【作者】 秦毅；

【导师】 秦树人；

【作者基本信息】 重庆大学 ， 机械电子工程， 2008， 博士

【摘要】 小波分析是近三十年从工程、物理及纯数学发展起来的一门新兴学科,其最大优点是具有“时频局部化”和“数学显微镜”性质,因此它非常适合于非线性、非平稳信号的分析,并已在许多领域得到广泛应用。目前,小波分析仍是国际研究的热点,各种新方法和新理论层出不穷,但小波分析仪器的发展却相对滞后。基于以上背景,本文系统地进行了多种小波分析方法的理论与应用研究,取得了一些创新性研究成果;然后基于以上理论成果,利用虚拟仪器技术和一体化仪器技术研制成功一体化小波变换分析仪,从而为机械工程领域中复杂信号的特征提取提供了一个有用的分析工具。本文首先综述了非平稳信号分析方法、小波理论与小波分析仪器及软件的研究现状,并指出了本文研究的意义。然后系统地回顾了经典的小波理论,包括连续小波变换、二进小波变换、离散小波变换、小波框架、多分辨分析、正交小波基、双正交小波基、小波包、小波追踪、二代小波变换,等。研究小波变换的实现算法对于小波分析仪器的开发具有重要的意义。首先介绍了实现二进小波变换的两种算法:多孔算法和小波变换直接算法;然后分析了Mallat算法中存在的问题,并详细介绍了一种改进的Mallat算法;最后,在对已有连续小波变换实现算法回顾的基础上,提出了一种利用带通滤波实现连续小波变换的快速算法,分析了其性能,并用实例验证了它的优越性。信号降噪是小波分析的一个重要应用,于是本文对信号的小波域降噪方法进行了系统的研究。介绍了四种主要的小波降噪算法:时频滤波降噪、小波系数模极大值降噪、空域相关降噪和阈值降噪,并讨论了它们的特点。通过结合阈值降噪与模极大值降噪两种方法,提出了一种新的二进小波降噪方法,该方法可以改进阈值降噪法的误差下界,因此它具有更高的降噪性能。此外,由于该方法是通过小波系数模极大值来重建信号,因而其降噪结果更好地保留了信号中的奇异性。通过仿真试验和工程实例验证了本文所提方法的降噪性能。利用小波脊线可以度量信号的瞬时频率和瞬时幅值,因而它在工程中具有很高的应用价值。针对小波脊线迭代提取算法中存在的迭代发散问题,提出一种在发散点处自适应改变迭代阈值的改进脊算法,并分析了它的抗噪特性和在提取多分量信号小波脊线中的特性,然后将新算法用于旋转机械故障诊断,取得了较好的分析效果。对于多分量信号,本文提出了一种基于重分配算法和奇异值分解的多脊提取方法,它也具有很好的抗噪性能,并能有效地用于机械系统的故障诊断。膨胀离散小波变换是小波分析理论的一个重要发展,目前研究最多的框架波变换也是属于膨胀离散小波变换。本文首先回顾了框架波理论的相关内容,介绍了几种典型的膨胀离散小波变换;然后重点研究了高密度离散小波变换,构造了它的最小不对称小波,分析了所用滤波器组的性质,证明了它的小波框架是L2 (R)空间上的紧框架,并提出了高密度离散小波变换的框架分解与重构算法。为了进一步提高对时频面的采样密度,还创新性地提出了高密度二进小波变换,同时给出了它的快速分解与重构算法。仿真实验和实际应用的结果都表明本文提出的小波变换具有很高的降噪性能。开发小波分析仪器是本文研究的主要目标之一。本文对虚拟仪器技术和一体化仪器技术进行了研究,并基于秦氏模型、一体化测试系统与前面的理论研究成果,研制成功了一体化小波变换分析仪。该仪器兼具虚拟仪器和传统硬件化仪器的优点,并具有强大的信号分析能力,适合于科学实验和工程中的复杂信号分析。本文还通过大量的仿真实验和实际工程应用,对仪器功能的正确性和稳定性进行了验证。文章最后对本文工作进行了总结,并展望了下一步的研究方向。更多还原

【Abstract】 Wavelet analysis is a new discipline developed from engineering, physics and pure mathematics during last thirty years, whose remarkable characteristics include the property of time-frequency localization and the“zoom-in”property. Therefore, it is very suitable for nonlinear and non-stationary signals analysis, and has been widely applied to many different fields. At present, wavelet analysis is still a hot theme all over the world, and a great many new methods and theories emerge in endlessly. However, the development of wavelet analyzers greatly lags behind the evolution of wavelet theories. Hence, on the above situation, this thesis systematically researches various wavelet analysis methods in theory and application, and some innovative achievements are obtained. Based on the above theoretical achievements, the integrated wavelet analyzer is developed with virtual instrument technology and integrated instrument technology, so as to provide a valuable analysis tool for feature extraction of complex signals in mechanical engineering.Firstly, the present research status of non-stationary signals analysis methods, wavelet theories and wavelet analysis instruments (software) is summarized, and the values of this thesis are presented. Subsequently, the classical wavelet theories are systematically reviewed, which refer to continuous wavelet transform, dyadic wavelet transform, discrete wavelet transform, wavelet frames, multiresolution analysis, orthogonal wavelet bases, biorthogonal wavelet bases, wavelet packet, wavelet pursuit and the second generation wavelet transform et al..Research on the implementation algorithms of various wavelet transforms has important significance for the development of wavelet analysis instrument. Firstly, two algorithms for implementing dyadic wavelet transform, i.e.àtrous algorithm and direct algorithm of wavelet transform, are introduced. Then, the problems in Mallat algorithm are indicated, and an improved Mallat algorithm is elaborated. Finally, after the review of the current algorithms for continuous wavelet transform, a new fast algorithm for implementing continuous wavelet transform by band-pass filtering is proposed, and its performance is analyzed. Experimental results show that this proposed algorithm has a higher performance than current algorithms.Signal denoising is one of the most significant applications of wavelet analysis, thus the denoising methods in wavelet domain are systematically studied. Four main wavelet denoising method, i.e. denoising method based on time-frequency filtering, denoising method based on modulus maxima of wavelet coefficients, denoising method based on spatial correlation and denoising method based on thresholding, are introduced, and their characteristics are discussed. A new denoising method based on dyadic wavelet transform is proposed by combining the modulus maxima denoising method with the thresholding denoising method. Compared with the denoising method based on soft thresholding, has the lower bound of denoising error of the proposed method are smaller, so it has a higher denoising performance the thresholding denoising method. Furthermore, since this method reconstructs the denoised signal with modulus maxima of wavelet coefficients, the denoised result well reserve the singularities of the original signal. The denoising performance of the proposed has been proved by simulation experiments and engineering applications.Instantaneous frequency and instantaneous amplitude can be calculated by the wavelet ridge, therefore wavelet ridge has high application value in engineering. An improved ridge algorithm which changes the iteration threshold adaptively at the divergence points is brought forward to solve the problem of iterative divergence that exists in the wavelet ridge iterative extraction algorithm. Its antinoise performance and the characteristic of extracting the wavelet ridge for the multi-component signal are investigated. This improved ridge algorithm is applied to the fault diagnosis of rotating machinery, and the analysis results are exciting. For multi-component signals, a new multi wavelet ridge extraction method based on reassigned algorithm and singular value decomposition is proposed. It has excellent antinoise performance and can be effectively applied for mechanical fault diagnosis.Expansive discrete wavelet transform is an important development of wavelet analysis theory. Framelet transform, which has been studied by many famous scientists in recent years, is also a kind of expansive discrete wavelet transform. First, some contents concerning framelet are reviewed, and several kinds of typical expansive discrete wavelet transforms. Then, the higher density discrete wavelet transform is primarily studied, its least asymmetric wavelets are constructed, and the properties of its combined filter bank are researched. Furthermore, this paper proves that the wavelet frame of the higher density discrete wavelet transform is a tight frame for L2(R), the corresponding frame decomposition and reconstruction algorithm is proposed. In order to improve the sampling density for the time-frequency plane, a higher density dyadic wavelet transform is innovatively proposed, and its fast decomposition and reconstruction algorithm is given. Simulation and application results show that the proposed new wavelet transform has quite high denoising performance.The development of wavelet analyzer is one of the main targets of this thesis. Virtual instrument technology and integrated instrument technology are researched. And then integrated wavelet analyzer is successfully developed, which is based on Qin’s model, integrated measurement system and the above theoretical achievements. This instrument has both the virtues of virtual instrument and the virtues of traditional hardware instrument, and has powerful abilities for signal analysis, thereby it is suitable for analyzing complex signals in scientific experiments and engineering. A large number of simulation experiments and practical engineering applications are implemented with this instrument, in order to validate the correctness and stability of its functions.Summarization of the thesis and expectations of the next research aspects are in the end of the thesis.更多还原