loofBiomechanical modeling of laryngeal dynamics using inver filtering of speech signals
Alan P. Pinheiro*, Carlos D. Maciel, José C. Pereira, Marcelo B. Joaquim, Lianet Selpúlveda-Torres
Department of Electrical Engineering
University of São Paulo
São Carlos, Brazil
*alanpp@sc.usp.br
Abstract— Voice production occurs within the larynx where the vocal folds produce the glottal flow signal through vibrational movements that generate the primary voice signal. In this context, this paper introduces a method bad on inver filtering of speech signals and a biomechanical model of vocal folds to simulate the production of this primary signal. This method allows the formulation of a deterministic model of the vocal folds that reproduces their dynamic behavior and can be ud to evaluate the functional state of the subject’s voice using only acoustic speech signals. The results indicate that the propod method can simulate the main components of the glottal flow signal.
Keywords-glottal flow; vocal folds; inver filtering.
I.I NTRODUCTION
The voice production process comprehends a t of biological systems that involves the lungs, larynx, pharynx, trachea, and nasal and oral cavities. This process starts in the larynx, where the vocal folds produce the excitation signal of vocal tract through vibratory motions that modulate the air (from the trachea) generating the glottal flow. This signal will define the fundamental frequency of voice and many of its basic features. Due to the inten activity in the larynx, many voice pathologies originate in this structure [1] and may result in a change in the behavior of its dynamics, producing a perturbation on the voice.
In this context, a detailed study of voice must include an evaluation of the properties of the glottal flow signal. For this purpo, some methods have been developed to evaluate the larynx activity and/or the waveform of the glottal flow generated, among which videolaryngoscopy [2], electroglottography [3] and inver filtering of speech signals [4] can be emphasized.
Videolaryngoscopy is considered the gold standard method [5], as it is capable of directly evaluating the functional state of vocal folds using visual recordings of their movements. However, it us an endoscopy linked to a video camera, which is inrted in the subject’s mouth (or nasal cavity) interfe
ring with the natural voice production during the exam. Moreover, its cost may be impracticable in many applications. Electroglottography us a pair of noninvasive
electrodes fixed on the neck skin, next to the larynx, nsitive to the vibrational activity prent in this region. Its drawback is associated with the fact that the tissues where the electrodes are fixed attenuate some signal components generating a distortion in the waveform of the glottal flow recorded by the device.
Lastly, the inver filtering method us acoustical speech signals recorded by a microphone to reconstruct the waveform of the glottal flow through an algorithm which can compensate the effects of vocal tract on the signal analyzed.
However, a single analysis of the glottal flow signal would not be enough to describe the complex mechanisms of voice production in the larynx. For this reason, many authors [6-7] have developed biomechanical models of vocal folds to reproduce their dynamics through their vibrational behavior. In this n, the u of inver filtering as a method to estimate the glottal flow waveform is a uful way to produce information regarding a determined subject.
This information can be ud for a biomechanical model to reconstruct the vocal folds dynamics of th
is subject and simulate their glottal flow signal. This approach needs few hardware resources and can generate valuable information concerning the evaluation of subject voice in clinical practice.
The aim of this paper is to describe a technique that allows the evaluation of the vocal folds dynamics of a subject using a biomechanical model. The glottal flow produced by the subject is extracted from his/her speech signal using an inver filtering method. This extracted signal is ud for an optimization procedure able to change the model parameters until it could reproduce, with a good precision, the waveform of the extracted glottal flow. As a contribution, this method allows the simulation of the vocal folds behavior of a specific subject, evaluation of the functional state of voice and its dynamics using only acoustic speech signals.
II.M ETHODOLOGY
better me是什么意思The first step in this rearch to simulate the behavior of vocal folds was the extraction of the glottal flow waveform using a speech signal recorded by a microphone. An inver filtering method is applied to the signal of four subjects (with healthy voices) that vocalize the sustained vowel “a”. Next, an optimization
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procedure combining genetic algorithm and simplex method is ud to find the best values for the parameters of the biomechanical model employed, such that the model can accurately reproduce the glottal flow waveform extracted from the subject voice signal. The methods employed in this rearch are described in the following ctions.
A.Estimation of the glottal flow waveform
The extraction of the glottal flow waveform is performed by the Iterative Adaptive Inver Filtering (IAIF) [8]. Basically, this method us the Linear Predictive Coding (LPC) to estimate the vocal tract transfer function and compensate the vocal tract effects on the analyzed signal using an inver filtering process. The IAIF adopts a voice production model bad on three interdependent process: production of glottal excitation, (2) vocal tract equalization and (3) lip radiation effect.
Following the IAIF method, to estimate the glottal waveform it is necessary to evaluate the contributions of the vocal tract and lips radiation in the signal. Considering that the lips radiation effects can be modeled accurately enough with a fixed differentiator, the problem concentrates on the estimation of the vocal tract transfer function. The glottal waveform is then estimated by an inver filtering which will cancel the vocal tract effects and posteriorly the lips radiation in the speech signal. Figure 1 illustrates the steps involved in the IAIF method.
