an enhanced empirical mode decomposition method for blind

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Article

An enhanced empirical modedecomposition method for blindcomponent separation of asingle-channel vibration signal mixture

Dong Wang1, Wei Guo2 and Peter W Tse1

Abstract

Blind component separation aims to decompose a single-channel vibration signal mixture into periodic components and

random transient components. In addition to periodic components, random transient components with a high degree of

impulsiveness are signals of interest in practice. An adaptive signal processing method called empirical mode decom-

position (EMD) decomposes a nonlinear and non-stationary signal into the sum of simple components termed intrinsic

mode functions (IMFs). Ensemble empirical mode decomposition (EEMD) is an improvement of EMD and aims to relieve

a mode mixing problem that exists in EMD. However, there is no universal standard formula that can be used to select

appropriate parameters of EEMD. Improper parameters of EEMD still cause a mode mixing problem that makes a signal

of a similar scale reside in some successive IMFs. An enhanced EEMD for the purpose of blind component separation is

developed in this paper to respectively extract periodic components and random transient components from a single-

channel vibration signal mixture. A revised spectral coherence is proposed to measure the spectral dependence between

two successive IMFs. The closer the revised spectral coherence is to one, the higher the spectral dependence of two

successive IMFs is. Additionally, a fusion rule based on locations of local minima of the revised spectral coherence is

proposed to automatically fuse successive IMFs with similar characteristics into a new IMF, called an enhanced IMF

(EIMF). Vibration signals including simulated and real multi-fault signals are used to verify the enhanced EEMD. A com-

parison with EEMD is conducted to show the superiority of the enhanced EEMD. The results demonstrate that the

enhanced EEMD has better performance than EEMD for automatically extracting periodic components and random

transient components from a single-channel vibration signal mixture.

Keywords

Blind component separation, ensemble empirical mode decomposition, single-channel vibration signal mixture, spectral

coherence

1. Introduction

Vibration-based signal analysis is widely applied to dis-cover the contributions of vibration signal components(Li et al., 2008; Yan and Gao, 2010). Linear filteringmethods, such as the Wiener filter and the Kalmanfilter, which are easy to design and implement, havebeen proposed to process vibration signals. However,in practice, machine vibration processes often containcomplex, non-stationary, noisy, and nonlinear charac-teristics (Hively and Protopopescu, 2004), andadvanced signal processing techniques are more suit-able for vibration signal analysis. The most popularsignal processing methods for vibration analysisare envelope analysis (e.g. Sheen, 2010) and wavelet

transform (e.g. Wang et al., 2009). Although envelopeanalysis is effective in many cases, the method requires

1Smart Engineering Asset Management Laboratory (SEAM), Department

of Systems Engineering and Engineering Management, City University of

Hong Kong, Hong Kong, China2School of Mechanical, Electronic and Industrial Engineering, University of

Electronic Science and Technology of China, Chengdu, China

Corresponding author:

Peter W Tse, Smart Engineering Asset Management Laboratory (SEAM),

Department of Systems Engineering and Engineering Management, City

University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China.

Email: [email protected]

Received: 27 December 2013; accepted: 28 July 2014

Journal of Vibration and Control

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the designer to know the bandpass filter around a res-onance frequency, and it is ineffective in the presence ofa high noise level (Chiementin et al., 2007). For wavelettransform and wavelet packet methods, one of the mainproblems is the non-adaptive basis. To ensure goodresults, a mother wavelet must be carefully chosen sothat the content of her daughter wavelets are largelysimilar to that of the analyzed signal. Although manynew and complicated basic functions have been pro-posed to improve the effectiveness of wavelet-basedmethods (Rafiee and Tse, 2009; Feng et al., 2011), todate, no general guideline is available for the correctselection of a mother wavelet. At the same time, littleattention has been paid to inherent deficiencies of thewavelet transform, such as border distortion andenergy leakage (Peng et al., 2009).

