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Pathological Voice Source Analysis System Using a Flow Waveform-Matched Biomechanical Model

Pathological Voice Source Analysis System Using a Flow Waveform-Matched Biomechanical Model Hindawi Applied Bionics and Biomechanics Volume 2018, Article ID 3158439, 13 pages https://doi.org/10.1155/2018/3158439 Research Article Pathological Voice Source Analysis System Using a Flow Waveform-Matched Biomechanical Model 1,2 2 2 2 1,2 1 Xiaojun Zhang , Lingling Gu, Wei Wei , Di Wu, Zhi Tao , and Heming Zhao School of Electronic and Information Engineering, Soochow University, Suzhou 215000, China College of Physics, Optoelectronics and Energy, Soochow University, Suzhou 215000, China Correspondence should be addressed to Wei Wei; weiwei0728@suda.edu.cn and Zhi Tao; taoz@suda.edu.cn Received 30 March 2018; Accepted 24 May 2018; Published 2 July 2018 Academic Editor: Liwei Shi Copyright © 2018 Xiaojun Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Voice production occurs through vocal cord and vibration coupled to glottal airflow. Vocal cord lesions affect the vocal system and lead to voice disorders. In this paper, a pathological voice source analysis system is designed. This study integrates nonlinear dynamics with an optimized asymmetric two-mass model to explore nonlinear characteristics of vocal cord vibration, and changes in acoustic parameters, such as fundamental frequency, caused by distinct subglottal pressure and varying degrees of vocal cord paralysis are analyzed. Various samples of sustained vowel /a/ of normal and pathological voices were extracted from MEEI (Massachusetts Eye and Ear Infirmary) database. A fitting procedure combining genetic particle swarm optimization and a quasi-Newton method was developed to optimize the biomechanical model parameters and match the targeted voice source. Experimental results validate the applicability of the proposed model to reproduce vocal cord vibration with high accuracy, and show that paralyzed vocal cord increases the model coupling stiffness. 1. Introduction parameters with pattern recognition algorithms to assist diagnosis of pathological voice [5, 6]. However, the selected voice signal parameters are not directly linked with the actual Vocal cord vibration interrupts the straight airflow expelled physical structure, and vocal structural changes that cause by the lungs into a series of pulses that act as the excitation vocal voice disorders require further study. source for voice and sound. Denervation or organic diseases of vocal cords, such as paralysis and polyps, can cause irreg- Nonlinear dynamics theory has provided a new avenue for dynamical system related research, for example, methods ular vibration with consequential changes, manifested as combining nonlinear theory with spectral analysis have been breathy or hoarse voice. These diseases generally affect one successfully applied to EEG and ECG signal analysis. It has side of vocal structure, causing significant imbalance in also been extended to study voice signals [7, 8]. bilateral vocal cord tension [1, 2]. Irregular vibration of the vocal cords corresponding to a variety of voice disorders Nonlinearity inherent in the vocal system can cause irreg- ular voice behavior, as indicated by harmonics, bifurcation, can be observed with electronic laryngoscope to assist diag- and low-dimensional chaos in high-speed recording of vocal nosing vocal cord disease. However, laryngoscopy examina- cord vibration signals [9, 10]. The degree of pathological tion is invasive, and the outcomes are relatively subjective. vocal fold is closely related to the nonlinear vibration of the Acoustic analysis can complement and in some cases replace the other invasive methods, which based on direct vocal fold vocal cords. [11]. Therefore, traditional analysis of acoustic parameters may not be accurate, but nonlinear dynamics the- observation [3, 4]. ory has been shown to have good applicability in characteriz- Clinical diagnosis and pathological voice classification ing such signals [12]. Time frequency shape analysis based on using objective methods is an important issue in medical embedding phase space plots and nonlinear dynamics evaluation. Previous studies have mainly combined acoustic 2 Applied Bionics and Biomechanics methods can be used to evaluate the vocal fold dynamics 2. Method during phonation [13]. Nonlinear models can also simulate 2.1. Symmetric Vocal Model. Vocal cords are two symmetri- various vocal sound phenomena and have been used for cal membranous anatomical structures located in the throat. dynamic prediction of disordered speech associated with lar- Airflow out of the trachea and lungs continuously impacts ynx pathology [14–16]. Many physical modeling methods for the vocal cords and causes vibration. The vibration behavior glottal excitation have been proposed, and the corresponding modulates the airflow to generate glottal pulses [25]. Based model parameters have been utilized to study various voice on the elastic and dynamic properties of the vocal cords, each disorders. The two-mass (IF) model is the most well-known fold is represented by two coupled oscillators with two classical physical model of the vocal cords, first proposed masses, three springs, and two dampers, where the quality by Ishizaka and Flanagan and simplified by Steinecke of the mass and spring constants denote vocal quality and and Herzel (SH model), to study vibration characteristics tension, respectively. Figure 1 shows the simplified two- of the vocal cords. Xue combined the work of Steinecke mass (SH) model, which can be expressed as and Herzel with Navier-Stokes equations and analyzed irregular vibrations caused by tension imbalance in bilateral x = υ , 1α 1α vocal cord, as well as sound effects [17]. Recently, Sommer modified the asymmetric vocal contact force of the SH υ = − F + I − r υ − k x − k x − x , 1α 1α 1α 1α 1α 1α 1α cα 1α 2α model based on Newton’s third law [18]. However, a com- 1α prehensive nonlinear analysis for the modified SH model x = υ , remains incomplete. 2α 2α Although physical modeling has enormous potential in υ = − I − r υ − k x − k x − x , speech synthesis and voice analysis, the large number of 2α 2α 2α 2α 2α 2α 2α 2α 1α 2α model parameters and the complexity of model optimization to match observational data have prevented its practical application [19]. Döllinger used the Nelder–Mead algorithm where to minimize the error between experimental curves obtained from high-speed glottography sequences and curves gener- LdP ated with the two-mass model (2MM) [20]. However, this F = , 1α 1α is an invasive method because an endoscope is required to c a record vocal cord vibrations during phonation. Gómez com- iα i I = −Θ −a , iα i puted biomechanical parameters based on the power spectral m 2L iα density of the glottal source to improve detection of voice 1, x >0 pathology [21]. Θ x = Other researchers have used genetic algorithms to opti- 0, x <0, mize model parameters to match recorded glottal area, tra- a = a +Lx + x , jectory, and glottal volume wave and have shown the i 0i il ir possibility of model inversion [22, 23]. Tao extracted the a = min a , a , min 1 2 physiologically relevant parameters of the vocal fold model from high-speed video image series [24]. index i =1, 2 denotes the upper and lower mass, respectively; The complex optimization process and large number of α = l, r