Victor WETZEL defended his thesis on the 9th of December, at 2.30 PM, made in the SEAM team (STMS Lab - Ircam, Ministère de la Culture, CNRS, Sorbonne Université) called :
« Lumped Power-Balanced Modelling and Simulation of the Vocal Apparatus: A Fluid-Structure-Interaction Approach. »
You can watch his defence via the Ircam MEDIA: https://medias.ircam.fr/x63f9f2
His jury was:
M. Brad Story (rapporteur), University of Arizona, College of Science: Speech, Lanuage and Hearing Sciences
M. Bernhard Maschke (rapporteur), Université Claude Bernard Lyon 1, LAGEPP
Mme. Nathalie Henrich Bernardoni (examinatrice), Grenoble INP, GIPSA-Lab
M. Yann Le Gorrec (examinateur), FEMTO-ST, Besançon
M. Pierre-Yves Lagrée (examinateur), IJLRA, Sorbonne-Université
M. Thomas Hélie (directeur de thèse), STMS-CNRS
M. Fabrice Silva (co-directeur de thèse), Aix Marseille Université, LMA
This work addresses the physical modelling and simulation of the vocal apparatus with a focus on the articulated vocal tract. The objective is to model both the propagation of acoustic waves and the fluid flow interacting with the tissues along the upper airways. Getting back to the basic principles of fluid mechanics and of thermodynamics, this thesis combines a set of hypotheses, approaches and tools to produce a nonlinear lumped-parameter model that accounts for acoustic propagation, but also for side branching (e.g., nasal coupling) and for articulation (with hard and soft moving tissues).
This work is carried out in the time-domain using the framework of port-Hamiltonian systems (pHs) that ensures the energy consistency and passivity of the models. The lumped-parameter model is built in several steps: (a) partition of the vocal tract into elementary tracts; (b) for each tract, decomposition of velocity and density fields on basis functions associated with the axial flow, transverse expansion flow, and fluid compression; (c) formulation of the projected mass and momentum conservation equations as a macroscopic pHs; (d) interconnection of these pHs through ports (possibly with side-branching) to build the nonlinear pHs model of the full vocal tract. Using electrical equivalent circuits, we show that this model provides new interpretations on Fluid-Structure Interactions (FSI) while preserving the modularity, physical interpretability and scalability of classical lumped-parameter models of the state-of-the-art.
To obtain an acoustical formulation an improve the numerical conditioning, we propose an equivalent (shifted) pHs, which variables are expressed in terms of fluctuations around a state at rest, using a variable change. The full vocal tract is obtained by interconnecting several tracts (using ports) and mechanical models of tissues on mobile walls, the latter being used to drive the geometry. This interconnection step involves algebraic relations that we solve with an assembly method based on directed graphs and differential-algebraic pHs. Power-balanced numerical simulations for simple co-articulations demonstrate the significant impact of the energy-consistent modelling of time-varying tracts on audible signals, while reproducing expected properties (power balance, acoustical resonances, transient effects, mass convection). As a corollary work based on the same hypotheses and approach, we propose lumped passive models of junction (of various complexity) between three tracts or pipes, that could be also used in musical acoustics for wind instruments. At last, we revisit the theoretical framework of the so-called indicator (or color) functions and level set methods for the time-space modelling of pHS with time-varying domains. This provides new insights on the interconnection and the coupling of infinite-dimensional FSI systems.