Voice Signals Produced With Jitter Through a Stochastic One-mass Mechanical Model.

BACKGROUND: The quasiperiodic oscillation of the vocal folds causes perturbations in the length of the glottal cycles, which are known as jitter. The observation of the glottal cycles variations suggests that jitter is a random phenomenon described by random deviations of the glottal cycle lengths in relation to a corresponding mean value and, in general, its values are expressed as a percentage of the duration of the glottal pulse. OBJECTIVE: The objective of this paper is the construction of a stochastic model for jitter using a one-mass mechanical model of the vocal folds, which assumes complete right-left symmetry of the vocal folds, and which considers motions of the vocal folds only in the horizontal direction. STUDY DESIGN: The jitter has been the subject for researchers due to its important applications such as the identification of pathological voices (nodules in the vocal folds, paralysis of the vocal folds, or even, the vocal aging, among others). Large values for jitter variations can indicate a pathological characteristic of the voice. METHOD: The corresponding stiffness of each vocal fold is considered as a stochastic process, and its modeling is proposed. RESULTS: The probability density function of the fundamental frequency related to the voice signals produced are constructed and compared for different levels of jitter. Some samples of synthesized voices in these cases are obtained. CONCLUSIONS: It is showed that jitter could be obtained using the model proposed. The Praat software was also used to verify the measures of jitter in the synthesized voice signals.

Experimental multiscale measurements for the mechanical identification of a cortical bone by digital image correlation.

The implementation of the experimental methodology by optical measurements of mechanical fields, the development of a test bench, the specimen preparation, the experimental measurements, and the digital image correlation (DIC) method, have already been the object of research in the context of biological materials. Nevertheless, in the framework of the experimental identification of a mesoscopic stochastic model of the random apparent elasticity field, measurements of one specimen is required at both the macroscopic scale and the mesoscopic scale under one single loading. The nature of the cortical bone induces some difficulties, as no single speckled pattern technique is available for simultaneously obtaining the displacement at the macroscopic scale and at the mesoscopic scale. In this paper, we present a multiscale experimental methodology based on (i) an experimental protocol for one specimen of a cortical bone, (ii) its measuring bench, (iii) optical field measurements by DIC method, (iv) the experimental results, and (v) the multiscale experimental identification by solving a statistical inverse problem.

Modeling of transient wave propagation in a heterogeneous solid layer coupled with fluid: application to long bones.

The aim of this work is to evaluate the effects of the heterogeneity and anisotropy of material properties of cortical bone on its ultrasonic response obtained by using axial transmission method. The heterogeneity and anisotropy of material properties are introduced by using a parametric probabilistic model. The geometrical configuration of the tested sample is described by a tri-layer medium composed of a heterogeneous and anisotropic solid layer sandwiched between two acoustic fluid layers of which one of these layers is excited by an acoustic linear source. The numerical results focus on studying of an interest quantity, called velocity of the first arriving signal, showing that it strongly depends on the dispersion induced by statistical fluctuations of stochastic elasticity field.

Equivalent contributing depth investigated by a lateral wave with axial transmission in viscoelastic cortical bone.

Cortical bone is a viscoelastic heterogeneous medium which may be assessed with axial transmission. This work aims at evaluating the average depth investigated by the lateral wave for radial variations of material properties in relatively thick cortical bone. The equivalent contributing depth (ECD) is derived from the finite element simulation results for spatial variations of a viscoelastic coefficient (η(11)) and of porosity. A value of ECD equal to around 1.6 mm is obtained for a spatial variation of η(11). The method fails to predict accurate values of the ECD for a spatial variation of porosity, because all parameters vary simultaneously.

Influence of viscoelastic and viscous absorption on ultrasonic wave propagation in cortical bone: Application to axial transmission.

Cortical bone and the surrounding soft tissues are attenuating and heterogeneous media, which might affect the signals measured with axial transmission devices. This work aims at evaluating the effect of the heterogeneous acoustic absorption in bone and in soft tissues on the bone ultrasonic response. Therefore, a two-dimensional finite element time-domain method is derived to model transient wave propagation in a three-layer medium composed of an inhomogeneous transverse isotropic viscoelastic solid layer, sandwiched between two viscous fluid layers. The model couples viscous acoustic propagation in both fluid media with the anisotropic viscoelastic response of the solid. A constant spatial gradient of material properties is considered for two values of bone thicknesses (0.6 and 4 mm). In the studied configuration, absorption in the surrounding fluid tissues does not affect the results, whereas bone viscoelastic properties have a significant effect on the first arriving signal (FAS) velocity. For a thin bone, the FAS velocity is governed by the spatially averaged bone properties. For a thick bone, the FAS velocity may be predicted using a one-dimensional model.

Nonlinear parabolic equation model for finite-amplitude sound propagation over porous ground layers.

The nonlinear parabolic equation (NPE) is a time-domain method widely used in underwater sound propagation applications. It allows simulation of weakly nonlinear sound propagation within an inhomogeneous medium. So that this method can be used for outdoor sound propagation applications it must account for the effects of an absorbing ground surface. The NPE being formulated in the time domain, complex impedances cannot be used and, hence, the ground layer is included in the computational system with the help of a second NPE based on the Zwikker-Kosten model. A two-way coupling between these two layers (air and ground) is required for the whole system to behave correctly. Coupling equations are derived from linearized Euler's equations. In the frame of a parabolic model, this two-way coupling only involves spatial derivatives, making its numerical implementation straightforward. Several propagation examples, both linear or nonlinear, are then presented. The method is shown to give satisfactory results for a wide range of ground characteristics. Finally, the problem of including Forchheimer's nonlinearities in the two-way coupling is addressed and an approximate solution is proposed.

Influence of a gradient of material properties on ultrasonic wave propagation in cortical bone: application to axial transmission.

