Estimation of Lyapunov exponents from multibody dynamics in differential-algebraic form

Pierangelo Masarati

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Estimation of Lyapunov exponents from multibody dynamics in differential-algebraic form

机译：利用微分代数形式的多体动力学估计李雅普诺夫指数

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This article discusses the estimation of Lyapunov characteristic exponents related to the solution of non-linear multibody dynamics problems expressed in the form of systems of differential-algebraic equations. Current literature on the topic projects the differential-algebraic equations in the state space of the underlying strangeness free ordinary differential equations. This article shows how Lyapunov exponents can be successfully estimated with the discrete QR method directly applied to the matrix pencil associated to the differential-algebraic equations, using algorithmically dissipative multistep methods. Numerical results show the soundness of the proposed approach.

机译：本文讨论了与以微分-代数方程组形式表示的非线性多体动力学问题的解决方案有关的李雅普诺夫特征指数的估计。有关该主题的最新文献将微分代数方程式投影在底层奇异自由常微分方程的状态空间中。本文介绍了如何使用算法耗散多步法，通过将离散QR方法直接应用于与微分-代数方程式相关的矩阵笔上的离散QR方法，可以成功地估计Lyapunov指数。数值结果表明了该方法的正确性。

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《Proceedings of the institution of mechanical engineers》 |2013年第k1期|23-33|共11页
作者
Pierangelo Masarati;
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作者单位

Dipartimento di Ingegneria Aerospaziale,Politecnico di Milano, via La Masa 34, 20156 Milano, Italy;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Constrained system dynamics; Lyapunov characteristic exponents; differential-algebraic equations;

机译：受限的系统动力学;Lyapunov特征指数;微分代数方程;

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1. An index 0 differential-algebraic equation formulation for multibody dynamics: Nonholonomic constraints [J] . Haug Edward J. Mechanics Based Design of Structures and Machines . 2018,第1a6期

机译：多体动力学索引0差分代数方程式：非全面约束
2. An index 0 Differential-Algebraic equation formulation for multibody dynamics: Holonomic constraints [J] . Haug Edward Mechanics Based Design of Structures and Machines . 2017,第1a4期

机译：多体动力学索引0差分代数方程式：定期限制
3. Lyapunov exponents spectrum estimation of fractional order nonlinear systems using Cloned Dynamics [J] . C. Fischer, K. Zourmba, A. Mohamadou Applied numerical mathematics . 2020,第Auga期

机译：Lyapunov指数使用克隆动力学的分数阶非线性系统的频谱估计
4. Estimation of the largest Lyapunov exponent for a multibody system with dry friction via chaos synchronization [C] . Fangfang Zhuang, Qi Wang The Sixth Asian conference on multibody dynamics . 2012

机译：通过混沌同步估计具有干摩擦的多体系统的最大Lyapunov指数
5. Application of the GSSSS Family of Algorithms to the Natural Index 3 Differential-Algebraic Equations of Multibody Dynamics [D] . Hoitink, Andrew John 2011

机译：GSSSS系列算法在多体动力学自然指数3微分代数方程中的应用
6. Estimation of Instantaneous Complex Dynamics through Lyapunov Exponents: A Study on Heartbeat Dynamics [O] . Gaetano Valenza, Luca Citi, Riccardo Barbieri -1

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7. EEG Signal Discrimination using Non-linear Dynamics in the EMD Domain S. M. Shafiul Alam,S. M. Shafiul Alam,Aurangozeb, and Syed TarekShahriar Abstract—An EMD-chaos based approach is proposed todiscriminate EEG signals corresponding to healthy persons,and epileptic patients during seizure-free intervals and seizureattacks. An electroencephalogram (EEG) is first empiricallydecomposed to intrinsic mode functions (IMFs). The nonlineardynamics of these IMFs are quantified in terms of the largestLyapunov exponent (LLE) and correlation dimension (CD).This chaotic analysis in EMD domain is applied to a large groupof EEG signals corresponding to healthy persons as well asepileptic patients (both with and without seizure attacks). It isshown that the values of the obtained LLE and CD exhibitfeatures by which EEG for seizure attacks can be clearlydistinguished from other EEG signals in the EMD domain.Thus, the proposed approach may aid researchers in developingeffective techniques to predict seizure activities. Index Terms—Electroencephalogram (EEG), empiricalmode decomposition (EMD), largest Lyapunov exponent (LLE),correlation dimension (CD), epileptic seizures. The Authors are with the Electrical and Electronic EngineeringDepartment, Bangladesh University of Engineering and Technology,Dhaka-1000, Bangladesh (e-mail: imamul@eee.buet.ac.bd) PDF Cite: S. M. Shafiul Alam,S. M. Shafiul Alam,Aurangozeb, and Syed Tarek Shahriar, "EEG Signal Discrimination using Non-linear Dynamics in the EMD Domain," International Journal of Computer and Electrical Engineering vol. 4, no. 3, pp. 326-330, 2012. PREVIOUS PAPER Perception of Emotions Using Constructive Learningthrough Speech NEXT PAPER Physical Layer Impairments Aware OVPN Connection Selection Mechanisms Copyright © 2008-2013. International Association of Computer Science and Information Technology Press (IACSIT Press) [O] . S. M. Shafiul Alam, Syed TarekShahriar 2012

机译：EEG信号在EMD域S. S. Shafiul Alam，S中的非线性动力学使用非线性动力学。 M. Shafiul Alam，Aurangozeb和Syed Tarekshahriar摘要 - 基于EMD Chaos的方法，提出了对应于健康人的EEG信号，癫痫发作期间的癫痫患者和Seizureattacks。脑电图（EEG）首先被凭经上分解为内在模式功能（IMF）。这些IMF的非线性动力学在最大范围的指数（LLE）和相关尺寸（CD）方面是量化的。本域中的混沌分析应用于与健康人相对应的大型脑电图（Asepileptic患者）（两者都有癫痫发作）。因此，所获得的LLE和CD表展的价值可以从EMD领域的其他EEG信号中清晰地区分脑电图的表达展示。本拟议的方法可以帮助研究人员以预测癫痫发作的癫痫发作技术。索引术语 - 脑电图（EEG），仿真态分解（EMD），最大的Lyapunov指数（LLE），相关维度（CD），癫痫发作。作者与电气电子和电子工程公司，孟加拉国工程和技术大学，孟加拉国达卡 - 1000（电子邮件：imamul@eee.buet.ac.bd）pdf cite：s. m. shafiul Alam，s。 M. Shafiul Alam，Aurangozeb和Syed Tarek Shahriar，“EEG信号歧视在EMD领域的非线性动态，”计算机电气工程卷国际杂志。 4，不。 3，pp。326-330,2012，上一篇论文对情绪的看法，使用建设性的学习言论下一篇论文物理层障碍意识到OVPN连接选择机制版权所有©2008-2013。国际计算机科学与信息技术协会出版社（IACSIT Press）

Estimation of Lyapunov exponents from multibody dynamics in differential-algebraic form

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