小波抗混叠单子带重构算法及其在轴承故障特征提取中的应用
发布时间：2018-11-03 18:53
【摘要】：傅里叶分析在信号分析处理中做出了杰出的贡献，但无论是在时域或者在频域，它都是定义在整个域上的，它不能分析出某段时间内某个频段的信号特征，，即，傅里叶变换没有时频的局部化性能。小波分析的出现为信号处理领域提供了一种自适应性的将时域和频域同时局部化的分析方法，无论是分析低频信号，还是分析高频信号，它都能自动调节时频窗的大小和形状，以适应实际分析的需要。同时，小波分析的多分辨率分析思想也给信号处理领域带来了新的思路。Mallat算法在小波多分辨率分析中拥有极为重要的应用，其地位和作用类似于快速傅里叶变换算法在傅里叶分析中的地位和作用。目前，小波分析仍然是国际上研究的热点，各种新的方法和新的理论不断的被推出。小波分析理论的这些特点使得它在时频分析和工程应用中得到了辉煌的发展。 本文首先介绍了小波分析的基本理论以及它的主要应用特点，如时频局部特性、多分辨率特性等。然后系统的介绍了多分辨率分析的思想，包括小波多分辨率分析和奇异值分解的多分辨率分析，并对两种分析方法的优劣进行了比较。接着，因为快速分解算法在实际应用中的重要作用，本文着重介绍了小波及小波包的快速分解算法，以及小波单子带重构算法等。 因为单子带重构算法在提取信号特征频率成分时有很好的效果，所以本文深入的研究了单子带重构算法的频域表现，在不断的演算分析中，本文发现小波分解算法中存在着严重的频率混叠现象，这是由于Mallat算法固有的因素造成的。即便是在单子带重构改进算法中，频率混叠现象仍然存在。因此，本文着重对小波分解算法产生频率混叠的原因进行了深入的剖析，并提出了一种完全抗混叠的单子带重构算法。此外，本文还将小波分解延伸到了小波包分析中，并且对小波包分解过程中出现的相似问题给出了详细的介绍和分析。针对改进后的单子带重构算法，本文把它运用到实际的故障信号中，并跟改进前的方法进行了对比，证实了该改进算法的有效性。 在全文的分析推理过程中，本文除了进行数学式子方面的推导外，还结合了数字信号处理方面的基础知识，进行了大量的模拟实验。这样，不仅可以看到抽象的理论演算，还能看到大量的直观易懂的数据和图像。 最后，文章对本文的工作进行了总结，并展望了接下来的研究方向。
[Abstract]:Fourier analysis has made an outstanding contribution in signal processing, but it is defined in the whole domain, whether in the time domain or in the frequency domain. It can not analyze the signal characteristics of a certain frequency band in a certain period of time, that is, Fourier transform has no time frequency localization performance. The appearance of wavelet analysis provides an adaptive method to localize the time domain and frequency domain for signal processing. It can automatically adjust the size and shape of time-frequency window, whether it is analyzing low frequency signal or analyzing high frequency signal. In order to meet the needs of the actual analysis. At the same time, the idea of multi-resolution analysis of wavelet analysis also brings new ideas to the field of signal processing. Mallat algorithm has a very important application in wavelet multi-resolution analysis. Its position and function are similar to that of fast Fourier transform algorithm in Fourier analysis. At present, wavelet analysis is still a hot topic in the world, and many new methods and theories have been put forward. These characteristics of wavelet analysis theory make it a brilliant development in time frequency analysis and engineering applications. This paper first introduces the basic theory of wavelet analysis and its main application characteristics, such as time-frequency local characteristics, multi-resolution characteristics and so on. Then the idea of multi-resolution analysis is introduced systematically, including wavelet multi-resolution analysis and multi-resolution analysis of singular value decomposition, and the advantages and disadvantages of the two analysis methods are compared. Then, because of the important role of fast decomposition algorithm in practical application, this paper mainly introduces the fast decomposition algorithm of wavelet and wavelet packet, and the reconstruction algorithm of wavelet single subband. Because the single subband reconstruction algorithm has a good effect in extracting the characteristic frequency component of the signal, the frequency domain performance of the single subband reconstruction algorithm is deeply studied in this paper. In this paper, we find that there is a serious frequency aliasing phenomenon in wavelet decomposition algorithm, which is caused by the inherent factors of Mallat algorithm. Even in the improved single subband reconstruction algorithm, frequency aliasing still exists. Therefore, in this paper, the causes of frequency aliasing in wavelet decomposition algorithm are deeply analyzed, and a completely anti-aliasing single subband reconstruction algorithm is proposed. In addition, wavelet decomposition is extended to wavelet packet analysis, and the similar problems in the process of wavelet packet decomposition are introduced and analyzed in detail. In this paper, the improved single subband reconstruction algorithm is applied to the actual fault signal, and compared with the improved method, the effectiveness of the improved algorithm is verified. In the process of the analysis and reasoning of this paper, besides the derivation of mathematical formula, the paper also combines the basic knowledge of digital signal processing, and carries out a large number of simulation experiments. In this way, we can not only see abstract theoretical calculus, but also see a large number of intuitive and easy-to-understand data and images. Finally, the paper summarizes the work of this paper, and looks forward to the future research direction.
