噪音干扰下的混沌同步分析及支持向量机方法的应用
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摘要
本文主要研究了在噪音干扰下的混沌系统或复杂动力系统的同步以及支持向量机方法在动态心电信号的心率变异性分析中的应用。
第一章介绍了混沌和混沌同步,随机微分方程稳定性和支持向量机方法的研究背景与进展,并给出了本文的结构。
第二章首先介绍了一类非线性项满足全局Lipchitz条件的泛函微分方程,以及其在白噪音干扰下的响应系统。由于全局Lipchitz条件的存在,我们只需要设计合适的线性耦合项就可以达到混沌同步的目的。于是应用LaSalle不变原理,我们得到了单向耦合方式下混沌同步的充分条件。然后,我们以Hopfield人工神经网络和Chua混沌电路系统为例,进行了具体分析和数值模拟。
第三章研究的是一类特殊的常微分方程,与第二章不同的是,其非线性项并不满足全局Lipchitz条件。虽然我们讨论的仍然是一类“特殊的”常微分方程,但却涵盖了如Lorenz混沌系统,Chen混沌系统,R(?)sslar混沌系统等多个著名的混沌系统。我们给出了非线性耦合的一般形式,并分析了混沌同步的充分条件,其中涉及到了原始系统的有界性。同时,我们还给针对3个具体的混沌系统设计了特殊的非线性耦合项,以避免对系统界值的估计。
第四章中,我们讨论了第二章中的系统在双向耦合方式下的同步条件,并从理论上分析了混沌系统在双向耦合的方式下同步到原始系统的可能性。同时,我们还以一个具体的Hopfield神经网络系统和Chua电路混沌系统为例进行具体的实例分析,并给出了相应的数值模拟。
在第五章中,我们将分别对有色噪音的情形以及平移意义下的广义同步进行讨论和分析,并对噪音干扰下的混沌同步进行小节。
第六章的目的在于运用支持向量机方法,对动态心电信号按心率变异的量化指标进行分类。多组试验表明,支持向量机方法的准确性和稳定性较传统线性分类方法均具有明显优势。此外,支持向量机方法与综合指标的结合,不仅可以区分自主神经系统功能的正常与不正常样本,甚至还可以对自主神经系统功能的正常与多种不正常样本进行多类划分,为机器自动诊断心电信号提供了一种新的可行性途径。
最后,我们在第七章中回顾本文的主要工作,并对相关课题的研究工作进行引申和展望。
In this thesis, we mainly investigate chaos synchronization with noise perturbed and the application of support vector machine (SVM) in the Holter ECG monitoring analysis based on the heart rate variability (HRV).
This thesis is organized as follows: In Chapter 1, we introduce the research background and progress for chaos and chaos synchronization, the stability of stochastic differential equations and support vector machine. Also we display the overall structure of the thesis in this chapter.
In the second chapter, we firstly introduce a class of functional differential equations, in which the nonlinear terms are satisfied with global Lipchitz conditions, as well as its response systems with noise perturbed. Because of existence of global Lipchitz conditions, we just need to design suitable linear coupling term to achieve chaos synchronization. Then, we employ the LaSalle invariance principle to conclude the sufficient conditions of chaos synchronization with unidirectional coupling method. In succession, we will provide the Hopfield artificial neural network(ANN) and Chua's chaotic circuits as the concrete examples with corresponding analysis and numerical simulations.
In Chapter 3, we will investigate a spacial class of ordinary differential equations, which covers serval famous chaos system, such as the Lorenz system, Chen system and R(o|¨)sslar system. The most different point with systems discussed in Chapter 2 is that the nonlinear term do not satisfy the global Lipchitz conditions. We give out the ordinary nonlinear coupling terms and deduce the sufficient conditions of chaos synchronization, which require the drive systems boundedness. Besides, we also design special nonlinear coupling terms for 3 concrete chaos systems, by which we can avoid estimating the bound of the drive system.
In Chapter 4, we turn to study chaos synchronization with bidirectional coupling method for the systems introduced in Chapter 2. We also investigate the probability that the two coupling systems synchronized to the original systems. As the same time, a concrete Hopfield artificial neural network(ANN) and Chua's chaotic circuits are proposed again as instances with corresponding analysis and numerical simulations.
In Chapter 5, we discuss the cases of colorful noise and generalized synchronization and provide a summary of chaos synchronization with noise perturbed.
In Chapter 6, we want to apply the support vector machine to the Holter ECG monitoring analysis to classify the different samples by the quantitative indexes of heart rate variability. Our tests show that the veracity and stability of support vector machine are both obviously superior to the traditional linear classifying methods. In addition, combined with compositive index of HRV, SVM can not only differentiate normal samples and abnormal samples of parasympathetic system, but also classify the normal samples and several abnormal samples of parasympathetic system. It is a new available approach to automatically diagnose the Holter ECG monitoring by computers.
