The evolution of reduced-order vocal fold models into clinically useful tools for subject-specific diagnosis and treatment hinges upon successfully and accurately representing an individual patient in the modeling framework. This, in turn, requires inference of model parameters from clinical measurements in order to tune a model to the given individual. Bayesian analysis is a powerful tool for estimating model parameter probabilities based upon a set of observed data. In this work, a Bayesian particle filter sampling technique capable of estimating time-varying model parameters, as occur in complex vocal gestures, is introduced. The technique is compared with time-invariant Bayesian estimation and least squares methods for determining both stationary and non-stationary parameters. The current technique accurately estimates the time-varying unknown model parameter and maintains tight credibility bounds. The credibility bounds are particularly relevant from a clinical perspective, as they provide insight into the confidence a clinician should have in the model predictions.
References
1.
I. R.
Titze
, “Parameterization of the glottal area, glottal flow, and vocal fold contact area
,” J. Acoust. Soc. Am.
75
, 570
–580
(1984
).2.
K.
Ishizaka
and J. L.
Flanagan
, “Synthesis of voiced sounds from a two-mass model of the vocal cords
,” Bell System Tech. J.
51
, 1233
–1268
(1972
).3.
B. H.
Story
, “Physiologically-based speech simulation using an enhanced wave-reflection model of the vocal tract
,” Ph.D. thesis, University of Iowa
(1995
).4.
I.
Steinecke
and H.
Herzel
, “Bifurcations in an asymmetric vocal-fold model
,” J. Acoust. Soc. Am.
97
, 1874
–1884
(1995
).5.
I. R.
Titze
and B. H.
Story
, “Rules for controlling low-dimensional vocal fold models with muscle activation
,” J. Acoust. Soc. Am.
112
, 1064
–1076
(2002
).6.
J. J.
Jiang
, C. E.
Diaz
, and D. G.
Hanson
, “Finite element modeling of vocal fold vibration in normal phonation and hyperfunctional dysphonia: Implications for the pathogenesis of vocal nodules
,” Annals Otol., Rhinol., Laryngol.
107
, 603
–610
(1998
).7.
W.
Zhao
, C.
Zhang
, S. H.
Frankel
, and L.
Mongeau
, “Computational aeroacoustics of phonation, part i: Computational methods and sound generation mechanisms
,” J. Acoust. Soc. Am.
112
, 2134
–2145
(2002
).8.
C.
Tao
, J. J.
Jiang
, and Y.
Zhang
, “Simulation of vocal fold impact pressures with a self-oscillating finite-element model
,” J. Acoust. Soc. Am.
119
, 3987
–3994
(2006
).9.
C.
Tao
, J. J.
Jiang
, and Y.
Zhang
, “Anterior-posterior biphonation in a finite-element model of vocal fold vibration
,” J. Acoust. Soc. Am.
120
, 1570
–1577
(2006
).10.
X.
Zheng
, R.
Mittal
, and S.
Bielamowicz
, “A computational study of asymmetric glottal jet deflection during phonation
,” J. Acoust. Soc. Am.
129
, 2133
–2143
(2011
).11.
X.
Zheng
, R.
Mittal
, Q.
Xue
, and S.
Bielamowicz
, “Direct-numerical simulation of the glottal jet and vocal-fold dynamics in a three-dimensional laryngeal model
,” J. Acoust. Soc. Am.
130
, 404
–415
(2011
).12.
R.
Mittal
, B. D.
Erath
, and M. W.
Plesniak
, “Fluid dynamics of human phonation and speech
,” Ann. Rev. Fluid Mech.
45
, 437
–467
(2013
).13.
B. D.
Erath
, M.
Zañartu
, K. C.
Stewart
, M. W.
Plesniak
, D. E.
Sommer
, and S. D.
Peterson
, “A review of lumped-element models of voiced speech
,” Speech Commun.
55
, 667
–690
(2013
).14.
D. A.
Berry
, H.