For machine fault diagnosis (Miao et al., 2011; Anet al., 2012; Sun et al., 2013), identification of vibrationresponses rather than vibration excitation forces in amechanical system is more useful to find potentialfaults arising in a machine. In recent years, Antoni(2005) proposed the concept of blind component sep-aration (BCS), which aims to decompose a vibrationsignal into periodic components and random compo-nents. Further, random components can be decom-posed into non-stationary transient signal componentsand stationary signal components. Here, periodic vibra-tion signals are usually caused by imbalances, misalign-ments, eccentricities, etc. The most interesting part ofrandom components is those caused by random transi-ent phenomena with a high degree of impulsiveness.A short-time Fourier transform (STFT)-based Fourierdomain algorithm was developed by Antoni (2005) toblindly extract periodic components. Other options(Randall and Antoni, 2011) for extraction of periodiccomponents are auto-regressive filtering, adaptive noisecancellation, discrete separation, and time synchronousaveraging. On the other hand, Randall and Antoni(2011) proposed spectral kurtosis to recover randomtransient components. The recovery of random transi-ent components can be realized by other candidates,such as an optimal wavelet filter (Bozchalooi andLiang, 2007; He et al., 2009; Tse and Wang, 2013a),an enhanced kurtogram (Wang et al., 2013), a sparso-gram (Tse and Wang, 2013b), continuous wavelettransform (Hong and Liang, 2007), and an adaptiveeigenvetor algorithm (Wang and Tse, 2012).

Ensemble empirical mode decomposition (EEMD)(Wu and Huang, 2009) was developed from empiricalmode decomposition (EMD) (Huang et al., 1998;Huang and Shen, 2005), which is an adaptive signalprocessing algorithm to represent a nonlinear andnon-stationary signal as the sum of signal componentswith amplitude and frequency modulated parameters,and is capable of revealing overlapping in both time

and frequency components (Feldman, 2009). EEMDimproves the scale separation capability of EMD andsolves a mode mixing problem, which is defined as asingle intrinsic mode function (IMF) either consistingof signals of widely disparate scales or a signal of asimilar scale residing in different IMFs (Wu andHuang, 2009). Synthetic signals were constructed toinvestigate the performance of EMD (Yan and Gao,2006). The results showed that EMD is suitable to cap-ture transient signals. Yang et al. (2007) combinedEMD and support vector machines for intelligent bear-ing fault recognition. EMD-based characteristic ampli-tude ratios were proposed as inputs to support vectormachines. He et al. (2011) proposed a midpoint-basedEMD to improve the performance of EMD by repla-cing local means with geometrical midpoints of succes-tive extrema for machinery fault diagnosis. Lei and Zuo(2009) considered that different IMFs were sensitive todifferent faults. Then, they developed a weight-basedmethod to select sensitive IMFs for rub-impact faultidentification. Peng et al. (2005) used wavelet packettransform as a pre-processor before EMD was appliedto process vibration signals. Li et al. (2010) designed aranged angle-EMD to detect an abnormal clearanceexisting in a diesel engine. Chan and Tse (2009) useda method that combined an EMD method with a dif-ferential pulse code modulation technology to providefast wireless data transmissions. Li and Liang (2011)developed a new method that included an integralenhancement, an EMD-based de-trending and anEMD-based de-noising for extracting oil debris signa-tures. Their results indicated that this method canbetter retain signature integrity. Fan and Zuo (2008)proposed the amplitude acceleration energy of IMFsas an indicator of impulsive features. The reason isthat the velocity change of amplitudes of the IMFsover a particular unit of time increases when the vibra-tion signal is generated by a faulty component. A spec-trum amplitude index was proposed to select the mostuseful IMF. Lei et al. (2011) used kurtosis to selectsensitive IMFs and combined EEMD with waveletneural network for intelligent bearing fault diagnosis.Lei et al. (2009) used EEMD to analyze the problemrelated to rub-impact faults. A comparison betweenEEMD and EMD demonstrated that EEMD is moreeffective in extracting rotating machinery fault signa-tures. Guo et al. (2012) had a similar idea to that ofPeng et al. (2005). Then, a hybrid signal processingmethod based on spectral kurtosis and EEMD wasdeveloped to deal with bearing fault signals corruptedby heavy noise. Zhang et al. (2010) systematically ana-lyzed the effects of different amplitudes of white noiseand ensemble numbers on the performance of EEMD.Then, they developed a modified EEMD whichreplaced white noise with band-limited noise to

2 Journal of Vibration and Control




reduce ensemble numbers and enhance computationalefficiency. Guo and Tse (2013) investigated the effectsof white noise on the decomposition performance ofEEMD and employed a root-mean-square error indexto find the optimal noise level for a faulty vibrationsignal. An et al. (2011) combined EEMD with Hilberttransform to extract bearing pedestal looseness faultfeatures of a wind turbine. Feng et al. (2012) employedEEMD and an energy separation algorithm for faultdiagnosis of a sun gear of a planetary gearbox.This method is a simple and effective way to findfault characteristic frequencies related to the sun gear.

