改进经验模态分解及其在齿轮故障诊断中的应用研究
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摘要
随着信号处理技术的迅速发展,信号的时频分析方法已经成为分析处理非线性、非平稳信号的重要方法之一。它从信号的时域和频域两个不同角度来综合研究信号的特征,能够同时了解信号在时域和频域的特征信息,是信号处理领域的一个重大突破。其中经验模态分解(Empirical Mode Decomposition,简称EMD)是近几年发展起来的一种新的时频分析方法,由美籍华人N. E.Huang等人于1998年首次提出,它已经成为信号时频分析的重要途径之一。
本文简要介绍了几种现代时频分析方法以及它们的优缺点,研究了经验模态分解理论的计算原理及其存在的不足之处,重点分析了经验模态分解在处理非线性、非平稳信号的“筛分”过程中产生端点效应的主要原因,在此基础上,提出一种新的抑制经验模态分解端点效应的方法,即将离散序列预测灰色理论GM(1,1)模型应用于在经验模态分解过程中,使得被分解的离散信号序列的端点值向外进行适当延拓,延拓后产生的新序列很好的反映了原信号的内部信息和发展趋势,使得在利用三次样条插值形成的上、下包络线时,端点效应被抑制而不污染到原始离散序列内部,从而可以保证分解出真实而有效的本征模函数。此外,齿轮是机械传动中重要传动部件之一,齿轮故障诊断方法对现代化工业发展有着举足轻重的推动作用。当齿轮在运转中出现有断齿、磨损和点蚀等故障时,就会引起齿轮强烈的啮合冲击振动,该振动信号中包含有周期性故障冲击振动成分,利用改进后的经验模态分解方法从齿轮啮合振动信号中提取齿轮故障特征,为齿轮故障诊断早期预测和诊断提供了一种更加可靠的方法。
实验是获取数据和验证理论是否正确的重要途径。本文数据全部来自于齿轮故障的物理模拟实验,该实验分别采集了齿轮在正常状态和故障状态下的齿轮啮合振动信号,然后借助于软件MATLAB对实验所得数据进行编程处理。
在试验数据基础上,分别使用改进和未改进的经验模态分解来处理同样的实验数据,由得到的本征模函数对比可以看出前者能有效地抑制经验模态分解的端点效应。然后再将故障齿轮振动信号和正常齿轮振动信号分别利用改进经验模态分解进行处理,得到他们各自的本征模函数,并对其进行希尔伯变换,进一步获得齿轮在故障状态和正常状态下振动信号的希尔伯特谱及边际谱,从对比中可以明显发现齿轮故障的存在,同时也进一步证明了灰色GM(1,1)模型能够有效地抑制经验模态分解的端点效应。
With the rapid development of signal processing technology, the time-frequency analysis method has already become one of the most important and effective ways in processing non-stationary and nonlinear signals, which is a major breakthrough in signal processing methods because more ample characteristics of signals are studied from the view of the time domain and frequency domain synchronously. Especially, Empirical Mode Decomposition (EMD for short) theory, first proposed by the Chinese-American N.E.Huang in 1998, has aroused more and more attention in recent years as a significant time-frequency method of signal processing.
In this paper, several time-frequency methods of signal processing are briefly introduced, including their advantages and disadvantages. At the same time, EMD, together with the reason for its defects in endpoint effect which exist in its decomposition iterative algorithm is discussed in detail. And then, a new method is put forward to restrain the serious endpoint effect of EMD in dealing with nonlinear and non-stationary signals by using the GM (1,1) model of Grey to extend some endpoints at both sides of original data sequence, and the data sequence extended, which reflect inner information and development trend of the original data sequence on the whole, could ensure that the upper and lower envelope obtained from three cubic interpretation are out of generating endpoint effect in the process of sifting. In this way, the endpoint effect does not destroy the internal information of original data sequence. Thus, this method greatly restrains the end effect of EMD and makes the Intrinsic Mode Function (IMF for short) obtained from the original data sequence reliable and effective. Furthermore, gear is one of the most important machine transmission parts, so the method of gear fault diagnosis plays a vital role in promoting modern industrial development. The gear faults such as teeth broken、n teeth wear and so on, will result in gear mesh impact vibration containing much periodicity fault impact components. And the improved EMD is used to find gear fault character from gear impact vibration signal. It is a reliable approach to predict and diagnose early gear fault.
