Reconstruction of Cracks in Carbon Fiber Reinforced Polymer Laminate Plate from Signals of Eddy Current Testing
Yali Du^{1,2}, Xudong Li^{1}, Shejuan Xie^{1}, Shiyou Yang^{3}, Zhenmao Chen^{1}
^{1}Xi’an Jiaotong University, China; ^{2}Xi’an Polytechnic University, China; ^{3}Zhejiang University, Hangzhou, China
To evaluate defects in carbon fiber reinforced polymer (CFRP) and to predict its size, a numerical scheme for quantitative eddy current testing (ECT) is proposed and validated in this study. At first, an efficient forward numerical solver based on a database approach is updated to simulate the ECT signals of defects in a CFRP plate. Second, a hybrid inverse analysis scheme is proposed and implemented for sizing the defects from measured ECT signals of high frequency. Third, both simulated signals with white noise and measured signals are adopted to reconstruct the profile of the slits in CFRP plate as examples to validate the proposed numerical scheme. The good agreement of the true and the reconstructed values demonstrated the validity of the new scheme for sizing defects in CFRP.
Alternative proposal of the High Order Gauss Quadrature for reference triangle in the Generalized Finite Element Method
Werley Gomes Facco^{1}, Renan Coswosk da Silva^{1}, Kaio Fábio de Oliveira Santos^{1}, Elson José da Silva^{2}, Rodney Rezende Saldanha^{2}, Alex Sander de Moura^{3}
^{1}Federal Institute of Espírito Santo, Brazil; ^{2}Federal University of Minas Gerais; ^{3}Federal University of Juiz de Fora,
In this paper the Generalized Finite Element Method (GFEM) with enriched plane wave is used to solve wave propagation problem in an electrically large domain. To calculate the integrals of the weak form of this method in the reference triangle two high order Gaussian quadrature approaches will be investigated: Traditional and one adaptive method. To validate the presented proposal the Generalized Finite Element Method will be used to solve a wave propagation problem.
Modeling and Analysis of GIC Effects on Power Grid and Power Transformer using Harmonic Balance Method
Junwei Lu^{1}, Xiaojun Zhao^{2}, Zhiguang Cheng^{3}
^{1}Griffith University, Australia; ^{2}North China Electric Power University, Baoding, China; ^{3}3Institute of Power Transmission and Transformation Technology, Baoding, China
Geomagnetically induced currents (GICs) caused by geomagnetic disturbances (GMDs) have a significant impact to power system and high voltage (HV) power transformers. The paper introduces an effective Harmonic Balance Method (HBM) for modeling and analyzing GIC effects on power grid and power transformers. The DC biased problems in HV transformers caused by GIC can be solved by using Harmonic Balance Finite Element Method (HBFEM), while the power system model including DCbiased transformer in GIC analysis can be derived by using HBM based transformer impedance matrix and power system model. During GIC flow, harmonic currents and voltages generated by saturated DCbiased transformers, and harmonic power losses can be directly calculated by using proposed HBFEM and Harmonic Balance Impedance Matrix (HBIM) model.
An IntegroDifferential Time Domain Scheme for Electromagnetic Field Modeling in HTS Materials
Hocine MENANA, Mohamad FARHAT, Melika HINAJE, Bruno DOUINE
Université de Lorraine, France
In this work, we developed an integrodifferential model in the time domain for electromagnetic field computation in high temperature superconducting (HTS) composite materials which are characterized by a nonlinear anisotropic electrical conductivity and multiscale dimensions. A relaxation method is applied to improve the convergence of the solution and to reduce the computation time. In the aim validation, a numerical example is considered where the numerical evaluation of AC losses in a BiSrCaCuO type HTS tape is compared to analytical modeling using measured parameters.
Performance analysis of finitedifference contrast source inversion and increment contrast source inversion
Wencong Jiang^{1}, Minjing Zhong^{1}, Liang Guo^{1}, Hong Yu^{2}
^{1}College of Information and Control Engineering, China University of Petroleum; ^{2}College of Science, China University of Petroleum
Contrast source inversion (CSI) is one of the wellknown methods for solving electromagnetic inverse scattering problem on the basis of integral equations. Two different approaches to reconstructing the unknown dielectric properties of objects are considered. These are finite difference contrast source inversion (FDCSI) and increment contrast source inversion (IncCSI). Both are based on CSI method and applicable for models under an inhomogeneous background. The former uses finite difference method to solve the integral equations which can expand the application scope of CSI. The latter does some adjustments to CSI. It reconstructs objects with the increment of measured scattered data after placing the objects of interest in imaging domain. Each method is described briefly. The performances of both methods are analyzed and compared in imaging accuracy and scope of application. Numerical results are displayed to verify the superiority of IncCSI.