In the first step of the IAIF method, the speech signal is high-pass filtered with a cond-order Butterworth filter with cut-off frequency of 30 Hz. If the low frequency components of the speech are not removed, the resulting glottal wave starts to fluctuate. In the cond step a preliminary estimate of excitation effects on the signal is computed by LPC analysis. The glottal contribution is eliminated from the signal through an inver filtering process (Step 3).
Figure 1. Block diagram of the IAIF method ud to estimate the glottal flow waveform. The input s(n) is a speech signal recorded by a microphone and the output g(n) is a time ries corresponding to a glottal flow which produced the signal s(n).
In Step 4 an LPC filter is again applied resulting in a vocal tract model ud in Step 5 to cancel the effects of
this vocal tract on the analyzed speech signal. At the end, the lips radiation is also canceled by the numerical integration in Step 6. The result of this first iteration is a preliminary estimate of the glottal flow wave in the Step
6 output. To increa the reliability of this estimate, the
IAIF us a cond iteration that comprehends Steps 7 to
11 in the diagram of Figure 1.
At the beginning of the cond iteration (Step 7), a new estimate of the glottal excitation is performed using an LPC analysis. Unlike the first iteration, the input of this step is the preliminary estimate of the glottal flow evaluated by former steps, and not by the speech signal, as in Step 2. This approach allows the glottal contribution to be evaluated more accurately when compared with the start of the first iteration. In Step 8 this glottal contribution is suppresd by inver filtering and a new LPC analysis (prent in Step 9) is applied to the signal who glottal contribution had been suppresd, constituting a final model for the vocal tract.
口号英文The glottal flow waveform is finally obtained by the inver filtering in Steps 10 (which had suppresd the vocal tract contributions from the original speech signal) and 11, canceling the lips radiation.
During the analysis, signals with about 25 ms were ud with a rectangular window. The LPC order described in Figure 1 diagram was p = r = 8 and g = 6. In agreement with Alku et al [8], the values are enough for this type of analysis.
B.Biomechanical modeling of vocal folds
The vocal folds consist of a t of tissue layers able to vibrate due to the aerodynamic interaction that this system has with the airflow from the trachea. Bad on its myoelastic and aerodynamic properties, Ishizaka and Flanagan [6] developed a biomechanical model of the vocal folds which simulates their main vibrational motions and reproduce their dynamics. This model, termed as two-mass model,
assumes one vocal fold to be reprented by a pair of two coupled oscillators using two mass, three springs and two dampers, as in Figure
2.
The two mass of the model were ud to reproduce the mucosal wave pha difference while the other lumped elements (springs and dampers) reprent
Figure 2. Biomechanical model of the vocal folds elaborated by Ishizaka and Flanagan [6].
a stiff layer and its viscoelastic properties. In this model
the mass are vibrated by aerodynamic forces caud by the interaction between the subglottal pressure and
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vocal fold tissues and can be described by Bernoulli laws. Steinecke and Herzel [7] propod an ada
ptation for this classical model in which some assumptions were adopted to simplify the model and decrea the computational cost, keeping the most important features of vocal fold dynamics and its physiological ba. The model equations are described in (1).
)
()()
,,,,()
()(2212221222211121111111αααααααααααααααααααααααα+−−−−=++−−−−=x F x x k x k x r x
m x x d L P F x F x x k x k x r x m I c s B I c &&&&&& (1)
The x i α variable corresponds to oscillation amplitudes of the mass. Index i reprents the lower (i =1) and upper (i =2) portion of vocal folds while index α reprents the left (α=L) and right (α=R) portion. The main parameters of the model are denoted by m i α (mass), k i α (stiffness coefficient), k c α (coupling spring constant), r i α (damping coefficients) and P s (subglottal pressure) and can be reprented by a parameter vector p such as p := [m i α, k i α, k c α, r i α, P s ]. The impact forces due to vocal fold collisions and Bernoulli forces were reprented as F I α and F B , respectively, and
are described in details in [7]. The standard parameters of this model, defined by the authors, are: m 1α=0.125, m 2α=0.025, k 1α=0.08, k 2α=0.008, k c α=0.025, r 1α=r 2α=0.02 and P s =0.008. All units are given in centimeters, grams, milliconds and their corresponding combinations. In this rearch, the equations showed in (1) were solved using the standard fourth-order Runge-Kutta method. All simulations were procesd using Matlab (Mathworks, USA).
C. Optimization of biomechanical model parameters By using the parameters of the two-mass model reprented above by p , it is possible to reproduce the glottal signal. As each subject has their own voice characteristics - which reflects their vocal fold dynamics - it is important to find the value of p that best reproduces the glottal flow extracted by IAIF method. For this purpo, an optimization procedure
combining genetic algorithms and the simplex method was ud. This method compares the signal extracted by IAIF method with the one simulated by the two-mass model. As the model equations are nonsmooth and might have a non-convex arch space, in the first step a genetic algorithm is applied to arch for a rough approximation in order to avoid inappropriate local minima. In the cond step, this approximate solution rves as the starting point for a simplex method refining the approximate solution. This approach will help to reduce the optimization time and avoid the problem
of convergence to local minima.
