EMD方法的研究与应用

【作者】 刘慧婷；

【导师】 程家兴；

【作者基本信息】 安徽大学 ， 计算机应用技术， 2004， 硕士

【摘要】 信号瞬时特征的提取在信号处理中具有重要的意义，然而复杂信号特别是非线性和非稳定信号真正意义上瞬时参数的定义都比较困难，更谈不上高精度测量信号的瞬时参数。如何利用数据分析方法提取非线性和非稳定信号的瞬时参数，并对该方法加以改善及应用是本文讨论的重点。 本文的主要工作包括： 1．在筛选过程中，插值是产生本征模函数关键的一步，是希尔伯特谱分析的基础。尽管埃尔米特插值方法在大多情况下十分有效，可仍存在着一些问题。本文通过实验结果证明了采用三次样条插值的有效性。 2．经验模态分解方法中，有两种端点效应：在样条插值中以及在希尔伯特变换中。如果对端点不加任何处理，立方样条就会产生大幅度的摆动，影响信号瞬时特征提取的准确性。已经存在一些解决方法，这些方法很有效地控制了大幅度的摆动。本文提出了多项式拟合算法，并利用实验数据和理论证明了这种方法的正确性和优越性。 3．利用算法实现了改进后的经验模态分解方法。 4．实现了经验模态分解方法在非线性和非稳态信号瞬时特征提取中的应用；同时利用实验数据证明了经验模态分解方法与多层反馈神经网络FP算法相结合，来完成股票数据预测中的相似模式匹配的可行性。更多还原

【Abstract】 Extracting instantaneous characters of the signals is very important in signal processing. But defining instantaneous parameters of complicated signals especially of the non-linear and non-stationary ones is difficult, measuring the parameters of them is even more difficult. How to extract the instantaneous parameters of the non-linear and non-stationary signals making use of the data analysis methods is the emphasis the thesis will discuss, as well as how to improve the method and apply it.The main work of the dissertation includes:1. In the course of filtration, interpolation is the essential step to produce the intrinsic mode functions, and the basis of the Hilbert spectral analysis. Although Hermite interpolation works well in most cases, there are still some problems existing. It proves the validity of the spline interpolation on the base of experiments.2. There are two types of end effects in the empirical mode decomposition method: in the spline interpolation and in the Hilbert transform. The cubic spline will swing widely if the end issue is left unattended, and it will affect the veracity of the instantaneous characters’ extracting. There are some methods to solve the problem, they have confined the large swings successfully. It has brought forward polynomial fitting algorithm, and has proved its correctness and superiority making use of datum and theories.3. Carrying out the improved empirical mode decomposition method utilizing the algorithm.4. Realizing the application of the empirical mode decomposition in the instantaneous characters extraction of the non-linear and non-stationary signals. In the meanwhile, it has proved that it is feasible to realize the similar pattern matching of the stocks’ forecasting, if the empirical mode decomposition and the forward propagation learning algorithm of multi layered neural networks with feed back connections are related.更多还原