【正文】 構造了具有緊支集地正交小波基，系統(tǒng)地建立了小波分析理論體系。 1986 年， 伸縮、平移小波基函數，掀起了小波研究熱潮。 論文研究現狀 小波分析現狀 小波變換 (Wavelet Transform)具有時頻局部化分析的優(yōu)良性能，最適合于非平穩(wěn)信號分析。而許多信號的急劇變化之處常常是分析信號特性的最關鍵之處。本文提出 一種 應用 Daubechies 小波包多層分解、重構提取滾動軸承各部件的故障特征頻率和能量特征 ，通過小波包多層分解確定滾 動軸承 機械 振動的奇異點的方法 , 實現 故障 的精確 診斷 。 本文在綜述小波變換的基本思想與具體性質和原理的基礎上，重點介紹了小波在 滾動軸承 機械故障檢測中的應用。論文 (設計 )主體均由本人獨立完成，沒有抄襲、剽竊他人已經發(fā)表或未發(fā)表的研究成果行為。如出現以上違反知識產權的情況，本人愿意承擔相應的責任。 滾動軸承 機械故障信號分析中基函數的不同 將 導致對信號 的 觀測角度和觀測方法的不同， 在小波基函數的選取方面 Fourier 變換、短時 Fourier 變換和小波變換 各自的基函數 有著 的本質區(qū)別。 關鍵詞： 小波分析 、 故障診斷 、 滾動軸承 、 多 層分解 Abstract Wavelet analysis as the latest time frequency analysis tool in signal analysis, image processing, feature extraction, fault diagnosis and other fields has been widely used. Characterization of the signal wavelet transform has the ability of local features and characteristics of multiresolution, therefore, it is very suitable for detection of transient signals and singular phenomenon, even to display its ponents. General speaking the summary of this paper, the basic ideas of wavelet transform and the specific nature, the most important of this paper is focusing on the wavelet applications of fault detection in the rolling machine. In the mechanical failure of the rolling bearing signal analysis, the different basis functions lead to a difference of signal point of observing views and observing methods, which are the essential differences among wavelet transform Fourier transform, shorttime Fourier transform. In this paper, by paring the performances and characteristics of a variety of mon used smallwavelet fonctions in fault diagnosis, I research on the internal relations between different characteristics of the fault signal and wavelet fonctions. Making using of continuous wavelet transform method, this paper changes the characteristics of rolling bearing vibration signal information into the relationship of energy spectrum and measure, ing to the establishment a feature vector corresponding to energy and scale, creats the new method for the rapid diagnosis of rolling bearings. In order to accurately diagnosis of fault type, this paper proposes the application of multideposition of Daubechies wavelet packet, reconfiguration of the extraction of fault characteristic frequency and energy feature in ponents rolling bearing ponents, by analysing multideposition of Daubechies wavelet packet, we can clearly see the failure point of mechanical vibration in rolling bearing. Key words： Wavelet analysis, fault diagnosis, rolling bearing, multideposition 目 錄 摘 要 Abstract 第 1 章 緒 論 .............................................................................................................. 1 論文選題背景和意義 ........................................................................................... 1 論文研究現狀 ..................................................................................................... 1 ：小波分析現狀 ......................................................................................... 1 ：機械故障診斷現狀 .................................................................................. 3 論文研究方法和內容 ........................................................................................... 6 第 2 章 小波分析的理論 基礎 ...................................................................................... 7 傅立葉分析及其優(yōu)缺點 ....................................................................................... 7 傅立葉變換 (Fourier Transform) ................................................................. 7 傅立葉變換 的優(yōu)點與缺點 .......................................................................... 7 小波分析 ............................................................................................................. 9 小波基性能研究 ..................................................................................................11 針對故障診斷處理的小波分類 ............................................................................ 13 小波變換對信號奇異性檢測的基本原理 .............................................................. 14 . 1 奇異性的定義 ......................................................................................... 14 . 2 小波變換的卷積表達形式 ....................................................................... 14 . 3 小波變換的極值點 、過零點與信號奇異性的聯系 .................................... 15 小波基的選擇 ................................................................................................... 16 最佳小波基的選取 ............................................................................................ 17 Daubechies 小波 ................................................................................................. 18 小波分解與尺度選擇 ......................................................................................... 19 第 3 章 滾動軸承的故障及診斷技術 ........................................................................ 20 滾動軸承的結構 ................................................................................................. 21 滾動軸承失效的基本形式 ................................................................................... 21 滾動軸承故障的振動診斷 ................................................................................... 22 滾動軸承的振動機理及故障特征頻率 ................................................................ 23 滾動軸承的振動機理 ............................................................................... 23 滾動軸承各元件單一缺陷的特征頻率 ....................................................... 24 由滾動軸承構造所引起的振動 ................................................................. 25 滾動軸承的非線性引發(fā)的振動 ................................................................. 25 滾動軸承損傷 (缺陷〕而引起的振動 ......................................................... 26 第 4 章 MATLAB 對故障奇異信號進行分析 .......................................................... 26 檢測第一類間斷點 ......................................................................