After EEMD is applied to a vibration signal, signalcomponents with disparate scales are distributed intodifferent IMFs. However, in some cases, a signal with asimilar scale may reside in different IMFs. In otherwords, the mode mixing problem still exists.Meanwhile, there is no universal standard formulathat is used to select appropriate parameters ofEEMD. Improper parameters may result in unsatisfac-tory signal components. According to the concept ofBCS, an enhanced EEMD is developed in this paper toextract periodic components and random transient com-ponents froma signal-channel vibration signalmixture. Inthe enhanced EEMD, a revised spectral coherence is pro-posed to measure the spectral dependence between twosuccessive IMFs and determine whether the two IMFshave a similar characteristic. A fusion rule based on loca-tions of local minima of the revised spectral coherence(RSC) is proposed to automatically fuse the IMFs withsimilar characteristics into a new IMF, termed anenhanced IMF. As a result, periodic components andrandom transient components in the single-channel vibra-tion signalmixture can be properly separated and reside indifferent enhanced IMFs (EIMF).

The remainder of this paper is organized as follows.Section 2 briefly introduces the procedure of EEMD. InSection 3, an enhanced EEMD is developed to adap-tively decompose a single-channel vibration signal mix-ture into periodic components and random transientcomponents. In Section 4, two vibration signals includ-ing simulated and real multi-fault signals collected froma traction motor are used to verify the enhancedEEMD. Furthermore, the enhanced EEMD is com-pared with EEMD. Finally, conclusions are drawn inSection 5.

2. Ensemble empirical modedecomposition

2.1. Brief introduction to EEMD

Ensemble empirical mode decomposition (Wu andHuang, 2009) consists of sifting an ensemble of addedwhite noise signals and treats an ensemble mean as a

final result. Although each individual signal decompos-ition generates a relatively noisy result, added whitenoise signals are necessary to force the sifting processto visit all possible solutions in the finite neighborhoodof real extrema and then generates different solutionsfor each final IMF (Wu and Huang, 2009). Meanwhile,the zero mean of white noise is useful for cancellationof added white noise in the final ensemble mean if thereare sufficient trials. Hence, only the signal itself cansurvive in the final decomposition result. It has beenapplied to analyze and identify vibrations generatedby rotating machines. The procedure of EEMD issummarized as follows:

Step 1: Initialize parameters: the amplitude of theadded white noise, a, which is a fraction, LN, ofthe standard deviation of the signal, x(t), to be ana-lyzed, and the ensemble number, NE. LN is callednoise level. The index, m, of the ensemble startsfrom 1, i.e. m¼ 1.

Step 2: Generate a white-noise-added signal,xm(t)¼x(t)þ nm(t), where nm(t) is white noise witha pre-setting amplitude.

Step 3: Perform the m-th signal decomposition. That isto say, decompose the above noisy signal, xm(t)using EMD. The decomposition results in someIMFs, ci,m, (i¼ 1, 2,. . ., N�1) and a non-zero low-order residue, rm, where N�1 is the number of IMFsobtained in each decomposition.

Step 4: Repeat Steps 2 and 3 with m¼mþ 1 until theensemble index m reaches the pre-setting maximumensemble number, NE.

Step 5: Obtain the final decomposition results by calcu-lating the means of corresponding IMFs and theresidues obtained from all of the signal decompos-ition processes.

Using this signal processing method, a multi-compo-nent signal, x(t), is represented as the sum of someIMFs and a residue, i.e.

x tð Þ ¼XN�1i¼1

�ci þ �r ð1Þ

where �ci is the i-th IMF that is the mean of the corres-ponding IMFs obtained from all decompositionprocesses, and �r is the mean of the residues from alldecomposition processes and can be considered as thelast IMF. In the rest of this paper, the number of IMFsis denoted as N.

2.2. Selection of EEMD parameters

In EEMD, two critical parameters, the amplitude of theadded white noise and the ensemble number, need to be

Wang et al. 3




prescribed before EEMD is applied to a signal. Wu andHuang (2009) gave a relationship among the ensemblenumber, NE, the amplitude of the added white noise, a,and the standard deviation of error, e, using the equa-tion: lne þ (a/2) lnNE¼ 0. The empirical setting is thatthe amplitude of the added white noise is approxi-mately 0.2 of the standard deviation of the originalsignal and the value of the ensemble is a few hundreds.Nevertheless, the empirical setting cannot guarantee theuniversal effectiveness for all practical applications.As of today, there is no universal equation reportedin the literature to automatically select appropriateEEMD parameters for a signal (Lei et al., 2009, 2011;Zhou et al., 2011).

