Theoretical and experimental validation of a non-linear vocal fold model (original) (raw)
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Experimental validation of some additional issues in physical vocal folds models
Insight in vocal folds oscillation mechanisms is important in the understanding of phonation, the synthesizing of voiced sound and the study of voice disorders. In general, simplifications of the physical ongoing 3D fluid-structure interaction between the living tissues and the airflow are favoured. Several simple models (lumped models) are obtained by representing the vocal folds as a distribution of elastic mass(es). The mass-spring-damper system is acted on by a driving force resulting from the pressure exerted by the intraglottal airstream. The outcome of theoretical models is 'in-vitro' validated using rigid or deformable vocal fold replicas mounted in a suitable experimental set-up. Previous research focused on the prediction of the phonation pressure threshold and oscillation frequency of the 'in-vitro' replica in absence and presence of acoustical feedback whereas in the theoretical model a vocal fold is represented by one or two masses. The model yielded accurate prediction of the oscillation threshold and frequency. In this paper we present a new in-vitro set-up which allows to overcome some limitations of this previous study. Thanks to the use of a digital camera synchronised with a light source and pressure sensors this set-up allows 1) to measure the area of the vocal folds opening and 2) to impose independent initial conditions as e.g. height of the initial opening and internal pressure in the vocal fold replica. Preliminary results are presented and their impact on physical modelling are discussed.
An in vitro setup to test the relevance and the accuracy of low-order vocal folds models
The Journal of the Acoustical Society of America, 2007
An experimental setup and human vocal folds replica able to produce self-sustained oscillations are presented. The aim of the setup is to assess the relevance and the accuracy of theoretical vocal folds models. The applied reduced mechanical models are a variation of the classical two-mass model, and a simplification inspired on the delayed mass model for which the coupling between the masses is expressed as a fixed time delay. The airflow is described as a laminar flow with flow separation. The influence of a downstream resonator is taken into account. The oscillation pressure threshold and fundamental frequency are predicted by applying a stability analysis to the mechanical models. The measured frequency response of the mechanical replica together with the initial ͑rest͒ area allows us to determine the model parameters ͑spring stiffness, damping, geometry, masses͒. Validation of theoretical model predictions to experimental data shows the relevance of low-order models in gaining a qualitative understanding of phonation. However, quantitative discrepancies remain large due to an inaccurate estimation of the model parameters and the crudeness in either flow or mechanical model description. As an illustration it is shown that significant improvements can be made by accounting for viscous flow effects.
Dynamics of a two-mass model of the vocal folds form men, women, and children
This paper analyzes how the oscillatory behavior of the vocal folds changes according to laryngeal size. A version of the popular two-mass model of the vocal folds is used, coupled to a two-tube approximation of the vocal tract in configuration for vowel /a/. The standard male configurations of these models are used as reference, and female and child configurations are derived by scaling the dimensions and biomechanical parameters of tissues. For simplicity, a single scaling parameter is used for all the dimensions of the vocal folds and vocal tract. Simulations of the vocal fold oscillation and oral output are produced by numerical solution of the equations, and for varying values of the size scaling parameter. The results show that the oscillation threshold conditions become more restricted for smaller larynges, such as the female and child larynges, in agreement with reported experimental results. They also show a clear hysteresis effect at voice onset-offset, with more severe threshold conditions to start the vocal fold oscillation than those to maintain it.
Simulation of vocal fold oscillation with a pseudo-one-mass physical model
Speech Communication, 2008
This paper presents a novel "pseudo-one-mass model" of the vocal folds, which is derived from a previously proposed two-mass model. Two-mass models account for effects of vertical phase differences in fold motion by means of a pair of coupled oscillators that describe the lower and upper fold portions. Instead, the proposed model employs a single mass-spring oscillator to describe only the oscillation of the lower fold portion, while phase difference effects are simulated through an approximate phenomenological description of the upper glottal area. This approximate description is derived in the hypothesis that 1 : 1 modal entrainment occurs between the two masses in the large-amplitude oscillation regime, and is then exploited to derive the equations of the pseudo-one-mass model. Numerical simulations of the reference two-mass model are analyzed to show that the proposed approximation remains valid when values of the physical parameters are varied in a large region of the control space. The effects on the shape of the glottal flow pulse are also analyzed. Comparison of simulations with the reference two-mass model and the pseudo-one-mass model show that the dynamic behavior of the former is accurately approximated by the latter. The similarity of flow signals synthesized with the two models is assessed in terms of four acoustic parameters: fundamental frequency, maximum amplitude, open quotient, and speed quotient. The results confirm that the pseudo-one-mass model fit with good accuracy the behavior of the reference two-mass model, while requiring significantly lower computational resources and roughly half of the mechanical parameters.