denotes the left and right parts, respectively; P is the parameters mean the matching result can be unstable. Thus, subglottal pressure; x and v are the displacement and cor- iα iα finding the important tuning parameters and selecting responding velocity of the masses, respectively; m , k , k , iα iα cα appropriate optimization algorithms are still important and r represent the mass, spring constant, coupling iα issues to be resolved for physical modeling applications, constant, and damping constant, respectively; L, d, and a 0i and simulations for asymmetric vocal cords also require fur- represent the vocal cord length, thickness of mass m , and 1α ther study. rest area, respectively; c =3k is an additional spring ia ia This paper designed a pathological voice source analysis constant for handling collision; a is the glottal area; F i 1a system using an optimized model to study the dynamics of and I are the Bernoulli force and restoring force due to ia asymmetric vocal cords. Incorporating spectral analysis, vocal cord collision, respectively; and P is the pressure on and bifurcation and phase diagrams, this paper investigates the lower masses. the impact of structural change of the vocal cord on its Using aerodynamic analysis, pressure drops at the glottal vibration and fundamental frequency. Sound effects due to entrance and viscous loss within the glottis is ignored. lung pressure are also studied. An optimized SH model In contrast to the IF model, Bernoulli flow exists below combined with particle swarm and quasi-Newton methods the narrowest glottis gap only, with a jet region above the (GPSO-QN) is proposed to determine biomechanical model contraction where pressure is considered to be constant parameters. Parameter adjustments and changing the oscilla- [26]. From Bernoulli’s equation, tion mode of the model allow normal and paralyzed voice sources to be simulated. Differences between optimized 2 2 U U ρ ρ g g model parameters are analyzed to assist in identifying the P = P + = P + , 3 s 1 0 2 a 2 a source of vocal paralysis. 1 min Applied Bionics and Biomechanics 3 K2l m1l Kcl r2l K1l m2l 1 r1l Figure 1: Schematic of the Herzel and Steinecke model. where P is the supraglottal pressure, U is volume flow upper and lower masses and glottal airflow waveforms 0 g are cyclical, and a fixed phase difference exists for the dis- velocity (glottal waveform), and ρ is air density. We ignore placement waveform (see Figure 2(a)). channel coupling, that is, P =0, and consider that Bernoulli pressure exists only when the glottis is open. Therefore, 2.2. Asymmetric Vocal Cord Model. Vocal polyps and paraly- sis often occur in one side of the vocal cords. Asymmetric min vocal cords cause tension imbalance, and overcritical imbal- P = P 1 − Ω a Ω a , 4 1 s min 1 1 ance may cause irregular vibration. Without loss of general- ity, we assume the left vocal cord is normal, that is, unchanged parameters, and lesions occur only on the right vocal cord. This imbalance is represented by an asymmetry U = 2P /ρa Θ a , 5 g s min min parameter β 0 4< β ≤ 1 , and right vocal parameters can be expressed as where tanh 50 x/x , x >0 ir m = , ir Ω x = 6 0, x <0, k = βk , ir ir with the units centimeters, grams, and milliseconds, respectively. k = βk , cr cr The standard parameters of this model are m =0 125, 1α c = βc ir ir m =0 025, k =0 08, k =0 008, k =0 025, r = r = 2α 1α 2α cα 1α 2α 0 02, Ps=0 008, d =0 25, a = a =0 05, and L =1 4. These 01 02 parameters are used by the symmetric model to simulate Small β means a high degree of asymmetry and leads vocal cord vibration, solving the differential equations to more complex vocal cord vibration. Consequently, sub- using the standard fourth order Runge-Kutta method with harmonic performance is enhanced and chaos occurs. initial conditions x 0 =0 01, x 0 =0 01, v 0 =0, Bifurcation diagrams and phase portraits can be used to 1α 2α 1α and v 0 =0, as shown in Figure 2. Displacement of describe the impact of β changes on the vocal system. 2α d 4 Applied Bionics and Biomechanics 0.15 0.1 0.05 −0.05 0 5 10 15 20 25 30 35 40 45 50 Time (ms) 1l 2l (a) 0.5 0 5 10 15 20 25 30 35 40 45 50 Time (ms) (b) Figure 2: Simulation of the standard symmetric model showing oscillation of (a) left lower and upper masses (x and x , resp.), and (b) 1l 2l glottal volume flow velocity U . When the vocal cords are asymmetric, contact forces are As the degree of asymmetry increases, right vocal amplitude modified as also increases with left amplitude remaining essentially unchanged. Consequently, phase difference increases, and the extrema ratio of both sides is no longer 1 : 1. c a 1 ir i I = −Θ −a , ir i Figure 3(d) shows the extrema ratio changes to 1 : 3, and m L β +1 ir quasiperiodic or irregular oscillations appear, leading to c a β il i irregular airflow velocity. I = −Θ −a il i m L β +1 Before and after bifurcation, evolution of the dynamical il systems in phase space can be described with phase diagrams of the displacement of bilateral vocal cord vibration in the 2.3. Analysis of Vocal Vibration. Vibration characteristics of x − x plane. Figure 4 shows that when β =0 8, no bifurca- the asymmetric two-mass model were analyzed with respect 1l 1r tion occurs, and the phase trajectory is a limit cycle. As β to time, frequency, and phase. The vocal mechanism of reduces to 0.53, asymmetry increases, bifurcation appears, clinical pathological voice was also investigated with respect and the phase trajectory becomes a complicated period dou- to physical simulation. As discussed above, we assumed the bling limit cycle. However, when β =0 45, the phase trajec- left vocal cord was normal, and lesions occurred only in the tory geometry simplifies, which is consistent with the right vocal cord. Clinical observation of vocal cord physio- results in the time domain. logical characteristics suggested 0 4< β ≤ 1 was an appropri- Considering the cases with fixed subglottal pressure ate range and subglottal pressure was fixed at 0.8 kPa. (0.8 kPa) and β = 0.45, 0.53, 0.6, 0.8, and 1, we compared Figure 3 shows displacement of the lower bilateral mass Fourier spectra corresponding to x , x , U , and the nat- for β =0 45, 0.53, 0.6, 0.8, and 1. Vocal cords on both sides 1l 1r g were structurally symmetrical for normal voice, and the ural frequencies obtained from an eigenvalue analysis of vibrational waveforms on both sides coincided completely. the system. Figures 5(a)–(e) show two vertical dashed lines Duration of the vocal opening and closing once is defined that represent the two natural frequencies of the left vocal as one pitch period, and there exists one maximum value of cord, and dash-dotted lines represent those of the right x in such a period. vocal cord. ir Asymmetric vocal cord vibrations are significantly more When β =1 (Figure 5(a)), the healthy phonation case complex. When the degree of asymmetry was relatively and the bilateral folds have the same natural frequency. small β =0 8 , right vocal amplitude was slightly larger This phonation frequency is approximately 145 Hz, located than the left side, and the phase was relatively advanced. between the two eigenfrequencies of the left (or right) side. x /x (cm) 3 1l 2l Ug (cm /s) Applied Bionics and Biomechanics 5 0.1 −0.1 0 10 20 30 40 50 60 70 80 90 100 (a) 𝛽 = 1 0.1 −0.1 0 10 20 30 40 50 60 70 80 90 100 (b) 𝛽 = 0.8 0.1 −0.1 0 10 20 30 40 50 60 70 80 90 100 (c) 𝛽 = 0.6 0.1 −0.1 0 10 20 30 40 50 60 70 80 90 100 (d) 𝛽 = 0.53 0.2 −0.2 0 10 20 30 40 50 60 70 80 90 100 (e) 𝛽 = 0.45 Time (ms) 1r 1l Figure 3: Mass displacements of the lower left and right sides. 