3. An enhanced EEMD for blindcomponent separation

According to the concept of blind component separ-ation (Antoni, 2005), EEMD possibly decomposes avibration signal into periodic components andrandom transient components. However, after EEMDis applied to some simulated and real signals, a modemixing problem still exists. In other words, a signalcomponent of a similar scale resides in some successiveIMFs. These resulting IMFs make the physical mean-ing of an IMF unclear and make the energy of thesignal disperse. Furthermore, there is no universalguideline for intelligently selecting appropriate EEMDparameters. In this paper, an enhanced EEMD is devel-oped to fuse IMFs which suffer from the mode mixingproblem and separate periodic components andrandom transient components from a single-channelvibration signal mixture, respectively.

The main idea of the enhanced EEMD comes from acyclic coherence (Antoni, 2007). A cyclic coherencebetween two signals, Y and X (one is another shiftedby a cyclic frequency), is a useful tool to measure thelinear spectral correlation at a specific frequency. Thevalue of the cyclic coherence is limited to the valuesbetween zero and one. Its remarkable property is thatthe cyclic coherence which is close to one for somecyclic frequency indicates that two signals are‘‘strongly’’ jointly cyclo-stationary at that cyclic fre-quency. As a result, these signals can be easily sepa-rated from other interfering signals even in the case ofoverlapping spectral supports; on the other hand, thecyclic coherence having a zero value indicates that sig-nals Y and X shares no cyclo-stationary at that cyclicfrequency.

In the enhanced EEMD, the cyclic coherence of spec-tral signals is extended to measure the spectral depend-ence of two successive IMFs obtained by EEMD. Afterapplying EEMD to the signal, each IMF is representedas �ciðtÞ (i¼ 1, 2, . . . ,N), where N is the number of IMFs.

Their corresponding frequency spectra are obtained byusing fast Fourier transform. Here, frequency counter-parts of IMFs are denoted as Ci(F) (i¼ 1, 2, . . . ,N). It isnoted that only the amplitudes of frequency spectra areused. To measure the spectral linear dependence of twosuccessive spectral components,Cj(F) andCjþ1(F), at thefrequency of F, a spectral coherence (SC), � j, jþ1(F), isdefined as

�j, jþ1 Fð Þ ¼ Cj Fð Þ � Cjþ1 Fð Þ, j ¼ 1, 2, . . . ,N� 1

ð2Þ

To quantify the spectral coherence of two successiveIMFs over the whole frequency spectrum, a revisedspectral coherence (RSC), �j, jþ1, is defined:

�j, jþ1 ¼

PF Cj ðFÞ � Cjþ1ðFÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP

F Cj ðFÞ � Cj ðFÞ� � P

F Cjþ1ðFÞ � Cjþ1ðFÞ� �q ,

j ¼ 1, 2, . . . ,N� 1

ð3Þ

The value of �j, jþ1 is constrained to the range fromzero to one. The closer equation (3) is to one, the stron-ger the spectral linear dependence of Cj(F) and Cjþ1(F)over the whole frequency domain. The definition givenin equation (3) can be used to measure the spectraldependence of two successive IMFs and then determinewhether these IMFs come from one signal of a similarscale. Specifically, if one signal component is decom-posed into some successive IMFs, the mode mixingexists in these IMFs, which distorts the physical mean-ing of the signal of interest. A fusion rule based onlocations of local minima of the RSC is proposed toautomatically fuse the successive IMFs with similarspectral characteristics into a new IMF, called anenhanced IMF. The details concerning the above illus-trations are introduced as follows.

One location of local minima of the RSC, �j, jþ1(j¼ 1, 2, . . . ,N�1), is denoted as ps (s¼ 1, 2, . . . ,L),where L is the number of the local minima.

In the case of �1, 2 5 �2, 3, ps is given as

ps ¼

1 s ¼ 1,

j�j�1, j 4 �j, jþ1 and �j, jþ1 5 �jþ1, jþ2,

25 j5N� 1, s ¼ 2, 3, . . . ,L

8>><>>:

ð4Þ

otherwise, if �1, 2 � �2, 3 is satisfied, ps is calcuated by

ps ¼ j,�j�1, j � �j, jþ1 and �j, jþ15�jþ1, jþ2,15 j5N� 1,

s¼ 1,2, . . . ,L ð5Þ





It is unnecessary to judgy whether the last RSC,�N�1,N, is a local minimum or not. When it comes tovibration signals, the last IMF obtained by EEMD isfrequently a residual trend. The amplitudes of the resi-dual are so small that the effect of the last IMF can beignored.

