【免费】信号的数学形态学分析方法及其应用研究资源-CSDN文库

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《信号的数学形态学分析方法及其应用研究》这篇博士学位论文主要探讨了如何运用数学形态学这一非线性分析工具来解决故障诊断领域的挑战。数学形态学通常用于图像处理，但在此研究中，它被扩展到了一维信号的分析，特别是针对机械故障信号。 1. **数学形态学与形态滤波**：论文提出了一种基于形态滤波的齿轮故障特征提取方法。通过使用扁平结构元素对齿轮断齿故障振动信号进行形态滤波，能显著增强信号的冲击特征，使故障频率及其倍频成分得以清晰显现。此外，还开发了一种自适应形态滤波算法，基于峭度最大原理，能自动调整结构元素长度，以更高效地提取故障特征，减少了人为选择参数的依赖。 2. **自适应多尺度形态学分析**：论文创新性地提出了自适应多尺度形态学分析方法，以适应不同尺度的信号特征。这种方法通过定义长度尺度和高度尺度来确定多尺度结构元素，依据信号的局部峰值实现自适应分析。相比于传统的单尺度分析和包络分析，这种方法在轴承故障诊断中表现出更强的形态特征提取能力，能有效揭示轴承内圈和外圈损伤的故障频率。 3. **形态小波降噪**：针对齿轮箱声信号分析，论文提出了基于形态小波的降噪算法。与传统线性小波相比，形态小波更适合分析具有形态特征的信号，尤其是在信噪比较低的情况下。通过软阈值降噪算法，形态小波能更有效地去除噪声，提取齿轮箱故障的冲击特征。 4. **多尺度Top-Hat变换的形态非抽样小波**：为了解决形态小波分解中的信息损失问题，论文提出了一种基于多尺度Top-Hat变换的形态非抽样小波算法，适用于转子冲击信号的特征提取。这种方法能够在不丢失信号信息的前提下，精确地从细节信号中捕捉到周期性冲击特征，证明了其在故障诊断中的实用性和准确性。这些研究成果不仅在故障诊断领域有显著的应用价值，而且在心电图（ECG）、脑电图（EEG）、语音处理、电力信号分析以及图像识别等多个领域都具有广阔的应用前景。通过数学形态学的引入，信号分析的非线性和非平稳特性得到了更好的处理，提高了故障检测的效率和准确性。

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北京科技大学博士学位论文

摘　　要

数学形态学是近年发展起来的一种非线性分析方法，已被广泛应用于图像处理等

领域，但在一维信号，特别是在机械故障信号中的处理与分析还不多见。本文把形态

学分析方法引入到一维信号的处理与分析，针对非线性非平稳信号的特征提取问题，

对采用形态滤波和形态小波等形态学的信号分析方法进行了较深入的研究。本文的研

究成果不仅可以应用于故障诊断领域，而且在心电/脑电、语音、电力信号处理和图像

识别等领域也有着广泛的应用前景。

论文的主要创新性成果有如下几个方面内容：

(1) 提出了基于形态滤波的齿轮故障特征提取方法，并基于峭度最大原理实现了

自适应形态滤波算法。

针对齿轮故障特征提取问题，提出了一种根据信号形态特征对齿轮故障信号进行

形态滤波的新方法。采用扁平结构元素对齿轮断齿故障振动信号进行形态滤波后，原

始信号的冲击特征幅值被提高了 10 倍，从而成功提取出了隐含在噪声中的齿轮断齿

故障频率及其 2 倍频和 3 倍频等频域特征。为了减少上述方法对结构元素长度选择的

依赖性，提出了一种基于峭度最大原理的自适应形态滤波算法。试验结果证明，该自

适应算法可以更有效地提取出相应的故障特征。

(2) 提出了一种自适应多尺度形态学分析方法，并将其应用于轴承的故障诊断。

为了把图像的多尺度形态学分析方法引入到一维信号中，本文分别定义了长度尺

度和高度尺度来确定多尺度形态学结构元素，并基于信号的局部峰值实现自适应多尺

度形态学分析。该方法减少了单尺度形态学分析在结构元素选择时的盲目性和对相关

先验知识的依赖性。仿真试验表明，该方法较传统的单尺度形态学分析及包络分析方

法更利于提取信号中的形态特征。新的方法应用于轴承内圈和外圈损伤的故障诊断，

可以清晰地提取出轴承的故障频率特征。

(3) 提出了基于形态小波降噪算法的齿轮箱声信号分析方法。

基于频率线性分解的传统小波，在分析某些具有形态特征的信号时具有一定的局

限性。而形态小波利用数学形态算子代替线性算子，有利于提取具有形态特征的信号。

由于齿轮箱声信号比振动信号更容易受外界干扰，使得信噪比降低，常规方法不易提

取相应的故障特征，本文提出了一种应用形态小波进行软阈值降噪算法的齿轮箱声信

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北京科技大学博士学位论文

Research on Mathematical Morphology Analysis of Signals

and Its Application

Abstract

As a nonlinear analysis method, mathematical morphology is recently developed and has

been widely applied to various fields of image analysis and processing. But the research of

morphology analysis in one-dimensional (1-D) signals, especially in the fault signals, is still

rare. The thesis introduces morphological analysis into 1-D signal, and aims at the problem of

feature extraction methods to the nonlinear and non-stationary signals. Morphological analysis

methods, such as morphological filtering, morphological wavelets and so on, are studied in the

thesis. The achievements of the thesis can be used to not only fault diagnosis, but also

ECG/EEG signal, speech signal, power signal, image recognition, etc.