0.1 0.1 0.1 0.1 0.1 0.05 0.05 0.05 0.05 0.05 0 0 0 −0.05 −0.05 −0.05 −0.05 −0.05 −0.02 0 0.02 0.06 −0.02 0 0.02 0.06 −0.02 0 0.02 0.06 −0.05 0 0.05 −0.05 0 0.05 x (cm) x (cm) x (cm) x (cm) x (cm) 1l 1l 1l 1l 1l (a) 𝛽 = 1 (b) 𝛽 = 0.8 (c) 𝛽 = 0.6 (d) 𝛽 = 0.53 (e) 𝛽 = 0.45 Figure 4: Phase space portrait in the x − x plane. 1l 1r 1 1 1 1 0.5 0.5 0.5 0.5 0.5 0 0 0 0 0 200 400 600 0 200 400 600 0 200 400 600 0 200 400 600 0 200 400 600 Frequency (Hz) Frequency (Hz) Frequency (Hz) Frequency (Hz) Frequency (Hz) (a) 𝛽 = 1 (b) 𝛽 = 0.8 (c) 𝛽 = 0.6 (d) 𝛽 = 0.53 (e) 𝛽 = 0.45 Figure 5: Fourier spectra corresponding to displacement of the two lower masses and the normalized glottal volume flow rate with Ps=0 8 kPa. Volume flow rate and left and right mass displacement are represented by the red, black, and green lines, respectively. Vertical dash lines represent the two left vocal cord natural frequencies, and the dash-dot lines represent those of the right vocal cord. Amplitude (normalized) x (cm) 1r x /x (cm) 1l 1r 6 Applied Bionics and Biomechanics Input voice Inverse Glottal pulse Vocal tract sl (n) sv (n) s (n) radiation inverse model model F (z) H (z) v model H(z) Vocal tract Glottal pulse inverse model model F (z) s (n) Hv (z) Figure 6: Estimation of the glottal pulse s n by iterative filtering. As β reduces, the eigenfrequencies do not coincide again Figure 6 shows the inverse filtering procedure. The radi- and more complex vibratory behaviors are observed. ation effect is first removed by H z , and the resulting radia- Figure 5(b) shows that for less asymmetry, β =0 8, tion compensated voice, s n ,is filtered by H z to l g although the intrinsic frequency changes, there is relatively reconstruct the deglottalized voice, s n , from which the little effect on the frequency spectrum. Figure 5(c) shows estimate of F z may be derived. The vocal tract inverse that when β =0 6, a frequency approximately 190 Hz with model fed with the F z filter parameters was used to relatively small amplitude appears between the two eigen- remove the influence of the vocal tract from s n , producing frequencies of the left normal folds. Figure 5(d) shows that a first estimate of the glottal pulse, s n . Another iteration when β =0 53, the overlapped frequencies of the preexist- was started with the new estimated H z loaded by F z , g g ing overtone separate and a small overtone frequency and the cycle repeated 2 or 3 times to obtain a good estima- appears between them at 110 Hz. Figure 5(e) shows that tion of the glottal source. when β =0 45, the overtone between the second eigenfre- The glottal flow will be defined as quency of the right fold and the first left fold disappears. However, the amplitude of the overtone frequency between u n = s n ‐s n 10 g g g the eigenfrequencies of the left normal folds becomes nearly as large as the pitch frequency. Thus, the fundamental frequency is mainly dependent on An example of the glottal flow estimation from inverse filtering is shown in Figure 7. the pathological vocal cords, while the normal folds mainly influence the overtone. 3.2. Objective Function Vocal Cord. Since the asymmetric SH model influences oscillations in both time and fre- 3. Model Parameter Optimization quency domains, the glottal flow, u , and simulated wave- We propose an optimization process to find appropriate forms, Ug, were also parameterized within those domains parameters for the biomechanical model that can accu- for comparison frequency, F , and time quotients based rately simulate normal and paralyzed voice sources. First, on the Lijiencrants-Frant model were calculated, including inverse filtering is implemented to reduce the channel speed quotient (SQ), the ratio of the glottal opening to effect on the speech signal, and glottal flow is extracted. closing time open quotient (OQ), the ratio of the open Glottal flow is separately parameterized in time and fre- time to the fundamental period; closing quotient (CIQ), quency domains to reduce computational complexity. the closing time divided by the fundamental period; and Then, an optimization algorithm is employed to optimize normalized amplitude quotients (NAQ), the ratio of ampli- SH model parameters to obtain a simulated glottal flow. tude quotients (maximum amplitude divided by corre- Finally, minimizing error between the parameters of the sponding maximum negative peak of its first derivative) simulated and extracted glottal flows allows the model to to the fundamental period. accurately reproduce the particular voice source, and cor- To describe the error between normal target glottal flow responding vocal parameters can also be obtained. and simulated waveforms, the objective function, FY, was defined as 3.1. Estimation of the Glottal Source. Reconstruction of the glottal source is based on the adaptive version of iterative ∣OQ − OQ ∣ ∣SQ − SQ ∣ ∣CIQ − CIQ ∣ inverse filtering developed by Alku [27]. The voice trace, s, FY = ω + + may be considered as the output of a generation model, f OQ SQ CIQ excited by a train pulse, δ, whose output is modeled by the ∣NAQ − NAQ ∣ ∣F − F ∣ 0 0 vocal tract transfer function, f to, yield voice at the lips, s , + + ω , v l NAQ F which is radiated as s, where r is the radiation model, that 0 is, means convolution of signals, where “′” means the parameters are derived from the simula- s = δ ∗ f ∗ f ∗ r = f ∗ f ∗r = s ∗ r 9 g v g v tion waveform. Applied Bionics and Biomechanics 7 0.5 −0.5 0 5 10 15 20 (a) Input voice 0.5 −0.5 0 5 10 15 20 Time (ms) (b) Glottal flow Figure 7: Example from vovel /a/ for a normal speaker. Traditional perturbation analyses have shown instability similar but have various strengths in dealing with different of pathological vocal sound. The resultant objective function problems [28]. is defined as: Therefore, we combined their advantages. PSO is an evolutionary computation technique based on swarm intel- ∣J − J ∣ ∣J − J ∣ ligence and is a community-based optimization tool. The OQ OQ SQ SQ FY = ω FY + ω + p 3 4 PSO algorithm first initializes a group of random particles J J OQ SQ with random solutions and then all individuals and the ∣J − J ∣ ∣J − J ∣ best individuals of groups breed. The optimal solution is CIQ CIQ NAQ NAQ + + found through an iterative process. We added selection J J CIQ NAQ and crossover processes similar to GA into PSO, generat- ∣J − J ∣ F0 F 0 ing a GPSO algorithm. + , In contrast, the quasi-Newton method is commonly used for solving nonlinear optimization problems, where the gra- dient of the objective function at each iteration step is obtained. An objective function can be constructed from where variables with superscript denote parameters of the the measured gradient to produce superlinear convergence. simulated glottal flow. However, this method is somewhat sensitive to the initial If the time-based quotients are equally weighted, the point, and results are mostly local optima. Therefore, we effect of frequency and time parameters on F are the combined the GPSO and quasi-Newton algorithm (GPSO- same, and their differential impact on F is equivalent QN) to optimize the biomechanical model parameters to to the original parameters, that is, ω =0 125 and ω = 1 2 match the target voice sources. ω = ω =0 5. When F or F reaches a global minimum, 3 4 p The masses, spring