According to the identified locations of the localminima, the EIMFs c

_

kðtÞ are defined as

c_

k tð Þ ¼

Ppki¼1

�ci tð Þ, k ¼ 1,

Ppki¼pk�1þ1

�ci tð Þ, k ¼ 2, 3, . . . ,L,

PNi¼pk�1þ1

�ci tð Þ, k ¼ Lþ 1

8>>>>>>>>><>>>>>>>>>:

ð6Þ

For the decomposition of a vibration signal intoperiodic components and random transient compo-nents, the procedure of the enhanced EEMD can befinally summarized in the following procedure:

Step 1: Apply EEMD to a single-channel vibrationsignal mixture and obtain some IMFs �ciðtÞ (i¼ 1,2, . . . ,N).

Step 2: Conduct fast Fourier transform on each IMFand then obtain its corresponding frequency spec-trum Ci(F) (i¼ 1, 2, . . . ,N).

Step 3: Calculate the RSCs �j, jþ1 (j¼ 1, 2, . . . ,N�1)using equation (3).

Step 4: Calculate each position of local minima ofRSCs ps (s¼ 1, 2, . . . ,L) using equations (4) and (5).

Step 5: Generate the EIMFs c_

kðtÞ (k¼ 1, 2, . . . ,Lþ 1),according to the fusion rule defined in equation (6).

4. Validation of the enhanced EEMD

4.1. Case 1 - a simulated multi-fault signalmixture

A simulated multi-fault signal mixture consisting of twolow-frequency periodic components and a high-frequency transient component is described as follows:

y kð Þ ¼Xr

exp �l� k� r� Fs=fm � �rð Þ=Fsð Þ

� sin 2�f0 � k� r� Fs=fm � �rð Þ=Fsð Þ

þ 0:7� sin 2�f1 � k=Fsð Þ þ sin 2�f2 � k=Fsð Þ

ð7Þ

where the damping coefficient l ¼ 900; the fault charac-teristic frequency fm¼ 100Hz; the sampling frequencyFs¼ 12 kHz; the resonant frequency f0¼ 2600Hz;

two low-frequency components, f1 and f2 are equal to50Hz and 100Hz, respectively; �r is a random numbersubjected to a uniform distribution; 1200 samplesfrom the above simulated signal mixture were usedfor analyses. An amount of a normally distributedrandom signal was added into equation (7) to corruptthe simulated signal. The simulated signal and itsfrequency counterpart are shown in Figure 1(a) and(b), respectively.

In order to separate the low-frequency componentsand the high-frequency component from the simulatedsignal mixture contaminated with noise, EEMD wasfirstly applied to the simulated signal mixture shownin Figure 1(a). The ensemble number, NE, and thenoise level, LN, were initially set to 30 and 0.1, respect-ively. The IMFs obtained by EEMD and their corres-ponding frequency spectra are shown in Figure 2,where the IMFs obtained by EEMD distort the distri-butions of the true signal components existing in thesimulated multi-fault signal. Ideally, IMF1–IMF3should have been fused into one IMF because theyare high-frequency transient components coming fromthe same transient component.

However, EEMD is not able to obtain such an IMFfor the extraction of the high-frequency transient com-ponent. Figure 2(d)–(f) shows the extracted IMF4,IMF5, and IMF6, respectively; and the correspondingfrequency spectra are shown in Figure 2(l)–(n). Fromthese figures, it can be observed that the same signalcomponent in IMF4 or IMF6, corresponding to thefrequency of 50Hz or 100Hz, is distributed intoIMF5, that is, the signal component, correspondingto the frequency of 50Hz, resides in two successiveIMFs, IMF4 and IMF5, and the signal component,corresponding to the frequency of 100Hz, resides intwo successive IMFs, IMF5 and IMF6. The same simu-lated multi-fault signal mixture was analyzed by the

Figure 1. A simulated multi-fault signal mixture mixed with

noise: (a) its temporal waveform; (b) its spectrum.

Wang et al. 5




enhanced EEMD. The local minima of the revised spec-tral coherences, �j, jþ1 (j¼ 1, 2, . . . , 9), are listed in Table1, where the locations of RSC local minima are identi-fied at two indices, p1¼ 3 and p2¼ 6.