Experiment is the basic way to obtain data and verify theory. The data in this paper are completely obtained from gear physical simulation experiment in which the gear vibration signals in normal and fault condition are respectively collected. Then the experimental data are dealt with depending on the software MATLAB.
Based on the above experimental data, the same gear vibration signal is decomposed into different IMFs by using improved EMD whose endpoint effect is restrained based on GM (1,1) and unimproved EMD whose endpoint effect is not, and the results show that the former is more effective than the latter. Equally, the gear fault vibration signals and the normal gear vibration signals are also divided into several IMFs by using improved EMD and unimproved EMD respectively. And then the IMFs obtained from fault and normal gear vibration signals are respectively transformed into Hilbert-Huang spectrum and Hilbert marginal spectrum. At last, the result of comparing Hilbert-Huang spectrum and Hilbert marginal spectrum obtained from gear fault vibration signals with those from normal gear vibration signals remarkably reveals the existing of gear fault character and also proves the GM (1,1) model can effectively restrain the endpoint effect of EMD.
本文简要介绍了几种现代时频分析方法以及它们的优缺点,研究了经验模态分解理论的计算原理及其存在的不足之处,重点分析了经验模态分解在处理非线性、非平稳信号的“筛分”过程中产生端点效应的主要原因,在此基础上,提出一种新的抑制经验模态分解端点效应的方法,即将离散序列预测灰色理论GM(1,1)模型应用于在经验模态分解过程中,使得被分解的离散信号序列的端点值向外进行适当延拓,延拓后产生的新序列很好的反映了原信号的内部信息和发展趋势,使得在利用三次样条插值形成的上、下包络线时,端点效应被抑制而不污染到原始离散序列内部,从而可以保证分解出真实而有效的本征模函数。此外,齿轮是机械传动中重要传动部件之一,齿轮故障诊断方法对现代化工业发展有着举足轻重的推动作用。当齿轮在运转中出现有断齿、磨损和点蚀等故障时,就会引起齿轮强烈的啮合冲击振动,该振动信号中包含有周期性故障冲击振动成分,利用改进后的经验模态分解方法从齿轮啮合振动信号中提取齿轮故障特征,为齿轮故障诊断早期预测和诊断提供了一种更加可靠的方法。
实验是获取数据和验证理论是否正确的重要途径。本文数据全部来自于齿轮故障的物理模拟实验,该实验分别采集了齿轮在正常状态和故障状态下的齿轮啮合振动信号,然后借助于软件MATLAB对实验所得数据进行编程处理。
在试验数据基础上,分别使用改进和未改进的经验模态分解来处理同样的实验数据,由得到的本征模函数对比可以看出前者能有效地抑制经验模态分解的端点效应。然后再将故障齿轮振动信号和正常齿轮振动信号分别利用改进经验模态分解进行处理,得到他们各自的本征模函数,并对其进行希尔伯变换,进一步获得齿轮在故障状态和正常状态下振动信号的希尔伯特谱及边际谱,从对比中可以明显发现齿轮故障的存在,同时也进一步证明了灰色GM(1,1)模型能够有效地抑制经验模态分解的端点效应。
With the rapid development of signal processing technology, the time-frequency analysis method has already become one of the most important and effective ways in processing non-stationary and nonlinear signals, which is a major breakthrough in signal processing methods because more ample characteristics of signals are studied from the view of the time domain and frequency domain synchronously. Especially, Empirical Mode Decomposition (EMD for short) theory, first proposed by the Chinese-American N.E.Huang in 1998, has aroused more and more attention in recent years as a significant time-frequency method of signal processing.
In this paper, several time-frequency methods of signal processing are briefly introduced, including their advantages and disadvantages. At the same time, EMD, together with the reason for its defects in endpoint effect which exist in its decomposition iterative algorithm is discussed in detail. And then, a new method is put forward to restrain the serious endpoint effect of EMD in dealing with nonlinear and non-stationary signals by using the GM (1,1) model of Grey to extend some endpoints at both sides of original data sequence, and the data sequence extended, which reflect inner information and development trend of the original data sequence on the whole, could ensure that the upper and lower envelope obtained from three cubic interpretation are out of generating endpoint effect in the process of sifting. In this way, the endpoint effect does not destroy the internal information of original data sequence. Thus, this method greatly restrains the end effect of EMD and makes the Intrinsic Mode Function (IMF for short) obtained from the original data sequence reliable and effective. Furthermore, gear is one of the most important machine transmission parts, so the method of gear fault diagnosis plays a vital role in promoting modern industrial development. The gear faults such as teeth broken、n teeth wear and so on, will result in gear mesh impact vibration containing much periodicity fault impact components. And the improved EMD is used to find gear fault character from gear impact vibration signal. It is a reliable approach to predict and diagnose early gear fault.
