统计学2001.05混沌时间序列分析

Posted 2021-05-02 MATLAB的科学与工程应用

 

本文将混沌时间序列分析方法应用于多个实验系统。对磁弹性带状时间序列的庞加莱截面进行分析，构造符号动力学，提取分形维数和李雅普诺夫指数等经验量。在脉冲热机中，通过对多组数据的分析，建立了高维、复杂的动力学模型。还分析了电动步进电机的数据集。观察并量化了低维混沌动力学。这些系统中的每一个都表现出非平稳性和其他行为，使得分析变得困难，并证明了现有时间序列分析技术的缺陷。因此，我们提出了一些方法来改进这些技术，并将它们合成为一个连贯的包。最后，提出了一种新的混沌sigma-delta调制器的设计方案。非线性动力学和混沌理论的技术证明，这种调制器是稳定的，并具有优于已有方法的良好的性能。

 

Chaotic time series analysis methods were applied to several experimental systems. Analysis of a Poincare section of magnetoelastic ribbon time series was used to construct symbolic dynamics and extract empirical quantities such as fractal dimension and Lyapunov exponents. In the pulse thermal combustion engine, analysis of several data sets was used to establish high dimensionality and complex dynamics. Data sets were also analyzed from an electric step motor. Low dimensional chaotic dynamics were observed and quantified. Each of these systems exhibited nonstationarity and other behaviors that made the analysis difficult and demonstrated flaws in established time series analysis techniques. Thus methods were devised to improve these techniques and synthesize them into a coherent package. Finally, a new design was proposed for a chaotic sigma delta modulator. Techniques from nonlinear dynamics and chaos theory were used to show that this modulator was stable and had desirable properties not exhibited in previously proposed designs.

 

1 引言

2 软件实现方法

3 搜索和排序方法

4 原始分析方法

5 多种数据的分析结果

6 结论 

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