According to the fusion rule defined by equation (6),three EIMFs obtained by using the enhanced EEMDare shown in Figure 3. Such decomposition resultsexactly exhibit true components embedded in the simu-lated signal, including the high-frequency transientcomponent and the low-frequency periodic components

which reside in EIMF1 and EIMF2, respectively.EIMF3 is a residue. The concept of the blind compo-nent separation is thus realized by the enhancedEEMD. The reason why EIMF2 shown in Figure 3(e)contains two discrete periodic frequencies, 50Hz and100Hz, is that the IMF5 obtained by EEMD inFigure 2(e) contains two such frequencies. Accordingto the characteristics of IMFs obtained by EEMD, theenhanced EEMD fuses the IMFs with similar spectralcharacteristics into one EIMF. The comparison of the

Figure 2. Intrinsic mode function (IMF)1–IMF8 obtained by ensemble empirical mode decomposition (EEMD) with NE¼ 30 and

LN¼ 0.1 for processing the simulated multi-fault signal mixture: (a)–(d) IMF1–IMF8; (e)–(h) frequency spectra of IMF1–IMF8.





decomposition results shown in Figures 2 and 3 indi-cates that the enhanced EEMD method is capable ofdecomposing a multi-fault signal into low-frequencyperiodic components and a high-frequency randomtransient component. The enhanced EEMD results inbetter decomposition performance, which has a reason-able explanation for the components embedded in themulti-fault signal mixture.

In order to investigate the effects of different ensem-ble numbers and noise levels on the decomposition ofthe same simulated signal mixture, the two parameterswere initialized to 100 and 0.3, respectively. EEMD wasfirstly applied to analyze the same simulated multi-faultsignal mixture. The obtained IMFs in time domain andfrequency domain are plotted in Figure 4, where theIMFs cannot exhibit the true components embeddedin the original simulated multi-fault signal mixture.The random transient component and the peri-odic component of 100Hz reside in several IMFs.

In order to extract these true components, the samesimulated multi-fault signal was processed by theenhanced EEMD. The minima of the RSCs �j, jþ1(j¼ 1, 2, . . . , 9) are shown in Table 2, where the loca-tions of RSC local minima are identified at the indices,ps¼ 3 and 5, (s¼ 1 and 2, respectively). In this case,three components consisting of a high-frequency tran-sient component and two low periodic components areproduced. IMF4 and IMF5 have the same frequency of100Hz, and are thus fused into EIMF2; only IMF6 hasthe frequency of 50Hz and is thus attributed to EIMF3according to equation (6). Therefore, two periodicEIMFs are obtained. Nevertheless, according to theconcept of BCS, the separation of periodic componentsand random transient component IMF1 from themulti-fault signal mixture is of great concern. Besides,for finely analyzing such periodic components shown inFigures 3 and 5, fast Fourier transform is capable ofdistinguishing them. Therefore, no matter whether two

Figure 3. Enhanced intrinsic mode function (EIMF)1–EIMF3 obtained by the enhanced ensemble empirical mode decomposition

(EEMD) with NE¼ 30 and LN¼ 0.1 for processing the simulated multi-fault signal: (a)–(c) EIMF1–EIMF3; (d)–(f) frequency spectra of

EIMF1–EIMF3.

Table 1. Revised spectral coherence (RSC) values obtained by the enhanced ensemble empirical mode decomposition with NE¼ 30

and LN¼ 0.1 for processing the simulated multi-fault signal mixture.

ps

p1¼ 3

(s¼ 1)

p2¼ 6

(s¼ 2)

RSC �1,2 �2,3 �3,4 �4,5 �5,6 �6,7 �7,8 �8,9 �9,10

Value 0.438 0.363 0.197 0.499 0.720 0.396 0.756 0.950 0.853

Wang et al. 7




Figure 4. Intrinsic mode function (IMF)1–IMF8 obtained by ensemble empirical mode decomposition (EEMD) with

NE¼ 100 and LN¼ 0.3 for processing the simulated multi-fault signal: (a)–(d) IMF1–IMF8; (e)–(h) frequency spectra

of IMF1–IMF8.


and LN¼ 0.3 for processing the simulated multi-fault signal.

ps

p1¼ 3

(s¼ 1)

p2¼ 5

(s¼ 2)

RSC �1,2 �2,3 �3,4 �4,5 �5,6 �6,7 �7,8 �8,9 �9,10

Value 0.518 0.417 0.211 0.880 0.186 0.402 0.731 0.899 0.818





periodic components are fused into one EIMF or sepa-rated into two individual EIMFs, periodic componentsobtained by the enhanced EEMD are reasonablyobtained. Finally, from the results shown in Figures 2

to 5, the EIMFs obtained by the enhanced EEMD haveclearer physical meaning than the IMFs obtained byEEMD for exhibiting the nature characteristics of theoriginal simulated signal mixture.