Main works and achievements of the thesis are as follows:

(1) An approach to extract gear fault features based on mathematical morphological

filtering and an adaptive algorithm of morphological filtering based on kurtosis maximization

principle are proposed.

Focusing on fault features extraction of gear, a novel approach is proposed according to

the signal characteristics based on morphological filtering. The vibration signal of gear tooth

broken is processed by morphological operation via the flat structuring element. After the

morphological filtering, the defined impact-feature-amplitude of the original signal is enhanced

over 10 times. The fundamental, second and third harmonical fault frequencies hidden in the

noise, can be successfully extracted by morphological filtering. And in order to reduce the

dependence on the length of the structuring element, an adaptive algorithm of morphological

filtering based on kurtosis maximization principle is presented. The experimental results show

that the adaptive algorithm can be more efficient to extract fault features.

(2) An adaptive multiscale morphology analysis (AMMA) algorithm and its application to

fault diagnosis of bearing are presented.

To introduce multiscale analysis in image processing into 1-D signal, the concepts of the

length scale and the height scale are defined to choose structuring elements of multiscale

morphology analysis of a signal. And an adaptive algorithm based on the information of local

peaks in a signal is presented. The AMMA algorithm avoids the drawbacks of the ambiguity of

selecting structuring elements and the dependence on empirical rules. Simulated experiments

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北京科技大学博士学位论文

show that the AMMA algorithm is better to extract morphological features in signal than the

traditional single-scale morphology analysis and envelop analysis. The AMMA algorithm is

examined in morphology analysis of the experimental signal measured from bearings with an

inner and an outer race fault. The results confirm that the AMMA algorithm is able to clearly

extract fault frequencies of bearings.

(3) A novel fault feature extraction method for the acoustic signal of gearbox based on

morphological wavelets denoising algorithm is introduced.

Classical wavelets based on linear decomposition via frequency have some limitations

when extracting morphological features. In morphological wavelets, linear operators are

replaced by morphological operators. So, morphological wavelets are better to extract

morphological features in signals. Because the acoustic signals are easier to be influenced by

external disturbance than the vibration signals, the signal-noise-ratio of the acoustic signals of

the gearbox is low and the fault features are difficult to be extracted by traditional methods. A

method based on morphological wavelets with soft threshold denoising is presented to extract

the fault features. Simulated experiment and analysis of the actual acoustic signal show that the

fault feature extraction method based on morphological wavelets denoising is more effective to

reduce noise and extract fault features than linear wavelets denoising.

(4) A new morphological undecimated wavelet (MUDW) based on multiscale Top-Hat

transform and its application to feature extraction of a rotor with impulsive features are

developed.

To avoid the decreasing of the signal length in morphological wavelets decomposition, a

MUDW framework is introduced, which is a seamless integration of morphological wavelets

and undecimated wavelets. And a new MUDW based on multiscale Top-Hat transform under

the MUDW framework is developed. The experimental results of impulsive features extraction

of the rotor show that the periodical impulsive series in the detail signal after the new MUDW

decomposition are accurately extracted in time domain. So, the new MUDW is feasible and

effective in fault diagnosis.

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Key Words: Morphological filtering, Morphological wavelet, Feature Extraction, Fault

diagnosis

北京科技大学博士学位论文
目　　录
  　 　摘 要.......................................................................................................................1
 Abstract..........................................................................................................................1
  　 　引 言.......................................................................................................................1
绪论............................................................................................................................3
1  课题的提出和意义...........................................................................................3
1.1  课题的来源和意义.................................................................................3
1.2  多分辨率形态学梯度...........................................................................19
基于形态滤波的信号降噪和齿轮振动信号特征提取方法....................................23
2  形态滤波的基本原理.....................................................................................23
2.1  形态算子对形态滤波的影响................................................................23
2.2  形态结构元素对形态滤波的影响........................................................26
3  基于形态滤波的非线性时间序列降噪方法..................................................27
3.1  Lorenz 信号的形态滤波.......................................................................28
3.2  结果分析...............................................................................................29
4  基于数学形态滤波的齿轮故障特征提取方法..............................................30
4.1  齿轮振动信号的特征...........................................................................30
4.2  试验方案介绍.......................................................................................30
4.3  齿轮振动信号的形态滤波...................................................................31
4.4  形态滤波的影响因素分析...................................................................34
4.5  形态滤波与其他算法的比较................................................................35
5  基于峭度的自适应形态滤波算法..................................................................36
5.1  峭度的基本概念...................................................................................36
5.2  自适应形态滤波的原理.......................................................................36
5.3  齿轮故障信号的自适应形态滤波........................................................37
6  本章小结.........................................................................................................39
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