Identification problem of acoustic media in the frequency domain based on the topology optimization method
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RESEARCH PAPER
Identification problem of acoustic media in the frequency domain based on the topology optimization method Juliano F. Gonc¸alves1 Em´ılio C. N. Silva1
˜ B. D. Moreira1 · Ruben A. Salas1 · Mohammad M. Ghorbani1 · Wilfredo M. Rubio2 · · Joao
Received: 20 January 2020 / Revised: 18 April 2020 / Accepted: 24 May 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract 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. Keywords Inverse problem · Topology optimization · Acoustics · Frequency domain · Parameter identification
1 Introduction
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Inverse problems are commonly found in many fields of engineering and science where observations are used to infer process parameters. This type of problem can be defined according to the nature of the variables that are inferred. Supposing that we have a mathematical model which describes a physical process, as presented in Fig. 1, three different problems can be stated as (Baumeister and Leit˜ao 2005):
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Responsible Editor: Hyunsun Alicia Kim Juliano F. Gonc¸alves
[email protected] 1
Department of Mechatronics and Mechanical Systems Engineering, School of Engineering, University of S˜ao Paulo, S˜ao Paulo, Brazil
2
Faculty of Mines, Department of Mechanical Engineering, Universidad Nacional de Colombia, Medell´ın, Colombia
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Forward problem: given the inputs Xi and the system parameters ρi , find out the outputs Yi of the model M; Reconstruction problem: given both system parameters ρi and outputs Yi , find out the inputs Xi ; Identification problem: given both inputs Xi and outputs Yi , find out the system parameters ρi of the model M.
The first type of problem is called Forward, or Direct, problem due to
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