4.2. Case 2 – a real multi-fault vibrationsignal mixture

4.2.1. Data acquisition. To validate the enhanced EEMDand compare it with EEMD, a real vibration signal wascollected from an industrial traction motor. In this case,the industrial traction motor comprises a 250 kg rotorsupported by two rolling element bearings, and thetested bearing is located on the non-drive end.Figure 6(a) shows the schematic diagram (top view)of the traction motor. The running speed of themotor was 1498 rpm. Figure 6(b) shows the tractionmotor and the tested bearing, a single row deepgroove ball bearing (SKF 6215). A raw vibrationsignal was collected by an accelerometer that wasmagnet-mounted onto the bearing housing of themotor at the axial direction, which is circled inFigure 6(b). The sampling frequency of data acquisitionis 32.8 kHz.

4.2.2. Results and comparisons. There were two faultsexisting in the tested traction motor. One was a rotoreccentricity problem due to poor workmanship on the


(EEMD) with NE¼ 100 and LN¼ 0.3 for processing the simulated multi-fault signal: (a)–(c) EIMF1–EIMF3; (d)–(f) frequency spectra of

EIMF1-EIMF3.

Figure 6. A traction motor and the tested bearing (SKF 6215):

(a) Schematic diagram (top view) of the motor; (b) the traction

motor, the tested bearing and the accelerometer, whose position

is circled.

Wang et al. 9




clearance between the rotor and the stator. The otherwas a defect that occurred on the outer race of theinspected bearing. A raw vibration signal collectedfrom such a traction motor is shown in Figure 7(a)and its frequency spectrum is shown in Figure 7(b).

The frequency spectrum shown in Figure 7(b) indi-cates that the raw vibration signal has two main com-ponents, one component located in a low-frequencyband and another component located in a high-frequency band. The temporal waveform shown inFigure 7(a) indicates that the raw vibration signalis dominated by the low-frequency signal. It is diffi-cult to identify another signal component, which is a

high-frequency signal component in the raw signal, thatis to say, the high-frequency signal is completely over-whelmed and is difficult to be identified from the tem-poral waveform of the raw signal. Considering that theraw vibration signal is dominated by the low-frequencycomponent, the amplitude of the added white noise(a fraction, LN, of the standard deviation of thesignal to be analyzed) is suggested to be a largervalue (Wu and Huang, 2009; Guo and Tse, 2013) toeffectively perform the EEMD method.

Firstly, EEMD was applied to the vibration signalshown in Figure 7(a). The ensemble number and thenoise level were initially set to 30 and 0.2, respectively.Twelve IMFs are obtained from the decomposition ofthe raw signal by EEMD. The first four IMFs havelarger amplitudes than the other eight IMFs and theyare shown in Figure 8(a)–(d). The frequency spectra ofthe first four IMFs are shown in Figure 8(e)–(h). IMF3and IMF4 have the same discrete frequency of 920 Hz,which corresponds to the signal component generatedby the low-frequency motor component. The frequencyspectrum of IMF1 is centered at the frequency of12 kHz and indicates that IMF1 is the bearing signalextracted from the raw vibration signal. Although thesignal processing of EEMD successfully separates thelow-frequency component (residing in IMF3 andIMF4) from the high-frequency component (residingin IMF1), there is still mode mixing in the decompos-ition results, i.e. the low-frequency component inthe raw signal resides in two successive IMFs, IMF3and IMF4.

Figure 7. The raw vibration signal collected from the traction

motor: (a) in time domain; (b) in frequency domain.

Figure 8. Intrinsic mode function (IMF)1–IMF4 obtained by ensemble empirical mode decomposition (EEMD) with NE¼ 30 and

LN¼ 0.2 for processing the real multi-fault signal mixture: (a)–(d) IMF1–IMF4; (e)–(h) frequency spectra of IMF1–IMF4, in which IMF3

and IMF4 with the frequency of 920 Hz correspond to the periodic signal caused by the low-frequency motor component.





