$${\mathscr {H}}$$ H -matrix acoustics BEM for vocal tract configuration optimization using genetic algo
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TECHNICAL PAPER
H ‑matrix acoustics BEM for vocal tract configuration optimization using genetic algorithms Álvaro Campos Ferreira1 · Gino Bertollucci Colherinhas1 · Éder Lima de Albuquerque1 · Marcela Rodrigues Machado1 · Marcus Vinicius Girão de Morais1 Received: 1 October 2019 / Accepted: 3 August 2020 / Published online: 17 August 2020 © The Brazilian Society of Mechanical Sciences and Engineering 2020
Abstract In this work, a genetic algorithm (GA) coupled to an H -matrices boundary element method (BEM) model was used to solve an inverse problem in order to obtain a vocal tract (VT) configuration from purely acoustic information. This methodology uses the acoustic flux through a straight line on the interior of the VT to define the fitness function used in the GA. The BEM model was built using Gmsh and Julia, and all of the code used in this paper is available online. The methodology was able to reproduce a goal VT configuration after 10,000 generations of 150 individuals. The obtained model was very close to the original; the mean error of all of the BEM results was 0.68%. Although the vowel /a/ was chosen to test the optimization methodology, the Gmsh and Julia scripts allow for the optimization of any vowel or consonant. Keywords Vocal tract · Acoustics · Genetic algorithms · Boundary element method · Hierarchical matrices
1 Introduction The human voice is a product of thousands of years of evolution. Other primates are not able to use voiced language because of their vocal tract limitations [27]. The human vocal tract, on the other hand, is incredibly flexible and can produce a wide variety of sounds. The physics of the vocal tract has been subject of study as a medical field for decades [1, 6, 18, 22, 41], and recent technology allowed a deeper comprehension on its mechanics and acoustics using Technical Editor: José Roberto de França Arruda. * Álvaro Campos Ferreira [email protected] Gino Bertollucci Colherinhas [email protected] Éder Lima de Albuquerque [email protected] Marcela Rodrigues Machado [email protected] Marcus Vinicius Girão de Morais [email protected] 1
Campus Darcy Ribeiro, Faculdade de Tecnologia, Universidade de Brasília, Bloco G, Asa Norte, Brasília, DF 70910‑900, Brazil
numerical methods together with advanced medical imaging technology. This new technology may even be used to infer the geometry of an scatterer or resonator from its sound behavior. This type of analysis is called inverse problems, and many solutions exist to solve them. One of them is a genetic algorithm approach, in which the variables of the problem are treated as different traits in an evolutionary process. Speech can be understood as a source-filter system, in which the vocal folds together with the lung generate a source like signal which is then filtered by the vocal tract (VT) [29, 35]. A schematic model of the speech system is shown in Fig. 1. The VT is the region contained between the glottis and mouth. The VT is composed by the supra-glottic portion of the larynx, oropharynx and oral
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