Research On Application Of Electromagnetic Wave Inverse Scattering For Structural Damage Identification

In general, there are large amount of flaws and inclusions in structure and material for the erosion and rust-eaten of environment as well as the affection of technology of production. With the help of elapse of time time, there happens with heavy damage, so much so that it leads to fracture, then it get rise to disaster consequence. So, how to use simple and fast method and to identify flaws and inclusions as well as their location and shape is the task of nondestructive testing all the time. In the dissertation, the research on identification of flaws in structure and practical application as well as corresponding mathematical method is discussed. All of that gives the theoretical basis for nondestructive testing.The relating to methods based on the research on international and domestic electromagnetic wave(elastic wave, acoustic wave) for the identification of flaws are all-round viewed. First, in virtual of identification of flaws is a typical of in-verse problems, proceeding from time-harmonic electromagnetic Maxwell's equa-tion and Helmholtz equation, the uniqueness and existence of direct scattering problems including the numerical algorithms of diverse of boundary conditions is given. Second, the uniqueness and existence of inverse scattering problems and the theory of ill-posed integral equation are briefly looked back upon. Finally, indicator function method for boundary identification is set up under all kinds of boundary conditions for inverse scattering of homogenous and inhomogenous objects, meanwhile, the proof of possibility for near-field measurements and nu-merical simulation are given. The research achievement are acquired as follows:1. From mathematical models for inverse scattering in two dimensional homoge-nous media including Dirichlet, Neumann, Robin, all kinds of probable mixed boundaries and cracks, direct and inverse scattering are discussed, and ill-posed integral equation and indicator function method are formulated for the diverse of boundary identification. It is shown that the kernel of the integral equation characters the boundary of scatterer, which is determined by solv-ing it by virtual of regularity method, meanwhile, some numerical tests are given.2. From mathematical models for inverse scattering in two dimensional inho-mogenous media including variable impedance, all kinds of probable mixed variable impedance boundaries and cracks, from interior and exterior trans-mission problems and radiation condition, ill-posed integral equation and indicator function method are formulated for the diverse of boundary iden-tification. It is shown that the kernel of the integral equation charactersthe boundary of scatterer, which is determined by solving it by virtual of regularity method, meanwhile, some numerical tests are given.3. Numerical tests shows that indicator function method is a simple and fast method, by which better reconstruction can be gained for no superior knowl-edge of the physical properties about media.