Combining topological sensitivity and genetic algorithms for identification inverse problems in anisotropic materials

The identification inverse problem is solved here for flaw detection in anisotropic materials by means of an innovative approach: the combination of Genetic Algorithm and the Topological Sensitivity in anisotropic elasticity. The Topological Sensitivity provides a measure of the susceptibility of a defect being at a given location. This is based on a linearized topological expansion, applying Boundary Integral Equations and using solely information of the non-damaged state. It is proved that the Topological Sensitivity provides an accurate tool for estimating the location and size of defects. First, it is shown that the minimum of the residual (cost function) topological sensitivity pinpoints the location and size of the actual flaws, and secondly, the minimization of the residual topological sensitivity is carried out using Genetic Algorithm. When the Genetic Algorithm is applied to the residual Topological Sensitivity instead of to the full residual, the applicability of this method is enhanced since the computational effort, which is the major drawback of this type of search methods, is drastically reduced. In this paper, the formulation for linearly anisotropic elastic media is composed for the case of circular flaws, although the procedure is extensible to other kinds of defects like elliptical cavities, elastic or rigid inclusions or cracks.