The genetic algorithm ud in this rearch
utilized the roulette wheel lection rule and elitism techniques [9] to accelerate the convergence. A population of five hundred individuals was adopted and the algorithm was programmed to process only 50 generations to avoid excessive processing time. The
arch space comprid the [0.0 to 0.4] interval for the
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first ven mechanical parameters of vector p while the eighth parameter should be contained in the [0.008 to 0.040] interval. The objective function ud for both methods was defined as
.])[][()(1
2∑=−
=
ψm
k S E k x k x
p
(2)
Were, m indicates the sample number of the speech signal. The value of Ψ reprents the approximation error between the signal simulated by the model (x S ) and the glottal flow signal extracted from the speech signal (x E ). The minimum value of Ψ gives the model parameters most able to reproduce the vibrational movements of the folds.
III. R ESULTS
Figure 3 illustrates some results involving the glottal signal extracted from the speech signal of a subject and the simulation performed by the biomechanical model. The described method could simulate the signal produced by glottal vibrations of a specific subject with relative precision. The difference between the extracted and simulated signals (Figure 3b) might be attributed to the model behavior, which cannot simulate certain patterns, and/or the optimization procedure, which does not produce an optimum solution. Stochastic
(dotted line) and its corresponding simulated signal (continuous line) generated by the biomechanical model. (c) Fourier spectrum of the extracted signal and (d) simulated signal. (e) Spectrum error between the simulated and extracted signals.
the error value. The graphics of Figures 3c and 3d show that the simulated signal can reproduce the most
important components of the extracted signal. Table 1 shows the mechanical parameters found by the optimization procedure for the four subjects analyzed. TABLE I. P ARAMETERS OF THE BIOMECHANICAL MODEL CALCULATED FOR THE FOUR SUBJECTS
Parameters
Subjects
1 2 3 4
m1, m20.1900,
0.0819
adventurous
0.1668,
0.0700
0.1894,
0.1065
0.1392,
0.0569
k1, k20.1234,
0.0491
0.0922,
0.0474
0.1666,
0.0046
0.1511,
0.0202现在完成进行时
r1, r20.0611,
0.0223
0.1960,
0.0087
0.0099,
0.0282
0.0097,
0.0245
k c, P s 0.1244,
0.0237
0.0824,
0.0232
0.1994,
0.0319
0.1918,
0.0222
Error a0.29 0.49 0.32 0.58
a.Error between the extracted and simulated signals calculated by equation (2).
IV.D ISCUSSION
This paper has described a method which allows simulating the vocal folds dynamics of a subject using his/her speech signal and a standard biomechanical model. Emphasis was given to the extracted and simulated glottal flow signals ud to describe the dynamical behavior of the larynx du
ring the phonation.parrot怎么读
As an example, the glottal flow waveform of a healthy subject (illustrated in Figure 1) was estimated by the IAIF method and later ud to optimize the parameters of the biomechanical model. The optimization procedure showed a good performance and the curves produced by the model could reflect the most important vibration patterns prent in the signal extracted from this subject. The error signal between the spectra confirms this result. Similar results were achieved in the analysis of the other subjects.
The mechanical parameters exhibited in Table 1 were significantly different from tho defined as standard to the model. This is a strong evidence that (1) the propod method can explore a large arch space, and (2) the model parameters are nsitive to the vibration pattern showed for each subject. Furthermore, the simulated signals do not take into account merely the amplitude, fundamental frequency or pha, but also the peculiar features of the extracted waveform.
Albeit the biomechanical model has been successfully ud to elucidate the vocal folds dynamics in scientific rearches [2, 3, 10], the physiologic relevance of the parameters, found here to four subjects, is limited. Nevertheless, the parameters had an association with some physiologic properties of fold tissues related to elasticity, Young module, viscosity, tension, etc [11].
The importance of the propod method is related to the clinical evaluation of voice and vocal folds [11], pathologies asssment [10], voice synthesis [12] and evaluation of voice dynamics [2, 3]. In this n, some authors [13] have demonstrated that dynamic analysis
methods can be ud as very uful tools to quantify voice properties and have equal or superior performance than classic methods, such as jitter and shimmer. The limitations of the this method here propod are related to the optimization procedure, which does not ensure a global optimum, and the IAIF drawbacks, which are very nsitive to noi in the signal input [8].
The development of a deterministic model of vocal folds has brought new perspectives to the u of emergent techniques in dynamic systems that can be applied to voice rearch. In particular, the nonlinear normal mode [14] theory has been ud to study the structural nonlinearities in dynamical systems, detection and identification of complex behaviors in systems like tho ud here. Future works involving the methods will contribute to the characterization of the dynamic behavior of voice production in the larynx.
A CKNOWLEDGMENT
The authors would like to acknowledge FAPESP (grant 09/516.982) and CNPq (grant 143453/2008-
4) for the financial support given to this project.
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