The aim of this work is to evaluate the effect of a spatial gradient of material properties (mass density and stiffness coefficients) of cortical bone on its ultrasonic response obtained with an axial transmission device. Therefore, a two-dimensional finite element time-domain method is derived to model transient wave propagation in a three-layer medium composed of an inhomogeneous transverse isotropic solid layer sandwiched between two acoustic fluid layers and excited by an acoustic linear source located in one fluid layer, delivering broadband ultrasonic pulses. The model couples the acoustic propagation in both fluid media with the elastodynamic response of the solid layer. A constant spatial gradient of material properties is considered for two values of bone thicknesses corresponding to relatively thick and thin bone widths. For a thin bone (0.6 mm) compared to wavelength (around 4 mm at 1 MHz), the results are in good agreement with a S(0) Lamb wave assuming a homogeneous material with spatially averaged material properties. For a thick bone (4 mm), the results are in agreement with the propagation of a lateral wave and allow the derivation of an equivalent contributing depth in the case of a transverse isotropic inhomogeneous solid layer.

Determination of the random anisotropic elasticity layer using transient wave propagation in a fluid-solid multilayer: model and experiments.

The aim of this paper is to introduce a simplified model for an uncertain solid layer sandwiched between two acoustic fluid layers and using the ultrasonic characterization with an acoustic source placed in one fluid layer. Uncertainties are taken into account with a probabilistic model of the elasticity tensor. Its parameters are the mean value of the random tensor and a dispersion parameter that controls the statistical fluctuation level. The characterization of the solid layer given a database of actual measurements consists in the determination of the (i) elastic parameters of the mean elasticity model, (ii) the dispersion parameter, and (iii) mass density of the solid. This is performed with a numerical solver of wave propagation and for in vivo data collected previously. The model is representative of measurements of human bone properties with the so-called axial transmission technique. The capability of the model to predict the velocity of the first experimental arriving signal in the statistical sense is proved. The identified anisotropic elasticity tensor of cortical bone from actual data based on the simplified model is given.

Fuzzy structure theory modeling of sound-insulation layers in complex vibroacoustic uncertain systems: theory and experimental validation.

The fuzzy structure theory was introduced 20 years ago in order to model the effects of complex subsystems imprecisely known on a master structure. This theory was only aimed at structural dynamics. In this paper, an extension of that theory is proposed in developing an elastoacoustic element useful to model sound-insulation layers for computational vibroacoustics of complex systems. The simplified model constructed enhances computation time and memory allocation because the number of physical and generalized degrees of freedom in the computational vibroacoustic model is not increased. However, these simplifications introduce model uncertainties. In order to take into account these uncertainties, the nonparametric probabilistic approach recently introduced is used. A robust simplified model for sound-insulation layers is then obtained. This model is controlled by a small number of physical and dispersion parameters. First, the extension of the fuzzy structure theory to elastoacoustic element is presented. Second, the computational vibroacoustic model including such an elastoacoustic element to model sound-insulation layer is given. Then, a design methodology to identify the model parameters with experiments is proposed and is experimentally validated. Finally, the theory is applied to an uncertain vibroacoustic system.

Structural-acoustic modeling of automotive vehicles in presence of uncertainties and experimental identification and validation.

The design of cars is mainly based on the use of computational models to analyze structural vibrations and internal acoustic levels. Considering the very high complexity of such structural-acoustic systems, and in order to improve the robustness of such computational structural-acoustic models, both model uncertainties and data uncertainties must be taken into account. In this context, a probabilistic approach of uncertainties is implemented in an adapted computational structural-acoustic model. The two main problems are the experimental identification of the parameters controlling the uncertainty levels and the experimental validation. Relevant experiments have especially been developed for this research in order to constitute an experimental database devoted to structural vibrations and internal acoustic pressures. This database is used to perform the experimental identification of the probability model parameters and to validate the stochastic computational model.

Elastoacoustic model with uncertain mechanical properties for ultrasonic wave velocity prediction: application to cortical bone evaluation.

The axial transmission technique can measure the longitudinal wave velocity of an immersed solid. An elementary model of the technique is developed with a set of source and receivers placed in a semi-infinite fluid coupled at a plane interface with a semi-infinite solid. The acoustic fluid is homogeneous. The solid is homogeneous, isotropic, and linearly elastic. The work is focused on the prediction of the measured velocity (apparent velocity) when the solid is considered to have random material properties. The probability density functions of the random variables modeling each mechanical parameter of the solid are derived following the maximum entropy principle. Specific attention is paid to the modeling of Poisson's ratio so that the second-order moments of the velocities remain finite. The stochastic solver is based on a Monte Carlo numerical simulation and uses an exact semianalytic expression of the acoustic response derived with the Cagniard-de Hoop method. Results are presented for a solid with the material properties of cortical bone. The estimated mean values and confidence regions of the apparent velocity are presented for various dispersion levels of the random parameters. A sensibility analysis with respect to the source and receivers locations is presented.

Experimental validation of a nonparametric probabilistic model of nonhomogeneous uncertainties for dynamical systems.

The paper deals with an experimental validation of a nonparametric probabilistic model of nonhomogeneous uncertainties for dynamical systems. The theory used, recently introduced, allows model uncertainties and data uncertainties to be simultaneously taken into account. An experiment devoted to this validation was specifically developed. The experimental model is constituted of two simple dural rectangular plates connected together with a complex joint. In the mean mechanical model, the complex joint, which is constituted of two additional plates attached with 40 screw-bolts, is modeled by a homogeneous orthotropic continuous plate with constant thickness, as usual. Consequently, the mean model introduces a region (the joint) which has a high level of uncertainties. The objective of the paper is to present the experiment and the comparisons of the theoretical prediction with the experiments.