Herzel
, I. R.
Titze
, and K.
Krischer
, “Interpretation of biomechanical simulations of normal and chaotic vocal fold oscillations with empirical eigenfunctions
,” J. Acoust. Soc. Am.
95
, 3595
–3604
(1994
).15.
I. R.
Titze
, “Nonlinear source–filter coupling in phonation: Theory
,” J. Acoust. Soc. Am.
123
, 2733
–2749
(2008
).16.
M.
Zañartu
, L.
Mongeau
, and G. R.
Wodicka
, “Influence of acoustic loading on an effective single mass model of the vocal folds
,” J. Acoust. Soc. Am.
121
, 1119
–1129
(2007
).17.
J. C.
Ho
, M.
Zañartu
, and G. R.
Wodicka
, “An anatomically based, time-domain acoustic model of the subglottal system for speech production
,” J. Acoust. Soc. Am.
129
, 1531
–1547
(2011
).18.
B. H.
Story
and I. R.
Titze
, “Voice simulation with a body-cover model of the vocal folds
,” J. Acoust. Soc. Am.
97
, 1249
–1260
(1995
).19.
P.
Alku
, C.
Magi
, S.
Yrttiaho
, T.
Bäckström
, and B.
Story
, “Closed phase covariance analysis based on constrained linear prediction for glottal inverse filtering
,” J. Acoust. Soc. Am.
125
, 3289
–3305
(2009
).20.
H. J.
Kuo
, “Voice source modeling and analysis of speakers with vocal fold nodules
,” Ph.D. thesis, Massachusetts Institute of Technology
(1998
).21.
Y.
Zhang
, C.
McGilligan
, L.
Zhou
, M.
Vig
, and J. J.
Jiang
, “Nonlinear dynamic analysis of voices before and after surgical excision of vocal polyps
,” J. Acoust. Soc. Am.
115
, 2270
–2277
(2004
).22.
J.
Horáček
, P.
Šidlof
, and J.
Švec
, “Numerical simulation of self-oscillations of human vocal folds with hertz model of impact forces
,” J. Fluids Struct.
20
, 853
–869
(2005
).23.
M.
Zañartu
, G. E.
Galindo
, B. D.
Erath
, S. D.
Peterson
, G. R.
Wodicka
, and R. E.
Hillman
, “Modeling the effects of a posterior glottal opening on vocal fold dynamics with implications for vocal hyperfunction
,” J. Acoust. Soc. Am.
136
, 3262
–3271
(2014
).24.
M.
Döllinger
, U.
Hoppe
, F.
Hettlich
, J.
Lohscheller
, S.
Schuberth
, and U.
Eysholdt
, “Vibration parameter extraction from endoscopic image series of the vocal folds
,” IEEE Trans. Biomed. Eng.
49
, 773
–781
(2002
).25.
R.
Schwarz
, U.
Hoppe
, M.
Schuster
, T.
Wurzbacher
, U.
Eysholdt
, and J.
Lohscheller
, “Classification of unilateral vocal fold paralysis by endoscopic digital high-speed recordings and inversion of a biomechanical model
,” IEEE Trans. Biomed. Eng.
53
, 1099
–1108
(2006
).26.
T.
Wurzbacher
, R.
Schwarz
, M.
Döllinger
, U.
Hoppe
, U.
Eysholdt
, and J.
Lohscheller
, “Model-based classification of nonstationary vocal fold vibrations
,” J. Acoust. Soc. Am.
120
, 1012
–1027
(2006
).27.
R.
Schwarz
, M.
Döllinger
, T.
Wurzbacher
, U.
Eysholdt
, and J.
Lohscheller
, “Spatio-temporal quantification of vocal fold vibrations using high-speed videoendoscopy and a biomechanical model
,” J. Acoust. Soc. Am.
123
, 2717
–2732
(2008
).28.
E.
Cataldo
, C.
Soize
, R.
Sampaio
, and C.