Nonlinear Eigenmode Computation of Plasmonic NanoResonators
Mondher Besbes, Christophe Sauvan
Laboratoire Charles Fabry, Institut d’Optique Graduate School, CNRS, France
This paper is dealing with the eigenmode computation of nanoresonators made of dispersive and absorptive materials. The presence of material dispersion leads to a nonlinear eigenvalue problem. We present two different approaches to linearize the nonlinear problem. The first one is based on the introduction of auxiliary fields and the second one uses a Taylor expansion. We present the implementation of these methods with the finite element method and apply them to calculate the quasinormal modes of a metallodielectric coreshell nanocube.
Numerically Inversed Multiscale Behavior Model and Vector Potential Formulation: Convergence Properties
Eduardo Leal Grade, Laurent Bernard, Nelson Sadowski, Patrick KuoPeng
Federal University of Santa Catarina, Brazil
Multiscale approaches are attractive solutions for the modelling of the magnetoelastic behavior of ferromagnetic materials in electromagnetic device simulations. For use in magnetic vector potential formulations, the material behavior model should consider the magnetic flux density as input parameter. To achieve this aim, a simplified multiscale model is considered with numerical inversion by NewtonRaphson’s method. This inverse model is implemented into the finite element method and a threephase transformer is considered, as an example, to analyze convergence properties and computational cost. The results are compared to the ones obtained using direct approaches. It is shown that the use of the numerically inversed multiscale model is a viable solution with parallel computing capabilities.
Acceleration Techniques for LinearSystem Solver in Shielding Current Analysis of Cracked HighTemperature Superconducting Film
Atsushi Kamitani, Teruou Takayama, Ayumu Saitoh
Yamagata University, Japan
Two acceleration techniques are applied to a linear system in the shielding current analysis of a cracked hightemperature superconducting (HTS) film. When the shielding current density is calculated in the HTS film, a linear system of special type has to be solved at each iteration cycle of the Newton method. Although the linear system can be stably solved by means of the variablereduction method (VRM), its numerical solution costs much computation time. In order to accelerate the VRM, a large portion of matrixvector multiplication is performed by means of the Hmatrix method and the variable preconditioned GMRES is adopted as a linear system solver. Consequently, the accelerated VRM becomes about 4 times faster than the conventional VRM.
An Efficient Parallel Computing Method for the SteadyState Analysis of Electric Machines Using the Woodbury Formula
Bo He, Chuan Lu, Ningning Chen, Dingsheng Lin, Ping Zhou
Ansys, United States of America
This paper describes a parallel computing method for the steadystate analysis of electric machines. In this method, due to the low rank of the coupling matrix, the Woodbury formula is exploited to develop a highly efficient parallel algorithm to solve the formulated linearized block matrix.
An Efficient Parallel Computing Method for the SteadyState Analysis of LowFrequency Electromagnetics Using an AntiPeriodic Condition
Bo He, Ningning Chen, Dingsheng Lin, Chuan Lu, Ping Zhou
Ansys, United States of America
This paper describes an efficient parallel computing method based on the Message Passing Interface (MPI) for the steadystate analysis of lowfrequency electromagnetics. In this method, two frames of reference are used to account for rigidbody motions, and an antiperiodic condition is exploited to reduce simulation time.
Study of the combined effects of the airgap transfer for Maxwell Tensor and the tooth mechanical modulation in electrical machines
Raphaël Pile^{1,2}, Yvonnick Le Menach^{1}, Jean Le Besnerais^{2}, Guillaume Parent^{3}
^{1}L2EP, France; ^{2}EOMYS ENGINEERING, France; ^{3}LSEE, France
The Maxwell Tensor (MT) method is widely used to compute global forces or local surface forces for vibroacoustic design of electrical machines under electromagnetic excitation. In particular the airgap Maxwell Tensor method is based on a cylindrical shell in the middle of the airgap. This communication proposes to quantify the differences between the airgap MT and the magnetic force wave experienced by the stator. In particular the airgap to stator transfer and the tooth mechanical modulation effect are studied. A numerical application is performed with a turboalternator to illustrate the respective and combined effects of both phenomena. The communication highlights that the tooth mechanical modulation alone is not necessary relevant for electrical machines with a high number of tooth. However the combination of both phenomena has a clear impact on the computed magnetic surface force.
