Topological imaging in layered plate by guided waves

The defect imaging by guided waves in layered plate is always an attractive project in non-destructive testing. The aim of this paper is to study the topological imaging theory and to determine whether it is possible to give the locations of all the defects in layered plate. A two-layered plate consist of aluminum and steel is considered. First, the formulas of the topological gradient are deduced theoretically. It is proved that the topological gradient is just a function in space domain and could indicate the defects' locations at the extreme value point. Then, according to the method of the topological imaging, the solutions of two situations are required, the forward problem and the adjoint problem, respectively. The model building and propagation of guided waves are all simulated in finite element software ANSYS. It is found that all the defects are located precisely at the topological image, which suggests that topological imaging can be an efficient method to obtain all the defects' locations in layered plate.