Desceliers
, “Probabilistic modeling of a nonlinear dynamical system used for producing voice
,” Computat. Mech.
43
, 265
–275
(2009
).29.
S. J.
Rupitsch
, J.
Ilg
, A.
Sutor
, R.
Lerch
, and M.
Döllinger
, “Simulation based estimation of dynamic mechanical properties for viscoelastic materials used for vocal fold models
,” J. Sound Vib.
330
, 4447
–4459
(2011
).30.
A.
Yang
, D. A.
Berry
, M.
Kaltenbacher
, and M.
Döllinger
, “Three-dimensional biomechanical properties of human vocal folds: Parameter optimization of a numerical model to match in vitro dynamics
,” J. Acoust. Soc. Am.
131
, 1378
–1390
(2012
).31.
T.
Wurzbacher
, M.
Döllinger
, R.
Schwarz
, U.
Hoppe
, U.
Eysholdt
, and J.
Lohscheller
, “Spatiotemporal classification of vocal fold dynamics by a multimass model comprising time-dependent parameters
,” J. Acoust. Soc. Am.
123
, 2324
–2334
(2008
).32.
C.
Tao
, Y.
Zhang
, and J. J.
Jiang
, “Extracting physiologically relevant parameters of vocal folds from high-speed video image series
,” IEEE Trans. Biomed. Eng.
54
, 794
–801
(2007
).33.
Y.
Zhang
, C.
Tao
, and J. J.
Jiang
, “Parameter estimation of an asymmetric vocal-fold system from glottal area time series using chaos synchronization
,” Chaos
16
, 023118
(2006
).34.
A.
Yang
, M.
Stingl
, D. A.
Berry
, J.
Lohscheller
, D.
Voigt
, U.
Eysholdt
, and M.
Döllinger
, “Computation of physiological human vocal fold parameters by mathematical optimization of a biomechanical model
,” J. Acoust. Soc. Am.
130
, 948
–964
(2011
).35.
J.
Kaipio
and E.
Somersalo
, Statistical and Computational Inverse Problems
(Springer-Verlag
, New York
, 2005
), pp. 1
–340
.36.
E.
Cataldo
, C.
Soize
, and R.
Sampaio
, “Uncertainty quantification of voice signal production mechanical model and experimental updating
,” Mech. Syst. Signal Process.
40
, 718
–726
(2013
).37.
R. E.
Hillman
, E. B.
Holmberg
, J. S.
Perkell
, M.
Walsh
, and C.
Vaughan
, “Objective assessment of vocal hyperfunction: An experimental framework and initial results
,” J. Speech, Lang., Hear. Res.
32
, 373
–392
(1989
).38.
L. K.
Bowen
, G. L.
Hands
, S.
Pradhan
, and C. E.
Stepp
, “Effects of Parkinson's disease on fundamental frequency variability in running speech
,” J. Med. Speech-Lang. Pathol.
21
, 235
–244
(2013
).39.
D. A.
Rahn
, M.
Chou
, J. J.
Jiang
, and Y.
Zhang
, “Phonatory impairment in Parkinson's disease: Evidence from nonlinear dynamic analysis and perturbation analysis
,” J. Voice
21
, 64
–71
(2007
).40.
J. J.
Jiang
, Y.
Zhang
, and C.
McGilligan
, “Chaos in voice, from modeling to measurement
,” J. Voice
20
, 2
–17
(2006
).41.
J.
Liu
, Monte Carlo Strategies in Scientific Computing
(Springer
, New York
, 2004
), pp. 1
–344
.42.
J.
Bernardo
and A.
Smith
, “Bayesian theory
,” in Wiley Series in Probability and Statistics
(John Wiley & Sons
, West Sussex, England
, 2000
), pp. 1
–610
.43.
A. F. M.
Smith
and A. E.
Gelfand
, “Bayesian statistics without tears: A sampling-resampling perspective
,” Am. Statistician
46
, 84
–88
(1992
).44.