Equivalent Circuit Allowing Loss Separation Synthesized from Field Computations: Application to Induction Heating
Toshihito Shimotani^{1,2}, Hajime Igarashi^{2}, Eiji Hashimoto^{1}, Hiroyuki Imanari^{1}
^{1}TOSHIBA MITSUBISHIELECTRIC INDUSTRIAL SYSTEMS CORPORATION, Japan; ^{2}Information Science and Technology Department, Hokkaido university, Japan
In this paper, the proper orthogonal decomposition (POD) is applied to reduce the electromagnetic finite element equation of the 3D model of an induction heater (IH) for hot strip mill. Based on the result of POD, the equivalent circuit of IH is synthesized where the circuit parameters are determined by fitting to the input impedance at sampling frequencies. The copper losses in the coil and heating plate can be separately evaluated using the equivalent circuit synthetized by the proposed method.
FEM Formulation with DirichletToNeumann map boundary condition for Eddy Current problems.
Anton Efremov^{1}, Antea Perrotta^{2}, Salvatore Ventre^{2}, Lalita Udpa^{1}, Antonello Tamburrino^{1,2}
^{1}Michigan State University, United States of America; ^{2}University of Cassino and Southern Lazio, Italy
In this work a differential formulation of the Eddy Current Problem, combined with exact boundary condition based on the DirichletToNeumann map (DTN) is proposed. The numerical model is obtained via a FEM discretization combined with the Galerkin approach. Specifically, the Reduced Vector Potential FEM formulation is truncated by an exact DTN boundary condition, thus reducing the size of the region to be discretized. An additional reduction of the computational cost can be achieved by properly sparsifying the dense submatrix corresponding to the DTN (boundary) operator. Several model problems are investigated, and the results are compared to those from classic approaches.
A neural approach for fast direct and inverse Preisach model
Gabriele Maria Lozito^{1}, Ermanno Cardelli^{2}, Antonio Faba^{2}, Valentina Lucaferri^{1}, Simone Quondam Antonio^{2}, Francesco Riganti Fulginei^{1}, Alessandro Salvini^{1}, Antonino Laudani^{1}
^{1}Universita degli Studi Roma Tre; ^{2}Università degli Studi di Perugia
A computationally efficient approach for the numerical modelling of hysteretic magnetic materials is presented. The approach exploits the simplicity of the identification procedure for the Preisach model of hysteresis and the reduced computational costs of Neural Networks. The model for hysteresis is implemented both in direct and inverse form. Validation is performed against independent dataset, with evident computational speedup, which can be a valuable asset for Finite Element Method simulations.
Boundary Element Methods for Field Reconstruction in Accelerator Magnets
Melvin Liebsch^{1,2}, Stephan Russenschuck^{1}, Stefan Kurz^{2}
^{1}CERN, Switzerland; ^{2}Technical University of Darmstadt, Germany
Most established approaches for magnetic measurement of accelerator magnets aim for a characterization of the magnetic ﬁeld by means of cylindrical eigenfunctions of the Laplace equation, which are known as ﬁeld harmonics. These ﬁeld harmonics are measured with long, rotatingcoil magnetometers covering the magnet and its fringeﬁeld region, and treating the results as a 2D ﬁeld problem. There are four major limitations of this ﬁeld representation:
 1) Limitation to circular apertures, and
 2) spectral coefﬁcients correspond to global ﬁeld distributions, i.e. uncertainties in coefﬁcients do not correspond to local measurement uncertainties. Moreover,
 3) limitation to straight magnets and
 4) no feedback on local ﬁeld distributions in the magnet extremities.
In this paper an alternative approach with the potential to migrate these issues is presented, which based on Kirchhoff's integral equation. Dirichlet and Neumann data are approximated on finite dimensional approximation spaces. It is shown that, dependent on the formulation, either the Dirichlet or Neumann data can be related to flux measurements along the chosen domain boundary. Exploiting Calderón's Projector, one can then recover the missing Cauchy datum in a numerical postprocessing. Results for the reconstruction of integrated fields are presented. In this case, the stretched wire measurement system is used to acquire boundary fluxes. In the paper to be submitted for COMPUMAG 2019, results of 3D ﬁeld reconstructions using a translatingcoil magnetometer will be included. Additionally, the propagation of measurement uncertainties to the boundary data will be analyzed. In this way, local measurement uncertainties can be detected and eliminated by resampling.
