基于奇异值分解的信号处理方法及其在机械故障诊断中的应用

发布时间：2019-04-17 21:17

【摘要】：奇异值分解(Singular Value Decomposition, SVD)是一种现代数值分析方法,而信号处理作为它所有应用中的一个重要分支,以矩阵变换的方式对信号进行加工处理,实现对非线性、非平稳信号的有效分析,是一种独特的信号处理工具。因此,本文从SVD的基本原理及其重要性质和意义的研究出发,对SVD的算法以及基于SVD的信号处理方法展开了深入的研究,主要工作和研究成果如下：首先,针对传统QR迭代算法用于大规模矩阵SVD计算时存在的不收敛问题,结合实例展开了深入的分析和讨论,并提出了一种多次分割双向收缩的QR迭代算法,实现了对大规模矩阵快速、精确的SVD计算。接着,研究了矩阵方式下SVD的信号分离原理,提出了一种在Hankel矩阵方式下,利用遗传算法优化矩阵结构及利用中心差商曲线选取有效奇异值的SVD信号去噪方法,并通过实例展示了它良好的去噪效果。此外,存连续截断信号构造的矩阵方式下,讨论了当所构造矩阵的结构不同时对信号处理效果产生的影响,发现了一种基于SVD的信号奇异性检测新方法,通过与小波变换的比较,研究了该方法独特的奇异性检测性能。然后,介绍了SVR(Singular Value Ratio, SVR)谱、改进的SVR谱以及Frobenious范数轨迹等几种周期探测法,分析了它们在信号周期探测中时常失效的原因,提出了一种基于固定矩阵结构的延时SVR谱法,在对几种试验信号的分析处理中,验证了它稳定的周期探测能力。最后,将基于SVD的不同信号处理方法应用于不同转子系统故障的诊断,在实际应用中,验证了这些方法的有效性和工程实用性。
[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.
【学位授予单位】：华南理工大学
【学位级别】：硕士
【学位授予年份】：2011
【分类号】：TN911.7;TH165.3

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