【学位授予单位】：重庆大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH165.3;TN911.7
本文编号：2308663
[Abstract]:Fourier analysis has made an outstanding contribution in signal processing, but it is defined in the whole domain, whether in the time domain or in the frequency domain. It can not analyze the signal characteristics of a certain frequency band in a certain period of time, that is, Fourier transform has no time frequency localization performance. The appearance of wavelet analysis provides an adaptive method to localize the time domain and frequency domain for signal processing. It can automatically adjust the size and shape of time-frequency window, whether it is analyzing low frequency signal or analyzing high frequency signal. In order to meet the needs of the actual analysis. At the same time, the idea of multi-resolution analysis of wavelet analysis also brings new ideas to the field of signal processing. Mallat algorithm has a very important application in wavelet multi-resolution analysis. Its position and function are similar to that of fast Fourier transform algorithm in Fourier analysis. At present, wavelet analysis is still a hot topic in the world, and many new methods and theories have been put forward. These characteristics of wavelet analysis theory make it a brilliant development in time frequency analysis and engineering applications. This paper first introduces the basic theory of wavelet analysis and its main application characteristics, such as time-frequency local characteristics, multi-resolution characteristics and so on. Then the idea of multi-resolution analysis is introduced systematically, including wavelet multi-resolution analysis and multi-resolution analysis of singular value decomposition, and the advantages and disadvantages of the two analysis methods are compared. Then, because of the important role of fast decomposition algorithm in practical application, this paper mainly introduces the fast decomposition algorithm of wavelet and wavelet packet, and the reconstruction algorithm of wavelet single subband. Because the single subband reconstruction algorithm has a good effect in extracting the characteristic frequency component of the signal, the frequency domain performance of the single subband reconstruction algorithm is deeply studied in this paper. In this paper, we find that there is a serious frequency aliasing phenomenon in wavelet decomposition algorithm, which is caused by the inherent factors of Mallat algorithm. Even in the improved single subband reconstruction algorithm, frequency aliasing still exists. Therefore, in this paper, the causes of frequency aliasing in wavelet decomposition algorithm are deeply analyzed, and a completely anti-aliasing single subband reconstruction algorithm is proposed. In addition, wavelet decomposition is extended to wavelet packet analysis, and the similar problems in the process of wavelet packet decomposition are introduced and analyzed in detail. In this paper, the improved single subband reconstruction algorithm is applied to the actual fault signal, and compared with the improved method, the effectiveness of the improved algorithm is verified. In the process of the analysis and reasoning of this paper, besides the derivation of mathematical formula, the paper also combines the basic knowledge of digital signal processing, and carries out a large number of simulation experiments. In this way, we can not only see abstract theoretical calculus, but also see a large number of intuitive and easy-to-understand data and images. Finally, the paper summarizes the work of this paper, and looks forward to the future research direction.
【学位授予单位】：重庆大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH165.3;TN911.7
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