At the end of this thesis, we review the former results and propose some important topics and prospective work on correlative topics.
第一章介绍了混沌和混沌同步,随机微分方程稳定性和支持向量机方法的研究背景与进展,并给出了本文的结构。
第二章首先介绍了一类非线性项满足全局Lipchitz条件的泛函微分方程,以及其在白噪音干扰下的响应系统。由于全局Lipchitz条件的存在,我们只需要设计合适的线性耦合项就可以达到混沌同步的目的。于是应用LaSalle不变原理,我们得到了单向耦合方式下混沌同步的充分条件。然后,我们以Hopfield人工神经网络和Chua混沌电路系统为例,进行了具体分析和数值模拟。
第三章研究的是一类特殊的常微分方程,与第二章不同的是,其非线性项并不满足全局Lipchitz条件。虽然我们讨论的仍然是一类“特殊的”常微分方程,但却涵盖了如Lorenz混沌系统,Chen混沌系统,R(?)sslar混沌系统等多个著名的混沌系统。我们给出了非线性耦合的一般形式,并分析了混沌同步的充分条件,其中涉及到了原始系统的有界性。同时,我们还给针对3个具体的混沌系统设计了特殊的非线性耦合项,以避免对系统界值的估计。
第四章中,我们讨论了第二章中的系统在双向耦合方式下的同步条件,并从理论上分析了混沌系统在双向耦合的方式下同步到原始系统的可能性。同时,我们还以一个具体的Hopfield神经网络系统和Chua电路混沌系统为例进行具体的实例分析,并给出了相应的数值模拟。
在第五章中,我们将分别对有色噪音的情形以及平移意义下的广义同步进行讨论和分析,并对噪音干扰下的混沌同步进行小节。
第六章的目的在于运用支持向量机方法,对动态心电信号按心率变异的量化指标进行分类。多组试验表明,支持向量机方法的准确性和稳定性较传统线性分类方法均具有明显优势。此外,支持向量机方法与综合指标的结合,不仅可以区分自主神经系统功能的正常与不正常样本,甚至还可以对自主神经系统功能的正常与多种不正常样本进行多类划分,为机器自动诊断心电信号提供了一种新的可行性途径。
最后,我们在第七章中回顾本文的主要工作,并对相关课题的研究工作进行引申和展望。
In this thesis, we mainly investigate chaos synchronization with noise perturbed and the application of support vector machine (SVM) in the Holter ECG monitoring analysis based on the heart rate variability (HRV).
This thesis is organized as follows: In Chapter 1, we introduce the research background and progress for chaos and chaos synchronization, the stability of stochastic differential equations and support vector machine. Also we display the overall structure of the thesis in this chapter.
In the second chapter, we firstly introduce a class of functional differential equations, in which the nonlinear terms are satisfied with global Lipchitz conditions, as well as its response systems with noise perturbed. Because of existence of global Lipchitz conditions, we just need to design suitable linear coupling term to achieve chaos synchronization. Then, we employ the LaSalle invariance principle to conclude the sufficient conditions of chaos synchronization with unidirectional coupling method. In succession, we will provide the Hopfield artificial neural network(ANN) and Chua's chaotic circuits as the concrete examples with corresponding analysis and numerical simulations.
In Chapter 3, we will investigate a spacial class of ordinary differential equations, which covers serval famous chaos system, such as the Lorenz system, Chen system and R(o|¨)sslar system. The most different point with systems discussed in Chapter 2 is that the nonlinear term do not satisfy the global Lipchitz conditions. We give out the ordinary nonlinear coupling terms and deduce the sufficient conditions of chaos synchronization, which require the drive systems boundedness. Besides, we also design special nonlinear coupling terms for 3 concrete chaos systems, by which we can avoid estimating the bound of the drive system.
In Chapter 4, we turn to study chaos synchronization with bidirectional coupling method for the systems introduced in Chapter 2. We also investigate the probability that the two coupling systems synchronized to the original systems. As the same time, a concrete Hopfield artificial neural network(ANN) and Chua's chaotic circuits are proposed again as instances with corresponding analysis and numerical simulations.
In Chapter 5, we discuss the cases of colorful noise and generalized synchronization and provide a summary of chaos synchronization with noise perturbed.
In Chapter 6, we want to apply the support vector machine to the Holter ECG monitoring analysis to classify the different samples by the quantitative indexes of heart rate variability. Our tests show that the veracity and stability of support vector machine are both obviously superior to the traditional linear classifying methods. In addition, combined with compositive index of HRV, SVM can not only differentiate normal samples and abnormal samples of parasympathetic system, but also classify the normal samples and several abnormal samples of parasympathetic system. It is a new available approach to automatically diagnose the Holter ECG monitoring by computers.
At the end of this thesis, we review the former results and propose some important topics and prospective work on correlative topics.
引文
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