constants, coupling coefficients, the corresponding model can accurately reproduce the damping constants, and subglottal pressure all need optimi- target glottal waveform. zation, which can be expressed as a vector Φ = m , k , k , iα iα cα r , P . With optimized Φ the model should simulate Ug in 3.3. Optimization Algorithm. Gradient techniques have iα s good agreement with u . proven to be inadequate, since the objective function is non- g convex and contains many local minima. The evolutionary Previous analysis has shown that asymmetric pathologi- cal vocal cords are the leading cause of irregular vibration. algorithm has high robustness, and broad applicability for global optimization can deal with complex problems that Consequently, we took Φ and β as matching parameters with traditional optimization algorithms cannot solve. Particle the search interval m , k , k , r ∈ 0 001, 0 5 , β ∈ 0 4, 1 , iα iα cα iα swarm optimization (PSO) and genetic algorithm (GA) are and P ∈ 0 001, 0 05 . Then suitable matching parameters s 8 Applied Bionics and Biomechanics Initialize particle swarm particle velocity, and the number of iterations k = 0 Mutation of M + N individuals, select N of them with high fitness Particle velocity location into the next generation update, fitness calculation Select M individuals crossover and mutation, M new obtained No Termination condition satisfied Yes Optimal solution Quasi-Newton algorithm Optimal solution Figure 8: Proposed GPSO-QN algorithm structure. can be obtained using the proposed GPSO-QN algorithm the number of particles for the initial population set as to ensure the optimized model accurately reproduces the 30 and the number of generations limited to 400. Learning glottal waveform. factors c and c were set = 2, and the range of weight 1 2 To avoid obtaining local minima in a nonconvex coefficient ω was set = [0.5, 0.9]. search space by direct application of the gradient method, the GPSO algorithm is first applied to provide a rough 4.2. Normal Voice Source Matching. Figure 9 shows the approximation, and then the QN method is applied to excitation sources (red dashed lines) extracted from the four locally optimize the approximate solution, providing the normal voice samples using the optimized model were globally optimal result. accurately simulated. Using sample 3 as an example, Figure 8 shows the parameter optimization process. Figure 10 shows that the simulated and actual spectra also Selection and crossover process utilizes the Monte Carlo have good consistency. selection rule to choose M individuals. The termination condition is that the obtained maximum fitness value 4.3. Paralysis Voice Source Matching. Figure 11 shows that exceeds a preset threshold or the preset number of iterations the model simulated waveforms for paralyzed voice sam- is reached. ples (red dashed lines) have significant errors to actual samples, particularly for samples 7 and 8. However, the spectra show good consistency with only magnitude bias, 4. Result and Discussion as shown in Figure 12. 4.1. Experimental Parameters. This paper selected sustained 4.4. Difference Analysis of Matching Results. To investigate vowel /a/ from the MEEI database [29], numbering the samples 1–8 (4 normal and 4 paralysis voices). Sampling the differences between normal and paralysis voice sources, frequency was 25 kHz, and the proposed GPSO-QN algo- we matched 9 consecutive frames of samples 1–8, and rithm was used to optimize the model parameters with Figure 13 shows the statistical distribution of the optimized Applied Bionics and Biomechanics 9 0.5 −0.5 0 2 4 6 8 10 12 0.5 −0.5 0 2 4 6 8 10 12 0.5 −0.5 0 2 4 6 8 10 12 0.5 −0.5 0 2 4 6 8 10 12 Time (ms) Simulated U Target U Figure 9: Matching result of normal voice source in the time domain. 2.5 1.5 0.5 −0.5 −1 0 500 1000 1500 2000 (F/Hz) Simulated frequency spectrum Frequency spectrum Figure 10: Matching result of sample 3 voice source in the frequency domain. parameters. There were no significant differences between voice source analysis system. It is designed and programmed stiffness, quality, and damping of normal and paralysis by MATLAB. models. However, the coupling stiffness of paralyzed vocal voice sources is greater than that of normal sources, and sig- 5. Conclusion nificant asymmetry in the paralyzed vocal cords was observed, as shown in the last two rows of Figure 13(b). This study analyzed nonlinear characteristics of asymmet- Therefore, coupling stiffness and the asymmetry ric vocal cord motion using an optimized biomechanical parameter, β, could be used as a basis for classifying normal model to design a pathological voice source analysis system. and paralyzed vocal sources. Figure 14 shows the pathological A proposed algorithm was employed to optimize the Amplitude/DB Normalized U g 10 Applied Bionics and Biomechanics 0.5 0 5 10 15 20 25 30 0.5 −0.5 0 5 10 15 20 0.5 0 5 10 15 20 25 30 −1 0 5 10 15 20 25 30 Time (ms) Simulated U Target U Figure 11: Matching result of paralysis voice source in the time domain. −2 0 500 1000 1500 2000 −2 0 500 1000 1500 2000 (F/Hz) Simulated frequency spectrum Frequency spectrum Figure 12: Matching results of samples 7 and 8 in the frequency domain. masses, spring constants, coupling coefficient, damping con- Period doubling bifurcation and frequency entrainment stants, asymmetry parameter, and subglottal pressure of the were observed in the bifurcation and phase diagrams, mass model. and spectrograms. The proposed biomechanical model accurately simulated Vibration system complexity and asymmetry do not have irregular vibration caused by unbalanced vocal tension. a simple proportional relationship. This study shows that Normalized U Amplitude/DB g Applied Bionics and Biomechanics 11 0.4 0.3 0.2 0.3 0.2 0.1 0.2 0.1 0.15 0.1 0.05 12 34 56 7 8 Sample Figure 13: Statistical distribution of normal (1–4) and paralyzed samples (5–8). Figure 14: Pathological voice source analysis system. pitch frequency is mainly affected by the asymmetric struc- Optimized model simulations will be of great value for ture of the vocal cord, whereas the impact of subglottal pres- understanding clinical hoarse voices corresponding to asym- sure is relatively small. metric vocal structure and predicting the effect on unilateral The optimal biomechanical model can accurately repro- vocal disease treatment. Future work will establish rational sound models for duce the voice source stream modulated by asymmetric vocal cords. Although the physiological parameters of voice vocal cord polyps and other organic diseases to match sources were different, the asymmetry and coupling stiffness real voice sources, assisting in classification of vocal parameters helped determine paralysis voice sources. cord diseases. m2 m1 k2 k1 12 Applied Bionics and Biomechanics Data Availability [10] M. Zañartu, D. D. Mehta, J. C. Ho, G. R. Wodicka, and R. E. Hillman, “Observation and analysis of in vivo vocal fold tissue The data used to support the findings of this study are instabilities produced by nonlinear source-filter coupling: a available from the corresponding author upon request. case study,” The Journal of the Acoustical Society of America, vol. 129, no. 1, pp. 326–339, 2011. [11] N. Wan, D. D. Peng, M. Sun, and D. Zhang, “Nonlinear Conflicts of Interest oscillation of pathological vocal folds during vocalization,” Science China Physics, Mechanics and Astronomy, vol. 56, The authors declare that there are no conflicts of interest no. 7, pp. 1324–1328, 2013. regarding the publication of this paper. [12] A. P. Pinheiro and G. Kerschen, “Vibrational dynamics of vocal folds using nonlinear normal modes,” Medical Engineer- ing & Physics, vol. 35, no. 8, pp. 1079–1088, 2013. Acknowledgments [13] A. P. Pinheiro, D. E. Stewart, C. D. Maciel, J. C. Pereira, and This project was funded by National Natural Science S. Oliveira, “Analysis of nonlinear dynamics of vocal folds using high-speed video observation and biomechanical model- Foundation of China under Grant no. 61372146 and no. ing,” Digital Signal Processing, vol. 22, no. 2, pp. 304–313, 2012. 61271359. The authors are thankful for the support from [14] Y. Zhang, A. J. Sprecher, Z. X. Zhao, and J. J. 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Pathological Voice Source Analysis System Using a Flow Waveform-Matched Biomechanical Model

