面向非平稳信号的整体经验模态分解研究

Nonstationary and nonlinear signal processing is a hot issue in the field of data analysis in recent years.Hilbert-Huang Transform(HHT)is an adaptive data analysis method for nonstationary and nonlinear data.The Empirical Mode Decompositon(EMD) is deeply studied both in theory and application in this project.The traditional EMD method will be introduced to the extreme point overshoot and undershoot problem.The wavelet function is used as the basis function, it makes full use of the time-frequency localization properties to improve the calculation efficiency.Ensemble Empirical Mode Decomposition(EEMD)method was raised to solve the issue of mixed mode in the traditional Empirical Mode Decomposition. The decomposition is based on the applications of ensemble empirical mode decomposition(EEMD) to slices of data in each and every dimension involved. The final reconstruction of the corresponding intrinsic mode function (IMF) is based on a comparable minimal scale combination principle. We will introduce a new EMD method based on the ensemble EMD, a noise assisted data analysis method that overcomes many drawbacks of EMD such as the sensitivity of decomposition to small perturbation of data. It will be demonstrated that, with good properties of EEMD, the inter-slice discontinuity existed in pseudo-BEMD is no longer a daunting problem. The method is based on a completely different approach from those serving as the foundations for traditional EMD methods. We will provide the application examples in terms of financial, image processing about EEMD methods. It has a good performance in noise immunity. Significant improvements also include the elimination of scale mixing and thereby the decomposed results should contain no artificial structures. It has important theoretical research value and broad prospects.

非线性、非平稳信号处理是近年来数据分析领域的热点问题。本项目系统研究希尔伯特-黄变换（HHT）中经验模态分解（EMD）方法所存在的问题，深入挖掘经验模态分解（EMD）的算法思想，针对传统的EMD方法会引入极值点过冲和欠冲问题，提出将小波函数作为基函数，利用其良好的局部性质，直接计算数据的均值，提高计算效率；针对EMD方法对实际数据分解造成的模态混叠现象，构建引入白噪声辅助分析的整体平均的经验模态分解（EEMD）算法，通过分析证明其可行性，具体给出EEMD方法在金融、图像处理方面的应用实例，证明EEMD算法在抗噪方面的良好性能。EEMD算法将会给数据处理等领域提供一种新的、有效的分析方法，为多元数据分析方法奠定了良好的基础，具有重要的理论意义和应用价值。

非线性、非平稳信号处理是近年来数据分析领域的热点问题。本项目系统研究希尔伯特-黄变换中经验模态分解方法所存在的问题，深入挖掘经验模态分解的算法思想，针对经验模态分解方法对数据分解造成的模态混叠现象，构建引入白噪声辅助分析的整体经验模态分解算法，并在实际问题中进行推广应用，表明其有效性和可行性。为了揭示我国股票市场的分形特征，利用经验模态分解及重标极差分析法来探究中国股票市场的特征。结果表明，这段时期的我国股票市场具有显著的自相似性，分解后的收益率序列为有偏的随机游走过程。通过采用整体经验模态分解方法分析北京市PM2.5，把原始时间序列分解成为了多个固有模态函数和趋势项，对各阶固有模态函数进行周期性分析，揭示了北京市PM2.5的周期性变化特点，对分解后的各阶固有模态函数和趋势项用支持向量回归方法进行预测。本预测模型为环保部门对北京市PM2.5的短期预测提供科学有效的方法，为政府对PM2.5的治理给予决策支持。准确的判断出滚动轴承在运作过程中的工作状态对零件更换、设备维修等意义重大。将改进的经验模态分解与多尺度熵结合起来，提出基于多尺度下的固有模态函数熵值的一个故障诊断识别方法，应用到滚动轴承的振动信号当中，其分析结果表明，通过改进的经验模态分解与多尺度熵结合起来，计算构造属性特征向量，可以准确识别机械故障诊断。高频金融数据波动率的估计在资产定价和金融工程中都发挥着重要的作用。采用希尔伯特-黄变换进行波动率估计，并将其与已实现波动率的方法进行比较，结果表明希尔伯特-黄变换方法估计高频数据波动率准确、有效。整体经验模态分解算法为数据分析领域提供一种新的、有效的计算方法，为多元数据分析方法奠定了良好的理论基础，具有重要的理论意义和应用价值。