【作者】 孟娟；

【导师】 王兴元；

【作者基本信息】 大连理工大学 ， 生物医学工程， 2008， 博士

【摘要】 非线性科学是一门研究非线性现象共性的基础科学,被誉为20世纪自然科学中的“三大革命之一”.在非线性科学中,对混沌的研究占了极大的份额。小波分析是目前国际上公认的最新时-频分析工具,在时间-频率域上具有良好的局部性,被称为“数学显微镜”.本文重点基于混沌理论和小波理论对生物电信号处理和神经网络的混沌同步进行了一系列的探索和研究。全文的主要研究工作包括:(1)对儿童癫痫脑电信号的非线性动力学特征进行了深入研究。现有关于脑电信号非线性分析的研究大多是对原始的脑电信号进行分析。癫痫脑电信号中混有较多的干扰信号,这些干扰信号极易与癲痫信号的尖波相混淆,从而导致错误的分析结果.本章首先利用独立分量分析算法将癲痫分量从原始脑电信号中分离出来,从而可以避免由干扰信号所带来的误差,简化分析过程。然后对分离出的癫痫分量的相图、功率谱、关联维数和Lyapunov指数等进行了对比研究,发现脑电独立分量的相图、功率谱、关联维数和Lyapunov指数反映了大脑的总体动态特征,它们可作为一种定量指标衡量大脑的健康状态;并且在正常的生理状态下脑电是混沌的,而在癫痫状态下则趋于有序.(2)提出了二维心电信号压缩算法。心电信号波形通常表现出两种类型的相关性:心跳内的相关性和心跳间的相关性。近年来大部分的心电压缩方法并没有很好地利用心跳间的相关性。本章首先将一维心电信号转化为二维序列信号,从而使心电信号的两种相关性得到充分地利用.然后对二维序列进行小波变换,根据小波系数的特点,分别将等级树集合分裂算法和矢量量化算法进行了改进,提出了两种二维心电压缩算法.利用所提算法与已有基于小波变换的压缩算法和其他二维心电信号的压缩算法,对MIT/BIH数据库中的心律不齐数据进行了对比压缩实验。结果表明:所提压缩算法适用于各种波形特征的心电信号,并且在保证压缩质量的前提下,可以获得较大的压缩比。(3)基于扩展的观测器理论和非线性控制方法,提出了混沌系统和超混沌系统的相同步、投影同步以及广义同步方案.理论分析和数值仿真实验进一步验证了所提出的各同步方案的可行性和有效性。主要成果包括:①基于状态观测器方法和极点配置技术,设计了一类混沌系统的相同步方法。适当地选取误差系统的特征值,即可实现系统的相同步。所提方案克服了现有基于主动控制的相同步方法的缺陷,易于工程实现,且可通过调整误差系统的特征值进而调整误差的收敛速率.②基于改进的观测器方法,设计了投影同步方法和广义同步方法。所提同步方案不仅适用于自治混沌系统,而且对于超混沌系统同样有效,具有一定的普遍性。所提方案简单易实现,不依赖于系统线性部分的特性,且具有较強的鲁棒性。③基于非线性控制方法,提出了一种超混沌系统的广义同步方案。合理地选取误差增益矩阵即可实现动力系统之间的广义同步。所设计的控制器具有一定的鲁棒性,不仅可以实现相同维数超混沌系统之间的广义同步,而且也适用于不同维数混沌系统之间的广义同步问题。(4)研究了神经网络的自适应同步、投影同步和广义同步等问题。首先.根据Lyapunov稳定性理论,为参数不确定的耦合神经网络系统设计了自适应控制器及参数更新规则。所提出的方法可以在不需考虑耦合强度的情况下实现耦合神经元系统的自适应同步。另外,将状态观测器的理论进行了扩展,并利用它提出了神经网络的投影同步和广义同步方案.所提同步方案易于实现,且可通过极点配置技术调整误差系统的特征值,进而调整同步的速度。通过对FitzHugh-Nagumo神经元系统、Winner-Take-All竞争型神经元系统和细胞神经网络等的数值仿真实验进一步验证了所提出的三种同步方案的有效性。(5)提出了延迟Cohen-Grossberg神经网络的反同步和投影同步方案。神经元之间有限的信息传输速度导致了延迟的存在。根据Lyapunov稳定性理论,分别为延迟Cohen-Grossberg神经网络设计了反同步控制器和投影同步控制器,并从理论上证明了所提同步方案的可行性.所设计的控制器收敛速度较快,合理的选择控制增益矩阵即可实现同步。数值仿真实验结果表明,所提出的两种同步方案具有一定的普适性和鲁棒性。(6)将自适应技术、观测器方法和模糊理论有机结合起来,设计了模糊观测器,提出了混沌系统和超混沌系统的自适应模糊同步方案。模糊控制器设计简单,适用于非线性系统,具有鲁棒性.所提方案可以实现混沌和超混沌系统的自适应同步和自适应投影同步。通过Lyapunov函数方法证明了所提出方案的可行性,并利用数值仿真实验验证了方案的有效性.本文得到了国家自然科学基金(60573172)以及辽宁省教育厅高等学校科学技术研究计划(20040081)联合资助。更多还原