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Copyright © 2018 Xiaojun Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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10.1155/2018/3158439
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Hindawi Applied Bionics and Biomechanics Volume 2018, Article ID 3158439, 13 pages https://doi.org/10.1155/2018/3158439 Research Article Pathological Voice Source Analysis System Using a Flow Waveform-Matched Biomechanical Model 1,2 2 2 2 1,2 1 Xiaojun Zhang , Lingling Gu, Wei Wei , Di Wu, Zhi Tao , and Heming Zhao School of Electronic and Information Engineering, Soochow University, Suzhou 215000, China College of Physics, Optoelectronics and Energy, Soochow University, Suzhou 215000, China Correspondence should be addressed to Wei Wei; weiwei0728@suda.edu.cn and Zhi Tao; taoz@suda.edu.cn Received 30 March 2018; Accepted 24 May 2018; Published 2 July 2018 Academic Editor: Liwei Shi Copyright © 2018 Xiaojun Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Voice production occurs through vocal cord and vibration coupled to glottal airflow. Vocal cord lesions affect the vocal system and lead to voice disorders. In this paper, a pathological voice source analysis system is designed. This study integrates nonlinear dynamics with an optimized asymmetric two-mass model to explore nonlinear characteristics of vocal cord vibration, and changes in acoustic parameters, such as fundamental frequency, caused by distinct subglottal pressure and varying degrees of vocal cord paralysis are analyzed. Various samples of sustained vowel /a/ of normal and pathological voices were extracted from MEEI (Massachusetts Eye and Ear Infirmary) database. A fitting procedure combining genetic particle swarm optimization and a quasi-Newton method was developed to optimize the biomechanical model parameters and match the targeted voice source. Experimental results validate the applicability of the proposed model to reproduce vocal cord vibration with high accuracy, and show that paralyzed vocal cord increases the model coupling stiffness. 1. Introduction parameters with pattern recognition algorithms to assist diagnosis of pathological voice [5, 6]. However, the selected voice signal parameters are not directly linked with the actual Vocal cord vibration interrupts the straight airflow expelled physical structure, and vocal structural changes that cause by the lungs into a series of pulses that act as the excitation vocal voice disorders require further study. source for voice and sound. Denervation or organic diseases of vocal cords, such as paralysis and polyps, can cause irreg- Nonlinear dynamics theory has provided a new avenue for dynamical system related research, for example, methods ular vibration with consequential changes, manifested as combining nonlinear theory with spectral analysis have been breathy or hoarse voice. These diseases generally affect one successfully applied to EEG and ECG signal analysis. It has side of vocal structure, causing significant imbalance in also been extended to study voice signals [7, 8]. bilateral vocal cord tension [1, 2]. Irregular vibration of the vocal cords corresponding to a variety of voice disorders Nonlinearity inherent in the vocal system can cause irreg- ular voice behavior, as indicated by harmonics, bifurcation, can be observed with electronic laryngoscope to assist diag- and low-dimensional chaos in high-speed recording of vocal nosing vocal cord disease. However, laryngoscopy examina- cord vibration signals [9, 10]. The degree of pathological tion is invasive, and the outcomes are relatively subjective. vocal fold is closely related to the nonlinear vibration of the Acoustic analysis can complement and in some cases replace the other invasive methods, which based on direct vocal fold vocal cords. [11]. Therefore, traditional analysis of acoustic parameters may not be accurate, but nonlinear dynamics the- observation [3, 4]. ory has been shown to have good applicability in characteriz- Clinical diagnosis and pathological voice classification ing such signals [12]. Time frequency shape analysis based on using objective methods is an important issue in medical embedding phase space plots and nonlinear dynamics evaluation. Previous studies have mainly combined acoustic 2 Applied Bionics and Biomechanics methods can be used to evaluate the vocal fold dynamics 2. Method during phonation [13]. Nonlinear models can also simulate 2.1. Symmetric Vocal Model. Vocal cords are two symmetri- various vocal sound phenomena and have been used for cal membranous anatomical structures located in the throat. dynamic prediction of disordered speech associated with lar- Airflow out of the trachea and lungs continuously impacts ynx pathology [14–16]. Many physical modeling methods for the vocal cords and causes vibration. The vibration behavior glottal excitation have been proposed, and the corresponding modulates the airflow to generate glottal pulses [25]. Based model parameters have been utilized to study various voice on the elastic and dynamic properties of the vocal cords, each disorders. The two-mass (IF) model is the most well-known fold is represented by two coupled oscillators with two classical physical model of the vocal cords, first proposed masses, three springs, and two dampers, where the quality by Ishizaka and Flanagan and simplified by Steinecke of the mass and spring constants denote vocal quality and and Herzel (SH model), to study vibration characteristics tension, respectively. Figure 1 shows the simplified two- of the vocal cords. Xue combined the work of Steinecke mass (SH) model, which can be expressed as and Herzel with Navier-Stokes equations and analyzed irregular vibrations caused by tension imbalance in bilateral x = υ , 1α 1α vocal cord, as well as sound effects [17]. Recently, Sommer modified the asymmetric vocal contact force of the SH υ = − F + I − r υ − k x − k x − x , 1α 1α 1α 1α 1α 1α 1α cα 1α 2α model based on Newton’s third law [18]. However, a com- 1α prehensive nonlinear analysis for the modified SH model x = υ , remains incomplete. 2α 2α Although physical modeling has enormous potential in υ = − I − r υ − k x − k x − x , speech synthesis and voice analysis, the large number of 2α 2α 2α 2α 2α 2α 2α 2α 1α 2α model parameters and the complexity of model optimization to match observational data have prevented its practical application [19]. Döllinger used the Nelder–Mead algorithm where to minimize the error between experimental curves obtained from high-speed glottography sequences and curves gener- LdP ated with the two-mass model (2MM) [20]. However, this F = , 1α 1α is an invasive method because an endoscope is required to c a record vocal cord vibrations during phonation. Gómez com- iα i I = −Θ −a , iα i puted biomechanical parameters based on the power spectral m 2L iα density of the glottal source to improve detection of voice 1, x >0 pathology [21]. Θ x = Other researchers have used genetic algorithms to opti- 0, x <0, mize model parameters to match recorded glottal area, tra- a = a +Lx + x , jectory, and glottal volume wave and have shown the i 0i il ir possibility of model inversion [22, 23]. Tao extracted the a = min a , a , min 1 2 physiologically relevant parameters of the vocal fold model from high-speed video image series [24]. index i =1, 2 denotes the upper and lower mass, respectively; The complex optimization process and large number of α = l, r denotes the left and right parts, respectively; P is the parameters mean the matching result can be unstable. Thus, subglottal pressure; x and v are the displacement and cor- iα iα finding the important tuning parameters and selecting responding velocity of the masses, respectively; m , k , k , iα iα cα appropriate optimization algorithms are still important and r represent the mass, spring constant, coupling iα issues to be resolved for physical modeling applications, constant, and damping constant, respectively; L, d, and a 0i and simulations for asymmetric vocal cords also require fur- represent the vocal cord length, thickness of mass m , and 1α ther study. rest area, respectively; c =3k is an additional spring ia ia This paper designed a pathological voice source analysis constant for handling collision; a is the glottal area; F i 1a system using an optimized model to study the dynamics of and I are the Bernoulli force and restoring force due to ia asymmetric vocal cords. Incorporating spectral analysis, vocal cord collision, respectively; and P is the pressure on and bifurcation and phase diagrams, this paper investigates the lower masses. the impact of structural change of the vocal cord on its Using aerodynamic analysis, pressure drops at the glottal vibration and fundamental frequency. Sound effects due to entrance and viscous loss within the glottis is ignored. lung pressure are also studied. An optimized SH model In contrast to the IF model, Bernoulli flow exists below combined with particle swarm and quasi-Newton methods the narrowest glottis gap only, with a jet region above the (GPSO-QN) is proposed to determine biomechanical model contraction where pressure is considered to be constant parameters. Parameter adjustments and changing the oscilla- [26]. From Bernoulli’s equation, tion mode of the model allow normal and paralyzed voice sources to be simulated. Differences between optimized 2 2 U U ρ ρ g g model parameters are analyzed to assist in identifying the P = P + = P + , 3 s 1 0 2 a 2 a source of vocal paralysis. 1 min Applied Bionics and Biomechanics 3 K2l m1l Kcl r2l K1l m2l 1 r1l Figure 1: Schematic of the Herzel and Steinecke model. where P is the supraglottal pressure, U is volume flow upper and lower masses and glottal airflow waveforms 0 g are cyclical, and a fixed phase difference exists for the dis- velocity (glottal waveform), and ρ is air density. We ignore placement waveform (see Figure 2(a)). channel coupling, that is, P =0, and consider that Bernoulli pressure exists only when the glottis is open. Therefore, 2.2. Asymmetric Vocal Cord Model. Vocal polyps and paraly- sis often occur in one side of the vocal cords. Asymmetric min vocal cords cause tension imbalance, and overcritical imbal- P = P 1 − Ω a Ω a , 4 1 s min 1 1 ance may cause irregular vibration. Without loss of general- ity, we assume the left vocal cord is normal, that is, unchanged parameters, and lesions occur only on the right vocal cord. This imbalance is represented by an asymmetry U = 2P /ρa Θ a , 5 g s min min parameter β 0 4< β ≤ 1 , and right vocal parameters can be expressed as where tanh 50 x/x , x >0 ir m = , ir Ω x = 6 0, x <0, k = βk , ir ir with the units centimeters, grams, and milliseconds, respectively. k = βk , cr cr The standard parameters of this model are m =0 125, 1α c = βc ir ir m =0 025, k =0 08, k =0 008, k =0 025, r = r = 2α 1α 2α cα 1α 2α 0 02, Ps=0 008, d =0 25, a = a =0 05, and L =1 4. These 01 02 parameters are used by the symmetric model to simulate Small β means a high degree of asymmetry and leads vocal cord vibration, solving the differential equations to more complex vocal cord vibration. Consequently, sub- using the standard fourth order Runge-Kutta method with harmonic performance is enhanced and chaos occurs. initial conditions x 0 =0 01, x 0 =0 01, v 0 =0, Bifurcation diagrams and phase portraits can be used to 1α 2α 1α and v 0 =0, as shown in Figure 2. Displacement of describe the impact of β changes on the vocal system. 2α d 4 Applied Bionics and Biomechanics 0.15 0.1 0.05 −0.05 0 5 10 15 20 25 30 35 40 45 50 Time (ms) 1l 2l (a) 0.5 0 5 10 15 20 25 30 35 40 45 50 Time (ms) (b) Figure 2: Simulation of the standard symmetric model showing oscillation of (a) left lower and upper masses (x and x , resp.), and (b) 1l 2l glottal volume flow velocity U . When the vocal cords are asymmetric, contact forces are As the degree of asymmetry increases, right vocal amplitude modified as also increases with left amplitude remaining essentially unchanged. Consequently, phase difference increases, and the extrema ratio of both sides is no longer 1 : 1. c a 1 ir i I = −Θ −a , ir i Figure 3(d) shows the extrema ratio changes to 1 : 3, and m L β +1 ir quasiperiodic or irregular oscillations appear, leading to c a β il i irregular airflow velocity. I = −Θ −a il i m L β +1 Before and after bifurcation, evolution of the dynamical il systems in phase space can be described with phase diagrams of the displacement of bilateral vocal cord vibration in the 2.3. Analysis of Vocal Vibration. Vibration characteristics of x − x plane. Figure 4 shows that when β =0 8, no bifurca- the asymmetric two-mass model were analyzed with respect 1l 1r tion occurs, and the phase trajectory is a limit cycle. As β to time, frequency, and phase. The vocal mechanism of reduces to 0.53, asymmetry increases, bifurcation appears, clinical pathological voice was also investigated with respect and the phase trajectory becomes a complicated period dou- to physical simulation. As discussed above, we assumed the bling limit cycle. However, when β =0 45, the phase trajec- left vocal cord was normal, and lesions occurred only in the tory geometry simplifies, which is consistent with the right vocal cord. Clinical observation of vocal cord physio- results in the time domain. logical characteristics suggested 0 4< β ≤ 1 was an appropri- Considering the cases with fixed subglottal pressure ate range and subglottal pressure was fixed at 0.8 kPa. (0.8 kPa) and β = 0.45, 0.53, 0.6, 0.8, and 1, we compared Figure 3 shows displacement of the lower bilateral mass Fourier spectra corresponding to x , x , U , and the nat- for β =0 45, 0.53, 0.6, 0.8, and 1. Vocal cords on both sides 1l 1r g were structurally symmetrical for normal voice, and the ural frequencies obtained from an eigenvalue analysis of vibrational waveforms on both sides coincided completely. the system. Figures 5(a)–(e) show two vertical dashed lines Duration of the vocal opening and closing once is defined that represent the two natural frequencies of the left vocal as one pitch period, and there exists one maximum value of cord, and dash-dotted lines represent those of the right x in such a period. vocal cord. ir Asymmetric vocal cord vibrations are significantly more When β =1 (Figure 5(a)), the healthy phonation case complex. When the degree of asymmetry was relatively and the bilateral folds have the same natural frequency. small β =0 8 , right vocal amplitude was slightly larger This phonation frequency is approximately 145 Hz, located than the left side, and the phase was relatively advanced. between the two eigenfrequencies of the left (or right) side. x /x (cm) 3 1l 2l Ug (cm /s) Applied Bionics and Biomechanics 5 0.1 −0.1 0 10 20 30 40 50 60 70 80 90 100 (a) 𝛽 = 1 0.1 −0.1 0 10 20 30 40 50 60 70 80 90 100 (b) 𝛽 = 0.8 0.1 −0.1 0 10 20 30 40 50 60 70 80 90 100 (c) 𝛽 = 0.6 0.1 −0.1 0 10 20 30 40 50 60 70 80 90 100 (d) 𝛽 = 0.53 0.2 −0.2 0 10 20 30 40 50 60 70 80 90 100 (e) 𝛽 = 0.45 Time (ms) 1r 1l Figure 3: Mass displacements of the lower left and right sides. 0.1 0.1 0.1 0.1 0.1 0.05 0.05 0.05 0.05 0.05 0 0 0 −0.05 −0.05 −0.05 −0.05 −0.05 −0.02 0 0.02 0.06 −0.02 0 0.02 0.06 −0.02 0 0.02 0.06 −0.05 0 0.05 −0.05 0 0.05 x (cm) x (cm) x (cm) x (cm) x (cm) 1l 1l 1l 1l 1l (a) 𝛽 = 1 (b) 𝛽 = 0.8 (c) 𝛽 = 0.6 (d) 𝛽 = 0.53 (e) 𝛽 = 0.45 Figure 4: Phase space portrait in the x − x plane. 1l 1r 1 1 1 1 0.5 0.5 0.5 0.5 0.5 0 0 0 0 0 200 400 600 0 200 400 600 0 200 400 600 0 200 400 600 0 200 400 600 Frequency (Hz) Frequency (Hz) Frequency (Hz) Frequency (Hz) Frequency (Hz) (a) 𝛽 = 1 (b) 𝛽 = 0.8 (c) 𝛽 = 0.6 (d) 𝛽 = 0.53 (e) 𝛽 = 0.45 Figure 5: Fourier spectra corresponding to displacement of the two lower masses and the normalized glottal volume flow rate with Ps=0 8 kPa. Volume flow rate and left and right mass displacement are represented by the red, black, and green lines, respectively. Vertical dash lines represent the two left vocal cord natural frequencies, and the dash-dot lines represent those of the right vocal cord. Amplitude (normalized) x (cm) 1r x /x (cm) 1l 1r 6 Applied Bionics and Biomechanics Input voice Inverse Glottal pulse Vocal tract sl (n) sv (n) s (n) radiation inverse model model F (z) H (z) v model H(z) Vocal tract Glottal pulse inverse model model F (z) s (n) Hv (z) Figure 6: Estimation of the glottal pulse s n by iterative filtering. As β reduces, the eigenfrequencies do not coincide again Figure 6 shows the inverse filtering procedure. The radi- and more complex vibratory behaviors are observed. ation effect is first removed by H z , and the resulting radia- Figure 5(b) shows that for less asymmetry, β =0 8, tion compensated voice, s n ,is filtered by H z to l g although the intrinsic frequency changes, there is relatively reconstruct the deglottalized voice, s n , from which the little effect on the frequency spectrum. Figure 5(c) shows estimate of F z may be derived. The vocal tract inverse that when β =0 6, a frequency approximately 190 Hz with model fed with the F z filter parameters was used to relatively small amplitude appears between the two eigen- remove the influence of the vocal tract from s n , producing frequencies of the left normal folds. Figure 5(d) shows that a first estimate of the glottal pulse, s n . Another iteration when β =0 53, the overlapped frequencies of the preexist- was started with the new estimated H z loaded by F z , g g ing overtone separate and a small overtone frequency and the cycle repeated 2 or 3 times to obtain a good estima- appears between them at 110 Hz. Figure 5(e) shows that tion of the glottal source. when β =0 45, the overtone between the second eigenfre- The glottal flow will be defined as quency of the right fold and the first left fold disappears. However, the amplitude of the overtone frequency between u n = s n ‐s n 10 g g g the eigenfrequencies of the left normal folds becomes nearly as large as the pitch frequency. Thus, the fundamental frequency is mainly dependent on An example of the glottal flow estimation from inverse filtering is shown in Figure 7. the pathological vocal cords, while the normal folds mainly influence the overtone. 3.2. Objective Function Vocal Cord. Since the asymmetric SH model influences oscillations in both time and fre- 3. Model Parameter Optimization quency domains, the glottal flow, u , and simulated wave- We propose an optimization process to find appropriate forms, Ug, were also parameterized within those domains parameters for the biomechanical model that can accu- for comparison frequency, F , and time quotients based rately simulate normal and paralyzed voice sources. First, on the Lijiencrants-Frant model were calculated, including inverse filtering is implemented to reduce the channel speed quotient (SQ), the ratio of the glottal opening to effect on the speech signal, and glottal flow is extracted. closing time open quotient (OQ), the ratio of the open Glottal flow is separately parameterized in time and fre- time to the fundamental period; closing quotient (CIQ), quency domains to reduce computational complexity. the closing time divided by the fundamental period; and Then, an optimization algorithm is employed to optimize normalized amplitude quotients (NAQ), the ratio of ampli- SH model parameters to obtain a simulated glottal flow. tude quotients (maximum amplitude divided by corre- Finally, minimizing error between the parameters of the sponding maximum negative peak of its first derivative) simulated and extracted glottal flows allows the model to to the fundamental period. accurately reproduce the particular voice source, and cor- To describe the error between normal target glottal flow responding vocal parameters can also be obtained. and simulated waveforms, the objective function, FY, was defined as 3.1. Estimation of the Glottal Source. Reconstruction of the glottal source is based on the adaptive version of iterative ∣OQ − OQ ∣ ∣SQ − SQ ∣ ∣CIQ − CIQ ∣ inverse filtering developed by Alku [27]. The voice trace, s, FY = ω + + may be considered as the output of a generation model, f OQ SQ CIQ excited by a train pulse, δ, whose output is modeled by the ∣NAQ − NAQ ∣ ∣F − F ∣ 0 0 vocal tract transfer function, f to, yield voice at the lips, s , + + ω , v l NAQ F which is radiated as s, where r is the radiation model, that 0 is, means convolution of signals, where “′” means the parameters are derived from the simula- s = δ ∗ f ∗ f ∗ r = f ∗ f ∗r = s ∗ r 9 g v g v tion waveform. Applied Bionics and Biomechanics 7 0.5 −0.5 0 5 10 15 20 (a) Input voice 0.5 −0.5 0 5 10 15 20 Time (ms) (b) Glottal flow Figure 7: Example from vovel /a/ for a normal speaker. Traditional perturbation analyses have shown instability similar but have various strengths in dealing with different of pathological vocal sound. The resultant objective function problems [28]. is defined as: Therefore, we combined their advantages. PSO is an evolutionary computation technique based on swarm intel- ∣J − J ∣ ∣J − J ∣ ligence and is a community-based optimization tool. The OQ OQ SQ SQ FY = ω FY + ω + p 3 4 PSO algorithm first initializes a group of random particles J J OQ SQ with random solutions and then all individuals and the ∣J − J ∣ ∣J − J ∣ best individuals of groups breed. The optimal solution is CIQ CIQ NAQ NAQ + + found through an iterative process. We added selection J J CIQ NAQ and crossover processes similar to GA into PSO, generat- ∣J − J ∣ F0 F 0 ing a GPSO algorithm. + , In contrast, the quasi-Newton method is commonly used for solving nonlinear optimization problems, where the gra- dient of the objective function at each iteration step is obtained. An objective function can be constructed from where variables with superscript denote parameters of the the measured gradient to produce superlinear convergence. simulated glottal flow. However, this method is somewhat sensitive to the initial If the time-based quotients are equally weighted, the point, and results are mostly local optima. Therefore, we effect of frequency and time parameters on F are the combined the GPSO and quasi-Newton algorithm (GPSO- same, and their differential impact on F is equivalent QN) to optimize the biomechanical model parameters to to the original parameters, that is, ω =0 125 and ω = 1 2 match the target voice sources. ω = ω =0 5. When F or F reaches a global minimum, 3 4 p The masses, spring constants, coupling coefficients, the corresponding model can accurately reproduce the damping constants, and subglottal pressure all need optimi- target glottal waveform. zation, which can be expressed as a vector Φ = m , k , k , iα iα cα r , P . With optimized Φ the model should simulate Ug in 3.3. Optimization Algorithm. Gradient techniques have iα s good agreement with u . proven to be inadequate, since the objective function is non- g convex and contains many local minima. The evolutionary Previous analysis has shown that asymmetric pathologi- cal vocal cords are the leading cause of irregular vibration. algorithm has high robustness, and broad applicability for global optimization can deal with complex problems that Consequently, we took Φ and β as matching parameters with traditional optimization algorithms cannot solve. Particle the search interval m , k , k , r ∈ 0 001, 0 5 , β ∈ 0 4, 1 , iα iα cα iα swarm optimization (PSO) and genetic algorithm (GA) are and P ∈ 0 001, 0 05 . Then suitable matching parameters s 8 Applied Bionics and Biomechanics Initialize particle swarm particle velocity, and the number of iterations k = 0 Mutation of M + N individuals, select N of them with high fitness Particle velocity location into the next generation update, fitness calculation Select M individuals crossover and mutation, M new obtained No Termination condition satisfied Yes Optimal solution Quasi-Newton algorithm Optimal solution Figure 8: Proposed GPSO-QN algorithm structure. can be obtained using the proposed GPSO-QN algorithm the number of particles for the initial population set as to ensure the optimized model accurately reproduces the 30 and the number of generations limited to 400. Learning glottal waveform. factors c and c were set = 2, and the range of weight 1 2 To avoid obtaining local minima in a nonconvex coefficient ω was set = [0.5, 0.9]. search space by direct application of the gradient method, the GPSO algorithm is first applied to provide a rough 4.2. Normal Voice Source Matching. Figure 9 shows the approximation, and then the QN method is applied to excitation sources (red dashed lines) extracted from the four locally optimize the approximate solution, providing the normal voice samples using the optimized model were globally optimal result. accurately simulated. Using sample 3 as an example, Figure 8 shows the parameter optimization process. Figure 10 shows that the simulated and actual spectra also Selection and crossover process utilizes the Monte Carlo have good consistency. selection rule to choose M individuals. The termination condition is that the obtained maximum fitness value 4.3. Paralysis Voice Source Matching. Figure 11 shows that exceeds a preset threshold or the preset number of iterations the model simulated waveforms for paralyzed voice sam- is reached. ples (red dashed lines) have significant errors to actual samples, particularly for samples 7 and 8. However, the spectra show good consistency with only magnitude bias, 4. Result and Discussion as shown in Figure 12. 4.1. Experimental Parameters. This paper selected sustained 4.4. Difference Analysis of Matching Results. To investigate vowel /a/ from the MEEI database [29], numbering the samples 1–8 (4 normal and 4 paralysis voices). Sampling the differences between normal and paralysis voice sources, frequency was 25 kHz, and the proposed GPSO-QN algo- we matched 9 consecutive frames of samples 1–8, and rithm was used to optimize the model parameters with Figure 13 shows the statistical distribution of the optimized Applied Bionics and Biomechanics 9 0.5 −0.5 0 2 4 6 8 10 12 0.5 −0.5 0 2 4 6 8 10 12 0.5 −0.5 0 2 4 6 8 10 12 0.5 −0.5 0 2 4 6 8 10 12 Time (ms) Simulated U Target U Figure 9: Matching result of normal voice source in the time domain. 2.5 1.5 0.5 −0.5 −1 0 500 1000 1500 2000 (F/Hz) Simulated frequency spectrum Frequency spectrum Figure 10: Matching result of sample 3 voice source in the frequency domain. parameters. There were no significant differences between voice source analysis system. It is designed and programmed stiffness, quality, and damping of normal and paralysis by MATLAB. models. However, the coupling stiffness of paralyzed vocal voice sources is greater than that of normal sources, and sig- 5. Conclusion nificant asymmetry in the paralyzed vocal cords was observed, as shown in the last two rows of Figure 13(b). This study analyzed nonlinear characteristics of asymmet- Therefore, coupling stiffness and the asymmetry ric vocal cord motion using an optimized biomechanical parameter, β, could be used as a basis for classifying normal model to design a pathological voice source analysis system. and paralyzed vocal sources. Figure 14 shows the pathological A proposed algorithm was employed to optimize the Amplitude/DB Normalized U g 10 Applied Bionics and Biomechanics 0.5 0 5 10 15 20 25 30 0.5 −0.5 0 5 10 15 20 0.5 0 5 10 15 20 25 30 −1 0 5 10 15 20 25 30 Time (ms) Simulated U Target U Figure 11: Matching result of paralysis voice source in the time domain. −2 0 500 1000 1500 2000 −2 0 500 1000 1500 2000 (F/Hz) Simulated frequency spectrum Frequency spectrum Figure 12: Matching results of samples 7 and 8 in the frequency domain. masses, spring constants, coupling coefficient, damping con- Period doubling bifurcation and frequency entrainment stants, asymmetry parameter, and subglottal pressure of the were observed in the bifurcation and phase diagrams, mass model. and spectrograms. The proposed biomechanical model accurately simulated Vibration system complexity and asymmetry do not have irregular vibration caused by unbalanced vocal tension. a simple proportional relationship. This study shows that Normalized U Amplitude/DB g Applied Bionics and Biomechanics 11 0.4 0.3 0.2 0.3 0.2 0.1 0.2 0.1 0.15 0.1 0.05 12 34 56 7 8 Sample Figure 13: Statistical distribution of normal (1–4) and paralyzed samples (5–8). Figure 14: Pathological voice source analysis system. pitch frequency is mainly affected by the asymmetric struc- Optimized model simulations will be of great value for ture of the vocal cord, whereas the impact of subglottal pres- understanding clinical hoarse voices corresponding to asym- sure is relatively small. metric vocal structure and predicting the effect on unilateral The optimal biomechanical model can accurately repro- vocal disease treatment. Future work will establish rational sound models for duce the voice source stream modulated by asymmetric vocal cords. 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