Identification problem of acoustic media in the frequency domain based on the topology optimization method

In this paper, the identification problem of acoustic parameters in the frequency domain is examined by means of a topology optimization (TO) approach. Data measured by acoustic receivers are collected from synthetic models and used as a reference in the optimization problem which aims at estimating the acoustic media properties that minimize a least-squares cost functional. A two-step optimization procedure is proposed to deal with multi-phase acoustic media problems by using linear and peak function material interpolation schemes. The idea is to use features from the multi-material topology optimization to reconstruct acoustic models with an increased level of sharpness. From the first step with linear interpolation, phase candidates are defined by a curve fitting process considering the summation of Gaussian curves and, therefore, this solution is used to create the peak material model for the second step. Thus, a multi-material model that is usually applied to design problems with predefined material candidates can be also used to solve this identification problem without prior knowledge of the exact properties of the model to be reconstructed. The optimization problem is solved by using a BFGS algorithm while the Levenberg-Marquardt Algorithm (LMA) is used to solve the least-squares curve-fitting problem. The proposed approach is analyzed through 2D numerical examples.