The enhanced EEMD was then applied to thesignal collected from the traction motor. The RSCsare shown in Table 3, where the locations of thelocal minima are identified at the indices, p1¼ 2,p2¼ 5, and p3¼ 7. Accordingly, four EIMFs are auto-matically generated and shown in Figure 9(a)–(d).Their corresponding frequency spectra are shown inFigure 9(e)–(h). As shown in Figure 9(e) and Figure9(f), EIMF1 and EIMF2 are the signal componentsgenerated by the bearing fault and the low-frequencymotor components, respectively. The signal compo-nent generated by the low-frequency motor compo-nents only resides in EIMF2, not in the successiveIMFs (IMF3 and IMF4) obtained by the EEMDmethod. Furthermore, EIMF2 has better shape simi-larity (higher linear relationship) with the raw vibra-tion signal than the main low-frequency component(IMF3) obtained by the EEMD method, of whichthe former is 0.88 and the latter is 0.79. Therefore,

the aim of the blind component separation for thedecomposition of the vibration signal mixture is wellrealized by the enhanced EEMD method.

To further investigate the performance of theenhanced EEMD and compare it with EEMD, foursets of different parameters were used to compare thedecomposition performance for the same real vibrationsignal shown in Figure 7(a). Figure 10 shows thedecomposition results obtained by EEMD andthe enhanced EEMD when the setting is the ensem-ble number NE¼ 30, and the noise level LN¼ 0.02.Figure 11 shows the results obtained by using the twomethods when setting the ensemble number NE¼ 30,and the noise level LN¼ 0.1. Figure 12 shows thedecomposition results obtained using the two methodswhen setting the ensemble number NE¼ 100, and thenoise level LN¼ 0.3. Figure 13 shows the decompos-ition results obtained using the two methods when set-ting the ensemble number NE¼ 1000, and the noise


and LN¼ 0.2 for processing the real multi-fault signal mixture.

ps

p1¼ 2

(s¼ 1)

p2¼ 5

(s¼ 2)

p3¼ 7

(s¼ 3)

RSC �1,2 �2,3 �3,4 �4,5 �5,6 �6,7 �7,8 �8,9 �9,10 �10,11 �11,12

Value 0.279 0.054 0.768 0.542 0.375 0.568 0.398 0.593 0.619 0.993 0.958


(EEMD) with NE¼ 30 and LN¼ 0.2 for processing the real multi-fault signal mixture: (a)–(d) EIMF1–EIMF4; (e)–(h) frequency spectra of

EIMF1–EIMF4.

Wang et al. 11




Figure 10. Comparison of the decomposition results obtained by ensemble empirical mode decomposition (EEMD) and the

enhanced EEMD with the parameters, NE¼ 30 and LN¼ 0.02 for processing the real multi-fault signal mixture: (a) Intrinsic mode

function (IMF)1–IMF4 obtained by EEMD; (b) Enhanced intrinsic mode function (EIMF)1-EIMF4 obtained by the enhanced EEMD.



function (IMF)1–IMF4 obtained by EEMD; (b) Enhanced intrinsic mode function (EIMF)1–EIMF4 obtained by the enhanced EEMD.







function (IMF)1–IMF4 obtained by EEMD; (b) Enhanced intrinsic mode function (EIMF)1–EIMF4 obtained by the enhanced EEMD.



function (IMF)1–IMF4 obtained using EEMD; (b) Enhanced intrinsic mode function (EIMF)1–EIMF4 obtained using the enhanced EEMD.

Wang et al. 13




level LN¼ 0.3. No matter which parameters were usedin EEMD, the phenomenon that the component of920Hz resides in two different IMFs can be found inthe decomposition results, i.e. IMF3 and IMF4. Theblind component separation cannot be well realizedbecause a single-scale signal is distributed in differentIMFs. Compared with EEMD, the enhanced EEMDmethod has better performance on extracting periodiccomponents and random transient components fromthe raw signal without the above mode mixing problem.Signal components in the raw signal are adaptivelydecomposed into the desired EIMFs including therandom transient components and the periodic compo-nents, that is to say, the signal component generated bythe faulty bearing always resides in EIMF1s shown inthe top diagrams of Figure 10(b), Figure 11(b), Figure12(b), and Figure 13(b), and the signal component withlow-frequency band caused by the motor fault residesin EIMF2s, as shown in the second diagrams of Figure10(b), