發(fā)布時間：2019-04-17 21:17

【摘要】：奇異值分解(Singular Value Decomposition, SVD)是一種現(xiàn)代數(shù)值分析方法,而信號處理作為它所有應用中的一個重要分支,以矩陣變換的方式對信號進行加工處理,實現(xiàn)對非線性、非平穩(wěn)信號的有效分析,是一種獨特的信號處理工具。因此,本文從SVD的基本原理及其重要性質和意義的研究出發(fā),對SVD的算法以及基于SVD的信號處理方法展開了深入的研究,主要工作和研究成果如下： 首先,針對傳統(tǒng)QR迭代算法用于大規(guī)模矩陣SVD計算時存在的不收斂問題,結合實例展開了深入的分析和討論,并提出了一種多次分割雙向收縮的QR迭代算法,實現(xiàn)了對大規(guī)模矩陣快速、精確的SVD計算。 接著,研究了矩陣方式下SVD的信號分離原理,提出了一種在Hankel矩陣方式下,利用遺傳算法優(yōu)化矩陣結構及利用中心差商曲線選取有效奇異值的SVD信號去噪方法,并通過實例展示了它良好的去噪效果。 此外,存連續(xù)截斷信號構造的矩陣方式下,討論了當所構造矩陣的結構不同時對信號處理效果產生的影響,發(fā)現(xiàn)了一種基于SVD的信號奇異性檢測新方法,通過與小波變換的比較,研究了該方法獨特的奇異性檢測性能。 然后,介紹了SVR(Singular Value Ratio, SVR)譜、改進的SVR譜以及Frobenious范數(shù)軌跡等幾種周期探測法,分析了它們在信號周期探測中時常失效的原因,提出了一種基于固定矩陣結構的延時SVR譜法,在對幾種試驗信號的分析處理中,驗證了它穩(wěn)定的周期探測能力。 最后,將基于SVD的不同信號處理方法應用于不同轉子系統(tǒng)故障的診斷,在實際應用中,驗證了這些方法的有效性和工程實用性。
[Abstract]:Singular value decomposition (Singular Value Decomposition, SVD) is a modern numerical analysis method, and signal processing is an important branch of all its applications. Effective analysis of non-stationary signals is a unique signal processing tool. Therefore, based on the study of the basic principle of SVD and its important properties and significance, this paper makes an in-depth study on the algorithm of SVD and the signal processing method based on SVD. The main work and research results are as follows: first of all, the algorithm of SVD and the signal processing method based on SVD are studied. In view of the non-convergence problem of traditional QR iterative algorithm used in large-scale matrix SVD calculation, this paper analyzes and discusses it in depth with an example, and proposes a QR iterative algorithm with multi-segmented bi-directional contraction. The fast and accurate SVD calculation for large-scale matrix is realized. Then, the signal separation principle of SVD in matrix mode is studied, and a denoising method of SVD signal based on Hankel matrix is proposed, which optimizes the structure of matrix by using genetic algorithm and selects the effective singular value by using the curve of central difference quotient. An example is given to show its good de-noising effect. In addition, under the matrix mode of continuously truncated signal construction, the influence of the structure of the constructed matrix on the signal processing effect is discussed, and a new method of signal singularity detection based on SVD is found. Compared with wavelet transform, the unique singularity detection performance of this method is studied. Then, several periodic detection methods, such as SVR (Singular Value Ratio, SVR) spectrum, improved SVR spectrum and Frobenious norm trajectory, are introduced, and the reasons why they often fail in signal periodic detection are analyzed. A delay SVR spectrum method based on fixed matrix structure is presented in this paper. In the analysis and processing of several experimental signals, its stable periodic detection ability is verified. Finally, different signal processing methods based on SVD are applied to fault diagnosis of different rotor systems. In practical applications, the validity and engineering practicability of these methods are verified.
【學位授予單位】：華南理工大學
【學位級別】：碩士
【學位授予年份】：2011
【分類號】：TN911.7;TH165.3

【參考文獻】

相關期刊論文 前6條

1 凌國民;SVD及其在譜分析中的應用[J];聲學與電子工程;1986年01期

2 楊文獻,任興民,姜節(jié)勝;基于奇異熵的信號降噪技術研究[J];西北工業(yè)大學學報;2001年03期

3 申忠宇;顧幸生;趙瑾;;基于奇異值分解的魯棒滑模觀測器設計與仿真[J];系統(tǒng)仿真學報;2009年03期

4 程發(fā)斌;湯寶平;鐘佑明;;基于最優(yōu)Morlet小波和SVD的濾波消噪方法及故障診斷的應用[J];振動與沖擊;2008年02期

5 李建,劉紅星,屈梁生;探測信號中周期性沖擊分量的奇異值分解技術[J];振動工程學報;2002年04期

6 龐茂;周曉軍;胡宏偉;孟慶華;;基于解析小波變換的奇異性檢測和特征提取[J];浙江大學學報(工學版);2006年11期

相關博士學位論文 前3條

1 馮長建;HMM動態(tài)模式識別理論、方法以及在旋轉機械故障診斷中的應用[D];浙江大學;2002年

2 牛大田;計算大規(guī)模矩陣部分奇異值分解的精化Lanczos型算法[D];大連理工大學;2003年

3 楊宇;基于EMD和支持向量機的旋轉機械故障診斷方法研究[D];湖南大學;2005年

相關碩士學位論文 前2條

1 關曉勇;基于奇異值分解的狀態(tài)監(jiān)測與故障診斷方法研究[D];大連理工大學;2005年

2 黃媛;改進的小波神經網絡在旋轉機械故障診斷中的應用研究[D];武漢理工大學;2009年

，

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