Experiment is the basic way to obtain data and verify theory. The data in this paper are completely obtained from gear physical simulation experiment in which the gear vibration signals in normal and fault condition are respectively collected. Then the experimental data are dealt with depending on the software MATLAB.
Based on the above experimental data, the same gear vibration signal is decomposed into different IMFs by using improved EMD whose endpoint effect is restrained based on GM (1,1) and unimproved EMD whose endpoint effect is not, and the results show that the former is more effective than the latter. Equally, the gear fault vibration signals and the normal gear vibration signals are also divided into several IMFs by using improved EMD and unimproved EMD respectively. And then the IMFs obtained from fault and normal gear vibration signals are respectively transformed into Hilbert-Huang spectrum and Hilbert marginal spectrum. At last, the result of comparing Hilbert-Huang spectrum and Hilbert marginal spectrum obtained from gear fault vibration signals with those from normal gear vibration signals remarkably reveals the existing of gear fault character and also proves the GM (1,1) model can effectively restrain the endpoint effect of EMD.
引文
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[17]李军,俞建定,徐铁峰.基于小波变换的故障诊断信号非平稳性分析[J].系统工程与电子技术,2006,28(7)：1110-1111.
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[2]丁康,李魏华,朱小勇等.齿轮及齿轮箱故障诊断实用技术[M].北京：机械工业出版社,2005：35-121.
[3]于德介,程军圣.机械故障诊断的Hilbert-Huang变换方法[M].北京：科学出版社.2007,24-190.
[4]李国华,张永忠.机械故障诊断[M].北京化学工业出版社.1999,38-103.
[5]张贤达,保铮.现代信号处理[M].北京：清华大学出版社,1 995,37-95.
[6]马辉,赵鑫,赵群超.时频分析在旋转机械故障诊断中的应用[J].振动与冲击.2007,26(3)：61-63.
[7]胡召音.灰色理论及其应用研究[J].武汉理工大学学报.2003,27(3)：405-411.
[8]许宝杰,张建民,徐小力.抑制EMD端点效应方法的研究[J].北京理工大学学报.2006,26(3)：197-199.
[9]胡广书.数字信号处理[M].北京：清华大学出版社,2003：57-184.
[10]王阳,刘红彦.频谱分析在齿轮故障诊断中的应用[J].机械工程,2010,13(3)：31-33.
[11]丁康,陈健林,苏向荣.平稳和非平稳振动信号的若干处理方法及发展[J].振动工程学报.2003,16(1)：1-9.
[12]安婧,伉大俪,郭海涛等.时-频分析方法在齿轮故障诊断中的应用[J].信息技术.2010,(3)：103-105.
[13]申永军.杨绍普.刘献栋.齿轮故障诊断中的信号处理技术研究与展望[J].机械传动.2004,28(3)：2-3.
[14]田昊,唐力伟,田广.基于盲源分离的齿轮箱复合故障诊断研究[J].兵工学报.2010,31(5)：646-649.
[15]苏中元,贾民平.周期平稳信号盲源分离算法及其应用[J].机械工程学报.2007,43(10)：144-148.
[16]肖瑛,冯长建.组合窗函数的短时傅里叶变换时频表示方法[J].探测与控制学报.2010,32(3)：43-45.
[17]李军,俞建定,徐铁峰.基于小波变换的故障诊断信号非平稳性分析[J].系统工程与电子技术,2006,28(7)：1110-1111.
[18]Fan Xianfeng, Zuo Ming J.Gearbox fault detection using Hilbert and wavelet packet transform [J]. Mechanical Systems and Signal Processing.2006,20:966～982.
[19]来五星,轩建平,史铁林Wigner-Ville时频分布研究及其在齿轮故障诊断中的应用[J].振动工程学报.2003,16(2)：247-250.
[20]于凤芹.基于三参数Chirp原子分解的语音信号的时频表示[J]. Signal Processing. 2005,21(zl):36～40.
[21]T. Ramesh Babu,S. Srikanth,A.S. Sekhar.Hilbert-Huang transform for detection and monitoring of crack in a transient rotor[J].Mechanical Systems and Signal Processing.2008,22:905～914.
[22]余磊Hilbert-Huang变换及其在故障检测中的应用[学位论文].武汉理工大学,2009.
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