二维小波变换及其在机械碰摩故障诊断中的应用
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摘要
以机械碰摩信号为例 ,采用具有“时频局部化”性能和“方向极化”性能的二维小波变换 ,成功地分辨出故障信号与正常信号 ,避免了由于多信号转化成单信号带来的信息冗余以及能量的转化 ,同时能方便地分辨出故障信号的相位角 ,为解决机械故障诊断领域多信号、多特征的分析问题提出新的思路
Mechanical fault diagnosis is always a key question that is focused by many researchers. And the theory of wavelet transformations has been widely used to draw the fault characteristics. But there is no a good method to analyze several sets of sampling data simultaneously, and they always have to be changed into a single set or dealt respectively. The theory of two dimensional (2d) wavelet transformations, which has been widely used to process images question, can deal with multi dimensional data simultaneously, and has the ability to show the detailed characteristics of the signals in time frequency region and in a certain direction. In this paper, taking a set of mechanical rub impact signals as an example, two dimensional wavelet transformations is applied to analyze a new multi dimensional matrix formed with this set of signals. To sure the ability to determine the phase of signals, a new set of data is sampled after rotating the rum pact mass a determined angle and its 2d wavelet analyzed result is compared with the frontal one. Thus the result shows that it can distinguish the fault signals from several sets of sampling data and confirm the phase of fault signals without data transformation. And it can avoid the redundancy and can be thought as a new method to deal with some multi signals or multi characteristics questions. It can be also thought as a promising trial for further application of two dimensional wavelet transformation to fault diagnosis.
Mechanical fault diagnosis is always a key question that is focused by many researchers. And the theory of wavelet transformations has been widely used to draw the fault characteristics. But there is no a good method to analyze several sets of sampling data simultaneously, and they always have to be changed into a single set or dealt respectively. The theory of two dimensional (2d) wavelet transformations, which has been widely used to process images question, can deal with multi dimensional data simultaneously, and has the ability to show the detailed characteristics of the signals in time frequency region and in a certain direction. In this paper, taking a set of mechanical rub impact signals as an example, two dimensional wavelet transformations is applied to analyze a new multi dimensional matrix formed with this set of signals. To sure the ability to determine the phase of signals, a new set of data is sampled after rotating the rum pact mass a determined angle and its 2d wavelet analyzed result is compared with the frontal one. Thus the result shows that it can distinguish the fault signals from several sets of sampling data and confirm the phase of fault signals without data transformation. And it can avoid the redundancy and can be thought as a new method to deal with some multi signals or multi characteristics questions. It can be also thought as a promising trial for further application of two dimensional wavelet transformation to fault diagnosis.
引文
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9 GAOZhenshan,LIQinxue,WANGXinjun,etal.Applicationof2Dwavelettransformincoherentnoiseelimination.JournalofChangchunUni versityofScienceandTechnology,1998,28(4):433～437(InChinese)(高振山,李勤学,刘 财,等.二维小波变换在消除相干噪声中的应用.长春科技大学学报,1998,28(4):433～437).
10 LIUXiandong,LIQihan.Applicationofwavelettransformtothediagnosisofearlyrub impactfaultbetweenrotorandstator.ActaAeronautAstronauti caSinica,1999,20(3):220～223(InChinese)(刘献栋,李其汉.小波变换在转子系统动静件早期碰摩故障诊断中的应用.航空学报,1999,20(3):220～223).
11 YANGJianguo,XIASongbo,XUGenfa.Distillingthecharacteristicsoftransientimpactfromperiodicsignalsbasedonwavelet.JournalofAerospacePower,1999,14(4):343～347(InChinese)(杨建国,夏松波,须根法.基于小波的周期信号中瞬态冲击特征提取.航空动力学报,1999,14(4):343～347).
12 YANGFusheng.Applicationandengineeringanalysisofwavelettransform.Beijing:SciencePress,2000(InChinese)(杨福生.小波变换的工程分析与应用.北京:科学出版社,2000).
13 HUChanghua,ZHANGJunbo,XIAJun,etal.SystemanalysisanddesignbasedonMATLAB———waveletanalysis.Xi′an:XidianUniversityPress,1999(InChinese)(胡昌华,张军波,夏 军,等.基于MATLAB的系统分析与设计———小波分析.西安:西安电子科技大学出版社,1999).
14 WANGNing,SHENGZhaohan.IdentificationtheorbitsofshaftcenterlinebasedonwaveletvectorsandAR model.SignalProcessing,1999,15(2):157～162(InChinese)(王 宁,盛昭瀚.基于小波向量和AR模型的轴心轨迹识别.信号处理,1999,15(2):157～162).
15 XIASongbo,ZHANGJiazhong,XUShichang,etal.Presentstationandex pectationofthediagnostictechnologyofrotatingmachinery.JournalofVi brationandShock,1997,16(2):1～5(InChinese)(夏松波,张嘉钟,徐世昌,等.旋转机械故障诊断技术的现状与展望.振动与冲击,1997,16(2):1～5).
16 ZHANGXianda,BAOZheng.Analysisandprocessingofunstablesignals.Beijing:NationalDefenceIndustryPress,1999(InChinese)(张贤达,保铮.非平稳信号分析与处理.北京:国防工业出版社,1999).
