Multiresolution analysis for reconstruction of conductivity profiles in eddy current nondestructive evaluation using probe impedance data

This paper presents a wavelet-based multiresolution analysis method for solving the inverse problem in eddy current testing (ECT). Using the probe impedance signals as the measurement data, the reconstruction of conductivity profiles can be performed by a minimization scheme. The method allows to identify the regions where the perturbation may be localized and to retrieve the unknown parameters only in those regions. Some numerical simulation results show the feasibility of the technique

Sequential optimization method for the design of electromagnetic device

Three sequential optimization methods, sequential least square method, sequential Kriging method, and sequential linear Bayesian method, are presented for the optimization design of electromagnetic device. Sequential optimization method (SOM) is composed of coarse optimization process and fine optimization process. The main purpose of the former is to reduce the design space; while the target of the latter is to update the optimal design parameters. To illustrate the performance of the proposed methods, an analytic test function and the TEAM Workshop Problem 22 are investigated. Experimental results of test function demonstrate that SOM can obtain satisfactory solutions; and practical application illustrates that the number of finite element sample points is less than 1/10 compared with that by direct optimization method, while the optimal results are even better than that by direct optimization method. © 2008 IEEE

Electromagnetic device design based on RBF models and two new sequential optimization strategies

We present two new strategies for sequential optimization method (SOM) to deal with the optimization design problems of electromagnetic devices. One is a new space reduction strategy; the other is model selection strategy. Meanwhile, radial basis function (RBF) and compactly supported RBF models are investigated to extend the applied model types for SOM. Thereafter, Monte Carlo method is employed to demonstrate the efficiency and superiority of the new space reduction strategy. Five commonly used approximate models are considered for the discussion of model selection strategy. Furthermore, by two TEAM benchmark examples, we can see that SOM with the proposed new strategies and models can significantly speed the optimization design process, and the efficiency of SOM depends a little on the types of approximate models. © 2006 IEEE

An improved multiquadric collocation method for 3-D electromagnetic problems

The multiquadric radial basis function method (MQ RBF or, simply, MQ) developed recently is a truly meshless collocation method with global basis functions. It was introduced for solving many 1- and 2-D partial differential equations (PDEs), including linear and nonlinear problems. However, few works are found for electromagnetic PDEs, especially for 3-D problems. This paper presents an improved MQ collocation method for 3-D electromagnetic problems. Numerical results show a considerable improvement in accuracy over the traditional MQ collocation method, although both methods are direct collocation method with exponential convergence. © 2007 IEEE

Z-transform-based FDTD analysis of perfectly conducting cylinder covered with unmagnetized plasma

In this paper, a novel and normalized Z-transform-based finite-difference time-domain (ZTFDTD) method is presented for simulating the interaction of the electromagnetic (EM) wave with unmagnetized plasma. The 2-D ZTFDTD formulations for unmagnetized plasma are derived. Using a simplified 2-D model for a perfectly conducting cylinder covered with unmagnetized plasma, the stealth effect of unmagnetized plasma is studied in different thicknesses of plasma, electron densities of plasma, EM wave frequencies, and plasma collision frequencies. Numerical results indicate that plasma stealth is effective in theory and reasonable selection for the plasma parameters can greatly enhance its effectiveness. © 2007 IEEE

Multiscale combined radial basis function collocation method for eddy currents analysis in high-speed moving conductors

A novel multiscale combined radial basis function (RBF) collocation method, as a truly meshless method, is presented to overcome the shortage of general RBF collocation method and is applied to analyze eddy currents in high-speed moving conductors in this paper. A typical example is set here to illustrate the accuracy and affectivity of the proposed method, including a comparison with general RBF collocation method and finite element method (FEM). © 2009 IEEE

Domain decomposition combined radial basis function collocation method to solve transient eddy current magnetic problems with moving conductors

Radial basis function (RBF) collocation method is a kind of pure meshless numerical method and has been applied to solve static and transient electromagnetic problems. Especially, it shows a great advantage in the computation of moving conductor eddy current magnetic problems. To simulate the conductor movement, the field equations are decoupled with superposition principle and solved by time-domain iteration under moving coordinate systems. One problem is that the coefficient matrix of RBF governing equations, which needs to be computed in each iteration step, is full. As the number of RBF nodes increases, the computational capacity will grow rapidly. The domain decomposition method (DDM), which divides the solving domain into several subdomains, could be conveniently combined with RBF collocation method. This paper first applies DDM combined RBF collocation method to compute transient eddy current magnetic field problems with moving conductors. With this novel method, the iteration only proceeds in the subdomains containing conductors. And the magnetic field in the subdomains without conductors needs to be computed just once before the iteration. The dimension of the coefficient matrix computed in the iteration is only determined by the number of nodes in the corresponding subdomains and on the interfaces. An engineering problem is computed to show that the DDM combined RBF collocation method is much more efficient than the normal one. © 2011 IEEE

A novel superposition RBF collocation method to solve moving conductor eddy current problems

This paper presents a novel radial basis function (RBF) collocation method to solve the moving conductor eddy current problem. The magnetic field is considered an addition of two fields generated respectively by the excitation current and the eddy current according to the source superposition principle. The corresponding governing equations are decoupled and solved with the RBF. Moving coordinate systems in which the separate fields are computed are also constructed to avoid the model reconfiguration caused by the motion. Electromagnetic field equations are analyzed with kinetic equations and circuit equations together to simulate the motion process. A practical engineering problem is computed to verify the method. © 2009 IEEE

A boundary meshless method for transient eddy current problems

This paper presents a boundary meshless method (BMLM) for transient eddy current problems. With difference to the traditional boundary element method (BEM), the BMLM combines a point interpolation method (PIM) for construction of spatial interpolation functions with a boundary integral formulation for the governing equations, thus the spatial interpolation functions satisfy the Kronecker delta function and the essential boundary condition can be directly imposed without any other procedure. Theoretical analysis in details is given and a transient eddy current example is also presented to prove the proposed theory. © 2005 IEEE

A comparison of point interpolative boundary meshless method based on PBF and RBF for transient eddy-current analysis

This paper presents the boundary polynomial point interpolation meshless method (BPPIM) and the boundary radial point interpolation meshless method (BRPIM) based on the polynomial basis function (PBF) and radial basis function (RBF), respectively, for transient eddy-current analysis, and their interpolation shape functions satisfy the Kronecker delta function, thus, the essential boundary conditions can be directly imposed on the boundary nodes. An example on analyzing transient eddy current of a square metal column is set to prove the validity of the proposed methods, and a comparison on accuracy between BPPIM and BRPIM is analyzed as well. © 2007 IEEE