Research On The Forward Problem Of Electromagnetic Tomography Technology

The forward problem of electromagnetic tomography (EMT) can be summarizedas a boundary value problem of electromagnetic field. In general, this kind of problemis composed by a partial differential equation and essential boundary conditions.Simply, if the boundary of the region is coincident with the coordinate, the solutioncould be analyzed by analytical method. However, it is difficult for most problems tofind the exact solutions. So it is necessary to obtain their solutions by numericalmethods with approximation. Among these methods, finite difference method (FDM),finite element method (FEM) and boundary element method (BEM) are most popularwith their respective characteristics and applications.BEM is an effective numerical method which is based on boundary integralequation. Begin with the basic mathematical theory of BEM, we have acomprehensive research on the application of the BEM on EMT and build theappreciate models for certain EMT systems. After that, simulations by MATLAB aredone. Conclusions are achieved through the comparison between the simulationresults and numerical analysis. Meanwhile, a preliminary study of the practicalapplication of the BEM on the electromagnetic detection is discussed.The thesis could be divided into five main parts:1. A perfect electric conductor (PEC) model for high frequency EMT system isbuilt. The scalar magnetic potential is introduced to the model as the basic unknownto substitute the vector magnetic potential in traditional BEM equations. An integralequation is obtained by computing the Maxwell equations. By MATALB simulation,four typical sensitivity maps are calculated. Results are compared with that achievedby H dot H method to confirm the validity of the model.2. On the basis of the PEC model, the thin skin depth approximation (TSA)model for the broad-frequency EMT system. Because the influence of the frequency isnot ignored, the multi-frequency response of EMT system, as well as the four typicalsensitivity maps is computed.3. The calculation methods of the scalar magnetic potential are summarized. Bycomparison, we know that the method used Gauss integral formula is most simple andquick.4. To solve the problem of singular integral which is occurred frequently in BEM, the method of auxiliary source (MAS) is introduced to the calculation ofsensitivity distribution of EMT. The auxiliary source on the auxiliary surface is faraway from the observation point and the singular integral is avoided fundamentally.5. By building the appreciate model, BEM is used in the electromagnetic testing.MATLAB simulation for indentifing the object shape is done. An optimized EMTsystem is chosen to dectect the surface flaw of the rail. The results provide newinsights into the application of magnetic induction sensing technique using BEM.By the brief summary of the work of the thesis, helpful suggestions for thefurther development of the application of BEM on EMT are presented.