Vocal Fold Modeling - Graz University of Technology · 2005. 10. 25. · Anatomy & Physiology (1)...

Vocal Fold ModelingMartin Hagmuller

[email protected]

Signal Processing and Speech Communication Laboratory

Institute for Communication and Wave Propagation

Graz University of Technology

Vocal Fold Modeling – p.1/20

Overview

Motivation

Anatomy and Physiology

Vocal Fold Models

Conclusion


Motivation (1)

Waveform ModelParametric description of waveforme.g. Liljencrants-Fant modelflow derivative with four parameters

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 0.002 0.004 0.006 0.008 0.01

Tp Te

TaT0

Ee

dU

g/d

t(t)

L F- model

tim e (s ) (T 0=1 0ms)

Physiologically motivated voice generationApproximation of human voice generationFlexible tool to generate different voices

Study of physiology of voiceBetter understanding of physiologyStudy of voice source dynamics


Motivation (2)

Voice SourceVoice Quality (Individuality of Voice)Prosody (Speech Melody)

sub- and supraglottalpressure

Vocal foldparameters

Boundaryconditions

Vocal foldmodel

Glottalflow

Glottalarea

DisadvantagesMany parametersNo intuitive mapping to perceptionHard to controlBased on measured data → hard to obtain


Anatomy & Physiology (1)

play movie


Anatomy & Physiology (1a)

Self oscillating system

Steady airflow from lungs is converted into series offlow pulses by opening & closing airspace betweenvocal folds (glottis)

”Myoelastic-aerodynamic theory of voice production(Van den Berg, 1958)→ Oscillation due to Bernoulli effect


Anatomy & Physiology (2)

Upper and lower portion display phase difference→ Mucosal wave


Vocal Fold Models

Lumped elements models (n-mass models)one mass model (Flanagan & Landgraf, 1968)two mass model (Ishizaka & Flanagan, 1972)three mass model (Story & Titze, 1994)

Physically informed model

Finite elements model


One Mass Model

m

xz

Dk

Psub

P1 P2

Psup

Ug

x 0

x

lc th

d

A

Very coarse model

Vocal fold lumped into one mass.Only lateral displacement

Modelling of basic principles of self-sustained oscillationVocal Fold Modeling – p.9/20

Two Mass Model - Mechanics

m1

r 2

xz

m2

r1k2

k1

k1,2

Psub

P1 P2 P3 P4

Psup

Ug

x 1,0

x1x 2 ,0

x2

lc d 1 d 2

A1A 2

Thyroid Cartilage

Vocal TractTrachea

supA

Includes representation of mucosal wave

Reasonable agreement with physiological data

Very popular

Equations for the mechanical system:

m1x1(t) + r1x1(t) + k1(x1)[x1(t) − x01] + k12[x1(t) − x2(t)] = lgd1pm1(t)

m2x2(t) + r2x2(t) + k2(x2)[x2(t) − x02] − k12[x1(t) − x2(t)] = lgd2pm2(t)


Two Mass Model - Pressure

PP

P

P

Psub

1

2

3

supm

P4

P0

1 m2

P

z

Pressure distribution along glottis:(assumes continuity of the flow)

psub − p1(t) = 1.371

2ρair

u(t)2

A1(t)2

p1(t) − p2(t) = 12νd1

l2gu(t)

A1(t)3

p2(t) − p3(t) =1

2ρairu(t)2

�

1

A2(t)2−

1

A1(t)2�

p3(t) − p4(t) = 12νd2

l2gu(t)

A2(t)3

p4(t) − psup(t) =1

2ρair

u(t)2

A2(t)2�

2A2(t)

Asup

�

1 −

A2(t)

Asup

��

ν . . . air shear viscosity coefficient

ρair . . . air density


Body – Cover Concept

Vocal folds are divided into 2 tissue layersCover: pliable, non-contractible mucosa tissueBody: muscle fiber & ligamentous tissue


Three Mass Model

m1

D

xz

m2

2D1 k2k1

k12

Psub

P1 P2 P3 P4

Psup

Ug

x 1,0

x1x 2 ,0

x2

lc th 1 th 2

d1

d2

A1A 2

D3k3

m3

Thyroid Cartilage

Vocal Tract

Trachea

m3: Body mass

m1,m2: Cover masses


Multiple Mass Model

PSfrag replacements

One fold, side view, y [mm] –>

z[m

m]–

>

x [mm]y [mm]

z[m

m]

Both folds, top view, x [mm] –>

y[m

m]–

>

-3 -2 -1 0 1 2 3

00.5

11.5

22.5

3

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

14

05

1015

-2

-1

0

1

2

3

4

-2-10123

+ Possible modification ofproperties inlongitudinal dimension

- Increased complexity

- High calculation times


Finite Elements Model

Alipour & Titze 1996 Does not assume lumpedelements

Describes geometry & phys.properties of vocal folds withhuge number of very smallelements

+ Very good solution if allproperties are known

- Calculation times very high

- Real-time models notpossible (yet)

- huge number of parameters(hard to determine)


Physically-informed model

Physical model not for entire systemMechanical Model of Oscillator(calculation of displacement, fundamental frequency)

Nonlinear Map for calulation of glottal flow(interaction of vocal fold motion xi, flow u g and pressure pl)

z−1

fNL

Hres(z )

z−1

ugpl

x1 x2Nonlinear Map

Oscillator


Conclusion

Large Variety of Vocal Fold models

Trade off between Accuracy & Complexityreliable data & level of detail

Rather study of physiology than speech synthesis


Small dictionary

mucosa Schleimhauttissue Gewebe

ligament Bandcartilage Knorpeltrachea Luftröhre

inertia Massenträgheitprosody Sprachmelodie

lumped elements konzentrierte Elemente


References[1] J. Flanagan and L. Landgraf. Self-oscillating source for

vocal-tract synthesizers. IEEE Transactions on Audioand Electroacoustics, 16(1):57–64, March 1968.

[2] K. Ishizaka and J. L. Flanagan. Synthesis of voicedsounds from a two-mass model of the vocal cords. BellSystems Techn. J., 51(6):1233–1268, 1972.

[3] Brad H. Story and Ingo R. Titze. Voice simulation with abody-cover model of the vocal folds. J. Acoust. Soc.Am., 97(2):1249–1260, 1995.


THANK YOU


Vocal Fold Modeling - Graz University of Technology · 2005. 10. 25. · Anatomy & Physiology (1)...

Documents

Transcript of Vocal Fold Modeling - Graz University of Technology · 2005. 10. 25. · Anatomy & Physiology (1)...