cipsA fault diagnosis method combined with LMD,sample entropy and energy ratio for roller
bearings
Minghong Han ⇑,Jiali Pan
School of Reliability and Systems Engineering,Beihang University,Beijing 100191,PR China
a r t i c l e i n f o Article history:
Received 26December 2014
Received in revid form 29July 2015Accepted 12August 2015
Available online 28August 2015Keywords:
Local mean decomposition Fault feature extraction Sample entropy Energy ratiooctober怎么读
a b s t r a c t
Since the vibration signals of roller bearings are non-linear and non-stationary,the fault diagnosis of roller bearings is very difficult to determine.Characterized by the lf-adaptive time–frequency,local mean decomposition (LMD)is suitable for analyzing this kind of complex signals.By using LMD method,vibration signals of roller bearings can be decompod into a number of product functions (PFs)and a residual trend.In order to diagno the fault of roller bearings,the PF components derived from LMD method are ud to extract the features of fault signals.Considering the fact that sample entropy and energy ratio can reflect the regularity and characteristics of vibration signals to some extent,the two factors are chon as PFs’feature vectors.Thus,a novel fault diagnosis method combining LMD method,sample entropy and energy ratio for roller bearings is put forward.By using the Support Vector Machine (SVM)classifier to make classification,the analysis results demonstrate that the propod fault diagnosis and feature extraction method is effective.
Ó2015Elvier Ltd.All rights rerved.
1.Introduction
Roller bearing is the most common component in rotat-ing machines,however,it would be invalidated by the impacts of wear,fatigue,corrosion,overloading and so forth.Becau the abnormal vibration of roller bearings could cau local defects,it is significant to diagno the faults of roller bearings and monitor its conditions.success什么意思
Obtaining fault feature information from vibration signals is always a significant issue in fault diagnosis.Traditional fault diagnosis methods are performed on the basis of time domain or frequency domain analysis meth-ods to extract features and identify the different working conditions of bearings [1–3].Due to the influence of factors including loads,friction,stiffness,etc.,the vibration signals usually display strong non-linear,non-Gaussian and non-stationary features.So it is complicated to accurately iden-tify the fault types of bearings in either time or frequency domain [4,5],and the time–frequency analysis methods such as the short time Fourier transformation (STFT),the Wigner Ville distribution (WVD),the wavelet transform (WT),the empirical mode decomposition (EMD)method and so on are needed.Nevertheless,the analysis window of STFT has fixed time width and bandwidth,it is not suit-able for fast changing signals [6].The Wigner Ville distri-bution would cau cross-term interference when dealing with the multi component signals [7,8].The
WT has been well applied in fault diagnosis [9–11]but different mother wavelets should be predefined for each component.The EMD method,which is commonly combined with Hilbert transform,is a lf-adaptive time–frequency analysis method.And some improved EMD methods were pro-pod.The defects of EMD are modes mixing problem and end effects [12,13].
dx.doi/10.asurement.2015.08.0190263-2241/Ó2015Elvier Ltd.All rights rerved.
⇑Corresponding author at:School of Reliability and Systems Engineer-ing,Beihang University,Room 531,Weimin Building,Beijing 100191,PR China.Tel./fax:+861082339760.
E-mail address:hanminghong@buaa.edu (M.Han).很快英语
Local mean decomposition (LMD)method was devel-oped by Smith in 2005and originally is ud as a time–frequency analysis tool of the electroencephalogram signals [14].The LMD analysis method can be ud to adaptively decompo any complicated multi-component signal into a ries of product functions (PFs),and each of them is the product of an amplitude envelope signal and a purely frequency modulated signal.Particularly,each PF,who instantaneous amplitude (IA)consisted of the amplitude envelope and instantaneous frequency (IF)can be derived from the fre
quency modulated signal,has a physical meaning.After the decomposition of original sig-nal,it is very likely that different fault conditions can be recognized by dealing with the decomposition results such
as PFs,IFs or IAs which may contain uful fault informa-tion.So LMD is introduced to perform fault feature extrac-tion of roller bearings in this paper.dissident
In the past,FFT and other spectrum analysis methods like the power spectrum analysis have been ud to trans-form the decomposition results to extract fault features [15,16].However,traditional spectrum analysis methods are suitable for stationary signals rather than non-stationary ones,and the analysis results may not be so sat-isfactory.Kinds of fault extraction methods,in which LMD is combined with the order tracking method,PCA or AR model,have been put forward and applied to the diagnosis of rotary machines [17–19].But establishing a new model after performing LMD analysis to the original signal would make the process of fault diagnosis longer and more complex.
Obviously,for the roller bearings,vibration signals of different fault patterns will show varying complexity [20]and therefore the sample entropy of vibration signals var-ies.Furthermore,signals of different fault types,after decompod by LMD method,will have different product functions and the product functions will have different energy distribution [21].Conquently,sample entropy and energ
y ratio are ud as the feature factor.And bad upon the above analysis,LMD demodulation technique and the two feature factors are combined and applied to the fault feature extraction of roller bearing.
This paper is organized as follows.The theory of LMD method is given briefly in Section 2.In Section 3,a
fault
Fig.1.Experimental tup.lei
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76(2015)7–19sunt
diagnosis approach combined with LMD,sample entropy and energy ratio is put forward,and then the propod approach is applied to the fault diagnosis of the roller bear-ing,which demonstrates its effectiveness and feasibility. Conclusions are given in Section4.2.LMD analysis method
A ries of frequency modulated signals and envelope signals can be obtained by decomposing the original multi-component signal through LMD method.The
product Fig.3.LMD results of the vibration signal of the normal roller bearing.
of each frequency modulated signal and the corresponding envelope signal is called a product function which has a physical meaning.After all needed product functions are obtained,the completed time–frequency distribution of the original signal can be determined.Given any signal x (t),it can be decompod as follows[14,17]:
(1)Find out all the local extrema n i and calculate the
mean of two successive extrema n i and n i+1.Thus
the i th mean value m i is given by
m i¼
n iþn iþ1
2
ð1ÞAll mean value m i of two successive extrema are con-nected by straight lines.The local means
are then smoothed using moving averaging to form a smoothly varying continuous local mean function m11(t).
(2)The i th envelope estimate a i is given by
a i¼
n iÀn iþ1
j j
2
ð2
ÞFig.4.LMD results of the vibration signal of the inner race fault.
The local envelope estimates are smoothed in the same way as the local means to derive the envelope the envelop function a1(n+1)(t)of s1n(t)equals to1. Therefore
Fig.5.LMD results of the vibration signal of the ball fault.
M.Han,J.Pan/Measurement76(2015)7–1911
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