混沌预测理论及其在VBR视频业务中的应用
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摘要
随着混沌理论和应用技术研究的不断深入，混沌时间序列分析及预测不仅已成为混沌信号处理研究领域的前沿研究热点，且能够解决工程实践中遇到难以用线性信号处理方法解决的大量非线性信号处理问题。
宽带网络及数字压缩技术的不断发展致使多媒体业务逐渐成为ATM网业务的主要来源，其大部分都采用变比特率方式(VBR)进行传输。近来研究表明VBR视频业务不仅具有短相关性，而且还具有长相关性，因此传统VBR视频业务模型在描述VBR视频业务存在不足之处，而分形模型能够很好地模拟VBR视频业务，分形中的自相似行为常常预示着混沌特性的存在，因此用混沌理论研究VBR视频业务，将有可能揭示用传统的分析方法发现不了的内在规律，有着非常重要的理论和实际意义。
本文主要围绕混沌时间序列预测方法及其在VBR视频业务中的应用展开研究，主要内容包括：(1)混沌时间序列分析与局域预测方法；(2)混沌时间序列的非线性自适应预测；(3)VBR视频业务的混沌特性分析及混沌方法预测。主要研究成果包括：
1、分析了三种局域零阶预测法的预测性能及其抗噪声性能；研究了混沌时间序列基于维纳解的局域一阶预测法：提出了一种基于离散余弦变换域的局域二次多项式预测法，仿真结果表明该方法不仅能准确地预测一些低维混沌时间序列，且实现简单。
2、在分析现有多项式非线性自适应预测法的基础上，提出了混沌时间序列预测的DCT域二次实时自适应滤波预测法；研究了自适应幅度的神经自适应滤波预测法对混沌时间序列预测的可行性及预测性能；并构造了收敛速度快、网络结构简单的时延Chebyshev正交多项式自适应滤波预测模型；研究结果表明三种预测模型均能够有效地预测一些低维混沌时间序列。这些均进一步发展了混沌时间序列非线性自适应预测结构及算法。
3、用Wolf法计算得到VBR视频业务在任何时间标度上均具有正的最大李亚谱诺夫指数，表明VBR视频业务具有混沌特性；在此基础上，用混沌局域一阶预测法对两条典型的VBR视频业务流进行了预测，预测结果表明混沌局域预测法能够对VBR视频业务进行有效预测，相比自适应线性预测法具有更高的预测精度且不存在时间延迟。
With the development of chaos theory and application technology study, analysis and prediction of chaotic time series have become the emphasis of chaotic signal precessing research domain, and can solve a lot of nonlinear signal process questions in engineering practice, which are difficult to be done by linear signal processing methods.
Multimedia traffic has become the chief source of ATM network gradually with the development of broadband network and digital compression technology, and most of them are transmitted through variable bit rate (VBR) mode. Recent researches indicate that VBR video traffic not only has short-term dependence, but also has long-term dependence. Consequently traditional models of variable bit rate video traffic are deficient in depicting variable bit rate video traffic, but fractal models can do it well. Gernerally, self-similar behaviors of fractal mean the existence of chaos, thereby analyzing variable bit rate video traffic through chaos theory will be likely to reveal intrinsic laws, which are not founded by traditional analysis method.
Research works focus on prediction methods of chaotic time series and its application in VBR video traffic in this dissertation, which mainly include analysis and local prediction method of chaotic time series, nonlinear adaptive prediction of chaotic time series, chaotic characteristics analysis and chaotic prediction of VBR video traffic. The main research fruits are as follows:
1 . Prediction capability and anti-noise performance of three kinds of local zero-order prediction methods are analysed completely. Local first-order prediction of chaotic time series based on Wiener solution is studied. DCT domain local quadratic polynomial prediction is presented, and simulation results indicate that this method not only can predict some low-dimension chaotic time series efficiently, but also can be implemented simply.
2. Based on the analysis of polynomial nonlinear adaptive prediction methods existed already, a DCT domain quadratic predictor for real-time prediction of low-dimension chaotic time series is proposed. The feasibility and prediction performance of chaotic time series with neural adaptive prediction method with adaptive amplitude are studied. Time-delay neural Chebyshev
orthogonal polynomial adaptive nonlinear prediction model is constructed. Experimental results indicate that three kinds of prediction models can predict some low-dimension chaotic 'time series efficiently. Moreover nonlinear adaptive prediction structure and algorithm of chaotic time series are developed further.
3. The positive maximum Lyapunov exponents of variable bit rate video traffic are calculated on any time scale using Wolfs algorithm, which indicates that variable bit rate video traffic has chaotic characteristics. Furthermore, chaotic local first-order prediction method is used to predict two typical variable bit rate video traffics. The prediction results show that chaotic local prediction methods can predict the variable bit rate video traffic efficiently, and are more accurate than adaptive linear prediction method without time delay.