A simple, quasi-linear, discrete model of vocal fold dynamics
2005
In current speech technology, linear prediction dominates. The linear vocal tract model is well justified biomechanically, and linear prediction is a simple and well understood signal processing task. However, it has been established that, in voiced sounds, the vocal folds exhibit a high degree of nonlinearity. Hence there exists the need for an approach to modelling the behaviour of the vocal folds. This paper presents a simple, nonlinear, biophysical vocal fold model.
Revisiting the two-mass model of the vocal folds
Papers in Physics, 2013
Realistic mathematical modeling of voice production has been recently boosted by applications to different fields like bioprosthetics, quality speech synthesis and pathological diagnosis. In this work, we revisit a two-mass model of the vocal folds that includes accurate fluid mechanics for the air passage through the folds and nonlinear properties of the tissue. We present the bifurcation diagram for such a system, focusing on the dynamical properties of two regimes of interest: the onset of oscillations and the normal phonation regime. We also show theoretical support to the nonlinear nature of the elastic properties of the folds tissue by comparing theoretical isofrequency curves with reported experimental
Influence of acoustic loading on an effective single mass model of the vocal folds
2007
Three-way interactions between sound waves in the subglottal and supraglottal tracts, the vibrations of the vocal folds, and laryngeal flow were investigated. Sound wave propagation was modeled using a wave reflection analog method. An effective single-degree-of-freedom model was designed to model vocal-fold vibrations. The effects of orifice geometry changes on the flow were considered by enforcing a time-varying discharge coefficient within a Bernoulli flow model. The resulting single-degree-of-freedom model allowed for energy transfer from flow to structural vibrations, an essential feature usually incorporated through the use of higher order models. The relative importance of acoustic loading and the time-varying flow resistance for fluid-structure energy transfer was established for various configurations. The results showed that acoustic loading contributed more significantly to the net energy transfer than the time-varying flow resistance, especially for less inertive supraglottal loads. The contribution of supraglottal loading was found to be more significant than that of subglottal loading. Subglottal loading was found to reduce the net energy transfer to the vocal-fold oscillation during phonation, balancing the effects of the supraglottal load.
Nonlinear vocal fold dynamics resulting from asymmetric fluid loading on a two-mass model of speech
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2011
Nonlinear vocal fold dynamics arising from asymmetric flow formations within the glottis are investigated using a two-mass model of speech with asymmetric vocal fold tensioning, representative of unilateral vocal fold paralysis. A refined theoretical boundary-layer flow solver is implemented to compute the intraglottal pressures, providing a more realistic description of the flow than the standard one-dimensional, inviscid Bernoulli flow solution. Vocal fold dynamics are investigated for subglottal pressures of 0.6 < p s < 1.5 kPa and tension asymmetries of 0.5 < Q < 0.8. As tension asymmetries become pronounced the asymmetric flow incites nonlinear behavior in the vocal fold dynamics at subglottal pressures that are associated with normal speech, behavior that is not captured with standard Bernoulli flow solvers. Regions of bifurcation, coexistence of solutions, and chaos are identified.
The Journal of the Acoustical Society of America, 2009
This paper analyzes the capability of a mucosal wave model of the vocal fold to predict values of phonation threshold lung pressure. Equations derived from the model are fitted to pressure data collected from a mechanical replica of the vocal folds. The results show that a recent extension of the model to include an arbitrary delay of the mucosal wave in its travel along the glottal channel provides a better approximation to the data than the original version of the model, which assumed a small delay. They also show that modeling the vocal tract as a simple inertive load, as has been proposed in recent analytical studies of phonation, fails to capture the effect of the vocal tract on the phonation threshold pressure with reasonable accuracy.