【Abstract】 Nonlinear science is a foundational discipline which concems the common properties of nonlinear phenomena.It is hailed as one of the three main revolutions in natural science in the 20^th century.Chaos theory is one important subdiscipline of nonlinear science.Wavelet analysis is the acknowledged time-frequency analysis method in the world.It has well local quality in the time-frequency fields and is named as "mathematics microscope".In this dissertation,based on chaos theory and wavelet theory,the electric biological signal processing and chaos synchronization of neural networks are explored and investigated. The main achievements contained in the research are as follows:Firstly,the nonlinear dynamics of the epilepsy electroencephalogram（EEG） of children are deeply studied.In most researches on EEG,the original EEG signals are analyzed.There is much interference in the original epilepsy EEG signals.It is easy to mix the interference with the spikes in the epilepsy signals.This will cause wrong analysis results.In this chapter, independent component analysis（ICA） is first adopted to isolate the epileptiform signals from the background EEG signals.Thus,errors caused by interference can be avoided.Then,the phase graph,power spectra,correlation dimension and Lyapunov exponents are studied comparatively.The results show that the phase graph,power spectra,correlation dimension and Lyapunov exponents of the EEG independent components reflect the general dynamical characteristics of brains,which can be taken as a quantitative index to weigh the healthy states of brains.Under normal physiological conditions,the EEG signals are chaotic;while under epilepsy conditions the signals approach regularity.Secondly,compression algorithms for two-dimensional（2-D） electrocardiogram（ECG） data are proposed.By studying the ECG waveforms,it can be concluded that the ECG signals generally show two types of correlation,namely the intrabeat correlation and the interbeat correlation.However,most existing ECG compression techniques do not utilize the interbeat correlation.In this chapter,a 1-D ECG data is first sliced and aligned to a 2-D data array,thus the two kinds of correlation of heartbeat signals can be fully utilized.And then 2-D wavelet transform is applied to the constructed 2-D ECG data array.Two compression methods are proposed according to the characteristics of the wavelet coefficients.Set partitioning hierarchical trees（SPIHT） algorithm and vector quantization（VQ） algorithm are modified. Records selected from the MIT/BIH arrhythmia database are tested contrastively using the proposed algorithm,some compression algorithms based on wavelet transform and the other 2-D ECG compression algorithms.The experimental results show that the proposed methods are suitable for various morphologies of ECG data,and that they can achieve higher compression ratios with the characteristic features well preserved.Thirdly,based on the modified observer algorithm and the nonlinear control method,the author presents the systematic design procedures for phase synchronization,projective synchronization and generalized synchronization of chaotic and hyperchaotic systems. Theoretical analyses and numerical simulations further demonstrate the feasibilities and effectiveness of the proposed synchronization schemes.Some valuable and important results are as follows:①A systematic approach to realize phase synchronization is proposed based on the state observer method and the pole placement technique.The phase synchronization of chaotic systems can be obtained by suitably selecting the eigenvalues of error systems.The proposed method overcomes the shortcomings of the phase synchronization method based on active control.It is simple and the convergence rate can be flexibly adjusted by choosing the eigenvalues.②New methods for projective synchronization and generalized synchronization are proposed based on the modified state observer method.The proposed schemes are not only suitable to autonomous chaotic systems,but also effective to hyperchaotie systems.The proposed methods are simple and robust.They are able to realize synchronization in a general class of nonlinear systems without the limitation of partial-linearity.③Using the nonlinear control theory,a control law is designed to achieve the generalized synchronization of hyperchaotic systems.If the error gain matrix is suitably chosen,the generalized synchronization between drive system and response system will be obtained.The designed controller not only can realize the generalized synchronization of hyperchaos systems with the same dimensions,but also is suitable to the generalized synchronization problems of systems with different dimensions.Fourthly,the problems of adaptive synchronization,projective synchronization and generalized synchronization of neural networks（NNs） are investigated.Based on the Lyapunov stability theory,an adaptive controller and the parameters update law are designed for unknown NNs.With the proposed method,synchronization of the coupled neurons can be achieved,without needing to consider the coupled strength.Furthermore,based on the modified nonlinear state observer algorithm,projective synchronization and generalized synchronization schemes are designed.The proposed schemes can be implemented easily,and the convergence rates of the errors can be adjusted by choosing the eigenvalues of the error systems.Numerical simulations of FitzHugh-Nagumo（FHN） neuron system,Winner-Take-All competitive neuron system and cellular neural network etc are provided to demonstrate the effectiveness of the proposed synchronization schemes. Fifthly,anti-synchronization and projective synchronization schemes are designed for delayed Cohen-Grossberg NNs.Limited speed of information transmission between neurons makes delays unavoidable.Based on the Lyapunov stability theory,controllers are designed for delayed Cohen-Grossberg NNs.Theoretical analyses verify the feasibility of the proposed schems.The convergence rate of the controller is very fast.The synchronizations can be achieved by appropriately choosing the controller gain matrices.Numerical simulations demonstrate that the proposed synchronization schemes are general and robust.Sixthly,combining the adaptive technique,observer algorithm and fuzzy theory,fuzzy observers are designed and adaptive fuzzy synchronization schemes for chaotic and hyperchaotic systems are proposed.Fuzzy controller is simple to design.It is robust and applicable to nonlinear systems.Adaptive synchronization and projective synchronization can be achieved by using the proposed schemes.Based on the Lyapunov stability theory,the feasibilities of the proposed schemes are proved theoretically.Numercial simulations are provided to verify the effectiveness of the schemes.The author would like to appreciate the joint supports to this project by the National Natural Science Foundation of China（60573172） and the Superior University Science Technology Research Project of Liaoning Province（20040081）.更多还原