M. C.
Jones
, J. S.
Marron
, and S. J.
Sheather
, “A brief survey of bandwidth selection for density estimation
,” J. Am. Stat. Assoc.
91
, 401
–407
(1996
).45.
J.
Kaipio
and E.
Somersalo
, “Statistical inverse problems: Discretization, model reduction and inverse crimes
,” J. Comput. Appl. Math.
198
, 493
–504
(2007
).46.
O.
Cappé
, E.
Moulines
, and T.
Ryden
, Inference in Hidden Markov Models
, Springer Series in Statistics (Springer-Verlag
, New York
, 2005
), pp. 1
–653
.47.
N.
Gordon
, D.
Salmond
, and A.
Smith
, “Novel approach to nonlinear/non-Gaussian Bayesian state estimation
,” IEEE Proc. Radar Signal. Process.
140
, 107
–113
(1993
).48.
K.
Omori
, D. H.
Slavit
, A.
Kacker
, and S. M.
Blaugrund
, “Influence of size and etiology of glottal gap in glottic incompetence dysphonia
,” Laryngoscope
108
, 514
–518
(1998
).49.
M.
Södersten
and P. A.
Lindestad
, “Glottal closure and perceived breathiness during phonation in normally speaking subjects
,” J. Speech Hear. Res.
33
, 601
–611
(1990
).50.
G.
Chen
, J.
Kreiman
, Y.-L.
Shue
, and A.
Alwan
, “Acoustic correlates of glottal gaps
,” Interspeech
4
, 2684
–2687
(2011
).51.
S. E.
Linville
, “Glottal gap configurations in two age groups of women
,” J. Speech, Lang., Hear. Res.
35
, 1209
–1215
(1992
).52.
H. M.
Hanson
, “Glottal characteristics of female speakers: Acoustic correlates
,” J. Acoust. Soc. Am.
101
, 466
–481
(1997
).53.
B. H.
Story
and K.
Bunton
, “Production of child-like vowels with nonlinear interaction of glottal flow and vocal tract resonances
,” Proc. Meet. Acoust.
19
, 060303
(2013
).54.
J. G.
Švec
and H. K.
Schutte
, “Videokymography: High-speed line scanning of vocal fold vibration
,” J. Voice
10
, 201
–205
(1996
).55.
H.
Takemoto
, K.
Honda
, S.
Masaki
, Y.
Shimada
, and I.
Fujimoto
, “Measurement of temporal changes in vocal tract area function from 3D cine-MRI data
,” J. Acoust. Soc. Am.
119
, 1037
–1049
(2006
).56.
R. S.
McGowan
, “An aeroacoustic approach to phonation
,” J. Acoust. Soc. Am.
83
, 696
–704
(1988
).57.
D.
Deliyski
and P.
Petrushev
, “Methods for objective assessment of high-speed videoendoscopy
,” in Proceedings of the 6th International Conference: Advances in Quantitative Laryngology, Voice and Speech Research
, AQL-2003, Hamburg, Germany (April 2003
), pp. 1
–16
.58.
G. E.
Galindo
, M.
Zañartu
, and J. I.
Yuz
, “A discrete-time model for the vocal folds
,” in IEEE EMBS International Student Conference
, Chile (2014
), pp. 74
–77
.59.
E. T.
Jaynes
, “Information theory and statistical mechanics
,” Phys. Rev.
106
, 620
–630
(1957
).60.
E. T.
Jaynes
, “Information theory and statistical mechanics. II
,” Phys. Rev.
108
, 171
–190
(1957
).61.
T.
Cover
and J.
Thomas
, Elements of Information Theory
(John Wiley & Sons, Inc.
, Hoboken, NJ
, 2006
), pp. 1
–776
.62.
J.
Nocedal
and S. J.
Wright
, Numerical Optimization
, 2nd ed. (Springer
, New York
, 2006
).© 2016 Acoustical Society of America.
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