17 ZHAOYuncheng.Researchondiagnostictheoryandmethodforrotatingmachinery〔PhDThesis〕.Xi′an:Xi′anJiaotongUniversity,2000(InChi nese)(赵玉成.旋转机械故障诊断理论及方法的研究〔博士学位论文〕.西安:西安交通大学,2000).
2 MallatS .Atheoryformulti resolutionsignaldecomposition:thewaveletrepresentation.IEEETrans.PatternAnal.MachineIntell.,1989,11(7):874～693.
3 WornellGW .Wavelet basedrepresentationsforthe1/ffamilyoffractalprocesses.Proc.IEEE ,1993,81:1428～1450.
4 UnserM ,AldroubiA .Areviewofwaveletsinbiomedicalapplications.Proc.IEEE ,1996,84:626～638.
5 FANLiuming,HUANGRunqiu,JISuiwang.Waveletanalysisforgroundmotionsignals.ComputingTechniquesforGeophysicalandGeochemicalEx ploration,2000,22(1):1～4(InChinses)(范留明,黄润秋,吉随旺.地震信号的小波分析.物探化探计算技术,2000,22(1):1～4).
6 DUYuanhu,HEChenghui,WANGXiaomei.Wavelettheoryandvibrationanalysis.JournalofNortheastForestryUniversity.1997,25(3):60～64(InChinese)(杜元虎,何成辉,王晓梅.小波理论与振动分析.东北林业大学学报,1997,25(3):60～64).
7 LIJianping,CHENTinghuai,XUWenzi,etal.Studyonthedevelopmentofwavelettheorybyanalyzingreferencesofwavelet.JournalofChongqingUniversity(NaturalScienceEdition),1997,20(1):82～87(InChinese)(李建平,陈廷槐,徐问之,等.从文献分析看小波理论的发展.重庆大学学报(自然科学版),1997,20(1):82～87).
8 PIAORongmin,LIShoushan.Applicationofthetheoryoftwo dimensionalwavelettransformationtokillnoiseoftheseismicsignals.JournalofShenyangInstituteofChemicalTechnology,1997,11(2):148～155(InChinese)(朴荣民,李寿山.二维小波变换理论在地震信号去噪中的应用.沈阳化工学院学报,1997,11(2):148～155).
9 GAOZhenshan,LIQinxue,WANGXinjun,etal.Applicationof2Dwavelettransformincoherentnoiseelimination.JournalofChangchunUni versityofScienceandTechnology,1998,28(4):433～437(InChinese)(高振山,李勤学,刘 财,等.二维小波变换在消除相干噪声中的应用.长春科技大学学报,1998,28(4):433～437).
10 LIUXiandong,LIQihan.Applicationofwavelettransformtothediagnosisofearlyrub impactfaultbetweenrotorandstator.ActaAeronautAstronauti caSinica,1999,20(3):220～223(InChinese)(刘献栋,李其汉.小波变换在转子系统动静件早期碰摩故障诊断中的应用.航空学报,1999,20(3):220～223).
11 YANGJianguo,XIASongbo,XUGenfa.Distillingthecharacteristicsoftransientimpactfromperiodicsignalsbasedonwavelet.JournalofAerospacePower,1999,14(4):343～347(InChinese)(杨建国,夏松波,须根法.基于小波的周期信号中瞬态冲击特征提取.航空动力学报,1999,14(4):343～347).
12 YANGFusheng.Applicationandengineeringanalysisofwavelettransform.Beijing:SciencePress,2000(InChinese)(杨福生.小波变换的工程分析与应用.北京:科学出版社,2000).
13 HUChanghua,ZHANGJunbo,XIAJun,etal.SystemanalysisanddesignbasedonMATLAB———waveletanalysis.Xi′an:XidianUniversityPress,1999(InChinese)(胡昌华,张军波,夏 军,等.基于MATLAB的系统分析与设计———小波分析.西安:西安电子科技大学出版社,1999).
14 WANGNing,SHENGZhaohan.IdentificationtheorbitsofshaftcenterlinebasedonwaveletvectorsandAR model.SignalProcessing,1999,15(2):157～162(InChinese)(王 宁,盛昭瀚.基于小波向量和AR模型的轴心轨迹识别.信号处理,1999,15(2):157～162).
15 XIASongbo,ZHANGJiazhong,XUShichang,etal.Presentstationandex pectationofthediagnostictechnologyofrotatingmachinery.JournalofVi brationandShock,1997,16(2):1～5(InChinese)(夏松波,张嘉钟,徐世昌,等.旋转机械故障诊断技术的现状与展望.振动与冲击,1997,16(2):1～5).
16 ZHANGXianda,BAOZheng.Analysisandprocessingofunstablesignals.Beijing:NationalDefenceIndustryPress,1999(InChinese)(张贤达,保铮.非平稳信号分析与处理.北京:国防工业出版社,1999).
17 ZHAOYuncheng.Researchondiagnostictheoryandmethodforrotatingmachinery〔PhDThesis〕.Xi′an:Xi′anJiaotongUniversity,2000(InChi nese)(赵玉成.旋转机械故障诊断理论及方法的研究〔博士学位论文〕.西安:西安交通大学,2000).
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