宽带网络及数字压缩技术的不断发展致使多媒体业务逐渐成为ATM网业务的主要来源，其大部分都采用变比特率方式(VBR)进行传输。近来研究表明VBR视频业务不仅具有短相关性，而且还具有长相关性，因此传统VBR视频业务模型在描述VBR视频业务存在不足之处，而分形模型能够很好地模拟VBR视频业务，分形中的自相似行为常常预示着混沌特性的存在，因此用混沌理论研究VBR视频业务，将有可能揭示用传统的分析方法发现不了的内在规律，有着非常重要的理论和实际意义。
本文主要围绕混沌时间序列预测方法及其在VBR视频业务中的应用展开研究，主要内容包括：(1)混沌时间序列分析与局域预测方法；(2)混沌时间序列的非线性自适应预测；(3)VBR视频业务的混沌特性分析及混沌方法预测。主要研究成果包括：
1、分析了三种局域零阶预测法的预测性能及其抗噪声性能；研究了混沌时间序列基于维纳解的局域一阶预测法：提出了一种基于离散余弦变换域的局域二次多项式预测法，仿真结果表明该方法不仅能准确地预测一些低维混沌时间序列，且实现简单。
2、在分析现有多项式非线性自适应预测法的基础上，提出了混沌时间序列预测的DCT域二次实时自适应滤波预测法；研究了自适应幅度的神经自适应滤波预测法对混沌时间序列预测的可行性及预测性能；并构造了收敛速度快、网络结构简单的时延Chebyshev正交多项式自适应滤波预测模型；研究结果表明三种预测模型均能够有效地预测一些低维混沌时间序列。这些均进一步发展了混沌时间序列非线性自适应预测结构及算法。
3、用Wolf法计算得到VBR视频业务在任何时间标度上均具有正的最大李亚谱诺夫指数，表明VBR视频业务具有混沌特性；在此基础上，用混沌局域一阶预测法对两条典型的VBR视频业务流进行了预测，预测结果表明混沌局域预测法能够对VBR视频业务进行有效预测，相比自适应线性预测法具有更高的预测精度且不存在时间延迟。
With the development of chaos theory and application technology study, analysis and prediction of chaotic time series have become the emphasis of chaotic signal precessing research domain, and can solve a lot of nonlinear signal process questions in engineering practice, which are difficult to be done by linear signal processing methods.
Multimedia traffic has become the chief source of ATM network gradually with the development of broadband network and digital compression technology, and most of them are transmitted through variable bit rate (VBR) mode. Recent researches indicate that VBR video traffic not only has short-term dependence, but also has long-term dependence. Consequently traditional models of variable bit rate video traffic are deficient in depicting variable bit rate video traffic, but fractal models can do it well. Gernerally, self-similar behaviors of fractal mean the existence of chaos, thereby analyzing variable bit rate video traffic through chaos theory will be likely to reveal intrinsic laws, which are not founded by traditional analysis method.
Research works focus on prediction methods of chaotic time series and its application in VBR video traffic in this dissertation, which mainly include analysis and local prediction method of chaotic time series, nonlinear adaptive prediction of chaotic time series, chaotic characteristics analysis and chaotic prediction of VBR video traffic. The main research fruits are as follows:
1 . Prediction capability and anti-noise performance of three kinds of local zero-order prediction methods are analysed completely. Local first-order prediction of chaotic time series based on Wiener solution is studied. DCT domain local quadratic polynomial prediction is presented, and simulation results indicate that this method not only can predict some low-dimension chaotic time series efficiently, but also can be implemented simply.
2. Based on the analysis of polynomial nonlinear adaptive prediction methods existed already, a DCT domain quadratic predictor for real-time prediction of low-dimension chaotic time series is proposed. The feasibility and prediction performance of chaotic time series with neural adaptive prediction method with adaptive amplitude are studied. Time-delay neural Chebyshev
orthogonal polynomial adaptive nonlinear prediction model is constructed. Experimental results indicate that three kinds of prediction models can predict some low-dimension chaotic 'time series efficiently. Moreover nonlinear adaptive prediction structure and algorithm of chaotic time series are developed further.
3. The positive maximum Lyapunov exponents of variable bit rate video traffic are calculated on any time scale using Wolfs algorithm, which indicates that variable bit rate video traffic has chaotic characteristics. Furthermore, chaotic local first-order prediction method is used to predict two typical variable bit rate video traffics. The prediction results show that chaotic local prediction methods can predict the variable bit rate video traffic efficiently, and are more accurate than adaptive linear prediction method without time delay.
引文
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