wave and a quasi-stationary integral formulation is introduced. The integral equation is solved by using the Method of Moments. The complex impedance of the coil is calculated and studied in a wide frequency band. Findings – The integral equation method is numerically efficient compared to finite element schemes, making possible its use in design optimisation problems. Research limitations/implications – The present model can treat homogeneous media only. Future research will focus on the extension of the approach to heterogeneous media. Practical implications – The method can be used in the design optimisation of WPT systems that apply magnetically coupled resonant coils. Originality/value – The prese...

Combination of Maximin and Kriging Prediction Methods for Eddy-Current Testing Database Generation

Eddy-current testing (ECT) is a widely used nondestructive evaluation technique. The numerical simulation of ECT methods involves high complexity and computational load. However, one needs reliable solutions (within a reasonable CPU time) for these problems to be able to solve the related inverse problem. One possible approach is to build a configuration-specific database, consisting of well-chosen samples (corresponding input data – output signal pairs). Once the database has been constructed, the sought information can be retrieved practically in no time. However, the optimal choice of samples raises complex optimization problems. This paper presents a sampling method which aims to achieve databases being optimal in a certain sense. The goal of our approach is to spread out the output samples in the whole conceivable output domain. The method is formalized as a maximin problem which is solved step-by-step using the kriging prediction.

Eddy-current testing with the Expected Improvement optimization algorithm

This paper presents an inverse problem methodology in the domain of non-destructive testing, and more precisely eddy-current testing. Our objective is to use a precise but expensive-to-evaluate model of the electromagnetic induction phenomenon in a conductive material and to estimate the characteristics of a flaw by minimization of a regularized cr iterion with the Expected Improvement (EI) global optimization algorithm. The EI algorithm is designed to estimate a global optimum of a function with a restricted budget of function evaluations. Thus, we expect to be able to estimate the characteristics of a flaw with a relatively low cost despite resorting to an exp ensive model of the induction phenomenon. The effi ciency of the approach is discussed in the light of preliminary numerical examples obtained using synthetic data. respectively. In this Subsection the method used for the solution of the forward problem is discussed. In other words, the method used for the calculation of the change of the impedance of the ECT coil due to the presence of the cracks (�Z) is described when the location and the orientation of S 1 and S 2 are arbitrary. During the solution of the inverse problem, however it will be assumed that the cracks are outer defects (OD) and they are parallel to each other, consequently ˆ1 = ˆ

Inverse problem characterization using an adaptive database

In this paper, the characterization of electromagnetic inverse problems is addressed. As it is well known, an inverse problem can be ill-posed, i.e., its solution is not necessarily unique and might be quite sensitive to the measured data. To characterize such an inverse problem a combination of a surrogate model —based on an optimal database— and an inverse mapping of some sort, both using kriging prediction as tools, is proposed. The database (a kind of discrete representation of the electromagnetic model) is generated using an adaptive sampling strategy aiming to find a set of optimal input parameter-output data pairs. Once the latter has been computed, both qualitative and quantitative conclusions about the related inverse problem can be drawn. The illustrative examples are drawn from eddy-current nondestructive testing.