Simulation of vocal fold oscillation behaviour by a self-oscillating glottis model

As a good compromise between simplicity and approximation of real human vocal vold oscillation behaviour the Ishizaka-Flanagan two-mass model [I] is widely used in articulatory speech synthesis. But its poor results in modelling the oscillatory behaviour during glottal abduction/adduction and in modelling leakage flow during normal phonation are drawbacks. The two-mass model can be improved without increasing its complexity, if a non-oscillating and aperture-dependent bypass is added. A self-oscillating glottis model leads to physiology-related control parameters. Only simple rules for generating time functions for these control parameters as well as for controlling supraglottal articulation are needed [2]. 2 THE TWO-MASS MODEL The acoustics and aerodynamics of the vocal tract are modelled by a reflection type line analog [3, 41 (fig. 1). The vibration behaviour of the vocal folds is modelled by a two-mass approximation (fig. 2), i.e. the mechanical part of the glottis model. In this model the upper and lower part of each vocal fold are represented by different harmonic oscillators (damped mass-spring-systems with mass mi, spring wnstant si, and damping ri; i=1,2). The masses are stiffness-coupled (kc). The mechanical part is driven by pressure-induced forces acting on the i ~ e r surfaces of the vocal folds. The forces acting on the masses can be approximated from the pressure values of the tube representing the glottis p during the open phase of the glottis, and from subglottal pressure psub during the closed phase of t%e glottis [I]. The wntrol parameters acting directly on the mechanical part of the glottis model are glottal aperture GA and cord tension CT (fig. 1). GA characterizes the equilibrium position of the vocal folds, i.e. the degree of abduction/adduction which can be controlled actively. The output of the mechanical part of the glottis model is the glottal area ag which describes the instantaneous area of glottal constriction resulting from the actively controllable positioning of the folds and from their vibration. 3. THE NON-0SCILTAI"I'NG BYPASS Even during normal phonation, vocal fold vibration is a complex three-dimensional process. The IshizakaFlanagan two-mass approximation models two of them: The first dimension is defined by the direction of the displacement for the oscillatory masses (lateral direction) and the second dimension is defined by the direction from trachea to pharynx (vertical or inferior-superior direction), i.e. the direction in which the two masses are ordered. These dimensions define the plane of figure 2. According to the phase lag between the two mass pairs during oscillation, the two-mass approximation is able to model the elliptical movement for the center of mass of the folds occuring during normal phonation: The opening of the folds is accompanied Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:1994595 C5-458 JOURNAL DE PHYSIQUE IV by an upward shift of glottal closure (e.g. [5], p. 2650. The third dimension is defined by the anteriorposterior direction, i.e. the direction given by the length of the glottal slit. According to the physiological fact that the anterior attachment of the folds is on the surface of the arytenoid cartilages and according to the fact, that these cartilages still form a part of the glottal slit (e.g. [6], pp. 135-140), the vocal folds can be devided into a cartilaginous and a membranous part (fig. 3). In our simple modification of the two-mass model, we take a non-oscillating bypass in order to model the cartilaginous part while the oscillating masses model the membranous part of the glottis (fig. 4). The ordinary two-mass model calculates the cross-sectional areas a1 and a2 between each mass pair m i and m2. The glottal area ag is calculated by taking the minimum of a1 and a2 and by adding the bypass area aby. The bypass can be implemented in two different ways as a linked leak or as a parallel chink [7,8]. Since we are interested in dynamical glottal abduction/adduction behaviour, we here used a linked leak.