Solution of inverse problems by using FEM and structural functions

An approach for identification of structural anomalies in physical systems is presented, which combines the advantages of the Finite Element method (FEM), the Controlled-Source Electromagnetic method (CSEM) and the Statistical Experiment Design method. It consists of three main steps: forward analysis, inverse analysis and regularization, At the first stage, an empirical model of the physical system, based on the FEM and the Design of Experiments (DOE) method, is created. Next, data which is easily observable is introduced into the model to form a nonlinear system of simultaneous equations. And third, after finding the solutions, an appropriate procedure of regularization determines the "best" one. The latter includes the unknown parameters of the anomaly to be identified. The paper outlines the advantages of the approach and its usefulness for identification problem solution.