Keywords: inclusion, genetic algorithm, measurements, Helmholtz equation, inverse problem, search space.

A major area in flaw identification consists of the solution of problems in which the parameters of a flaw are to be inferred from measured scattering data. In such problems, a model of the system response to a given flaw chosen from a large class of possible flaws is constructed. This model is used in conjunction with a non-destructive testing (NDT) procedure; the latter provides measurements representing the effect of the actual flaw on the structure. The actual flaw is then identified as the candidate flaw whose response, based on the model, is the closest to the measured response in some pre-defined norm.

The purpose of this paper is to investigate the accurate detection and identification of inclusions in two-dimensional structures. For the sake of simplicity we consider here the time-harmonic response of flat linear membranes. Given certain measurements, typically along part of the boundary of the membrane, the problem consists of first estimating whether the membrane contains a soft inclusion, and if so, finding the accurate parameters (location, shape) of the inclusion that produces a response closest to the given measurement data in the chosen norm

We consider a closed, bounded two-dimensional membrane Omega with a boundary Gamma. Homogeneous Dirichlet and Neumann boundary conditions are imposed on Gamma and an excitation in the form of inhomogeneous Neumann boundary conditions is applied at Gamma^S subset of Gamma. Assuming time-harmonic vibrations we obtain that the amplitude of the membrane's vibration is governed by the Helmholtz equation. The domain is partitioned into two subdomains, with different material properties - a matrix and an inclusion. The inverse identification problem consists of identifying the shape and location of the inclusion.

The optimization was carried out using a genetic algorithm. Each possible inclusion was encoded into a binary string of length nel, where each bit in the string corresponds to an element in the mesh according to the numbering of the elements in that mesh. A bit receives the value 1 if the corresponding element is included in Omega_I, otherwise it receives the value 0. It was assumed that the inclusion spans a whole number of elements in the finite element mesh. Under these general conditions the algorithm can not find the sought inclusion. In order for the algorithm to be successfull the inclusion sought must be small (and must fit into a small square domain) but larger than a single element.

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