﻿ 声带计算机仿真的新型数学–力学模型综述 Review on New Mathematical and Mechanical Models for the Computer Simulation of Vocal Cord

Computer Science and Application
Vol.06 No.07(2016), Article ID:18140,9 pages
10.12677/CSA.2016.67053

Review on New Mathematical and Mechanical Models for the Computer Simulation of Vocal Cord

Jinxiao Huang

Electronic Information Engineering College, Qingdao University, Qingdao Shandong

Received: Jul. 5th, 2016; accepted: Jul. 26th, 2016; published: Jul. 29th, 2016

Copyright © 2016 by author and Hans Publishers Inc.

ABSTRACT

A review on new mathematical and mechanical models of the vocal cords is given. The basic model is a two-mass nonlinear oscillator system which is accepted to be the basic one for mechanical description in voice production. The model is not only extended into three, five, and more mass systems, systems with time variable parameters and three-dimensional systems, but also simplified into one-mass system with coupled two-direction deflection and damping functions. The corresponding mathematical models are the systems of coupled second-order differential equations which describe the vibrations of the symmetric and asymmetric vocal folds. The models give the conditions for the regular and irregular motions like bifurcation and deterministic chaos in vocal folds. The obtained results are of special interest for detecting the pathology of vocal cords, when there is no visual effect of disease. Based on the results given in the paper, the objectives for future investigation in this matter are given.

Keywords:Mathematical Models, Mechanical Models, More Mass Systems, Two-Direction Deflection

1. 引言

2. 单质量块声带模型

3. 对称声带的非线性双质量块模型

Lucero和Koenig [10] 将声带组织的非线性特性，引入到声带的基本双质量块模型中，提出了一种改进的对称声带的非线性双质量块模型。

(3.1)

(3.2)

(3.3)

(3.4)

4. 非对称声带的双质量块模型

Isshiki [13] 等人讨论了非对称声带张力的临床意义，不对称可能意味着声带的病理，病变的力学性能和不对称声带的不稳定性，从定性上可能会导致喉部产生不同的声音。在动态模型中包含一些典型的效果，比如左右两声带之间的张力不平衡而造成的影响。

(4.1)

(4.2)

Figure 1. Model of the asymmetric vocal folds

(4.3)

(4.4)

(4.5)

(4.6)

5. 非对称声带的非稳定双质量块模型

(5.1)

(5.2)

(5.3)

6. 非对称声带的多质量块模型

Figure 2. Two-mass models of the asymmetric vocal folds with time variable parameters

Figure 3. Three-dimensional model of voice folds

(6.1)

7. 非固定的声带多质量块模型

(7.1)

8. 总结

(1) 在这些数学模型中，声带的非线性属性必须包括在内。微分方程有一些整数和非整数阶次的非线性项。不仅数值型的，而且近似解析方法也可以用来开发利用以解决这些微分方程。

(2) 对于系统中所有模拟声带的质量块，应该分为三个方向的运动：横向，纵向，和垂直。如果能有这样一个完全符合要求的模型，对于声带振动会给出一个更好的解释。

(3) 声带模型中，负库仑阻尼假定为线性的。为了改进模型，我们建议引入整数或非整数阶次的非线性阻尼，这个建议是经过了多次诊断测量的经验而提出，这样的模型将会给更准确的结果。为了解决运动的微分方程，必须延伸一些分析方法，也必须开发一些新的解决方法。

(4) 非平稳的声带振荡对许多语音障碍是比较典型的，其稳定性需要更深入的分析。

Figure 4. Multimass model of the vocal folds

(5) 特别注意的有：不规则声带的运动模型、这些运动的微分方程的定性和定量分析描述。声带的不稳定和不规则运动可能意味着疾病或异常。

(6) 声带振动的发生机理与很多学科的发展都息息相关，比如：喉病理学、人工器官、语音识别、语音合成、神经动力学等等。在声带振动原理方面的研究对喉科疾病的非侵入诊断、嗓音保护、歌唱声学、嗓音医学等等有非常重要的意义，对语音识别与合成、语音通信、人机对话以及其他语音产品的开发和产品质量的改善也具有非常广阔的研究前景。

Review on New Mathematical and Mechanical Models for the Computer Simulation of Vocal Cord[J]. 计算机科学与应用, 2016, 06(07): 434-442. http://dx.doi.org/10.12677/CSA.2016.67053

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