改进的希尔伯特-黄变换及其应用-检测技术与自动化装置专业论文.docxVIP

摘 摘 要 I I 摘 要 希尔伯特-黄变换(Hilbert-Huang Transform, HHT)是 1998 年由美籍华人科学家 N. E. Huang 提出的，用于分析非线性和非平稳信号的时频特征。与 Fourier 分析和 小波分析相比较，HHT 过程没有指定的基函数，所谓的基函数由信号本身自适应产 生，这不仅提高了分解效率，而且具有非常高的时频分辨率。 HHT 算法包括两个 部分：经验模态分解(EMD)和希尔伯特谱(HS)分析。EMD 是其核心也是创新部分， 任何复杂的信号可以经由 EMD 分解成有限数目的固有模态函数(IMFs)。IMF 是单 分量信号，它可以确定非线性和非平稳信号的瞬时频率，以及每一个瞬时频率的局 部能量。 因此，最终呈现的结果是一个“时间-频率-能量”分布图，称之为希尔伯 特谱。 HHT 虽然从数学上确立了基本的理论框架，但还不够完善，特别是 EMD 还只 是建立在经验基础之上，必然存在诸多不足。基于此，本文针对 HHT 过程中的分 解不彻底以及端点效应进行了深入的研究探讨，提出将非均匀 B 样条插值应用于 EMD 过程，解决了信号分解不完全的问题；另外，采用季节性时间序列模型预测 (SMF)，来解决端点效应，并通过与灰色预测和神经网络预测仿真实验的对比，验 证了新算法的可行性和有效性。最后对比小波变换的分解结果，显示了改进的 HHT 算法在分析处理非平稳和非线性信号时的优势。 关键词：希尔伯特-黄变换；经验模态分解；固有模态函数；B 样条；季节模型预测 Abs Abstract II II Abstract Hilbert-Huang transform (HHT) is presented by N. E. Huang, a Chinese-American scientist, in 1998, and it is applied to the analysis of nonlinear and non-stationary signals. Compared with Fourier analysis and wavelet analysis, HHT process doesn’t has specified base function and its base function is produced adaptively by signal, which not only improves the efficiency of decomposition, but also has very high time-frequency resolution. HHT algorithm includes two parts: Empirical Mode Decomposition (EMD) and Hilbert Spectrum (HS) analysis. Empirical Mode Decomposition is the core and the mostly innovative part of HHT, with which any complex signal can be decomposed into a finite number of Intrinsic Mode Functions (IMFs). The IMF is a single component signal, it can determine the instantaneous frequency of nonlinear and non-stationary signals, and the local energy of each instantaneous frequency. So, the final result is a time-frequency-energy distribution, called Hilbert spectrum. Although HHT established the basic theoretical frame in mathematics, it is still not perfect. Especially based on experience, EMD must have some shortcomings. In allusion to not thorough decomposition and endpoint effect of HHT, we research HHT deeply in this paper. Firstly, we put forward that using the non-uniform B-spl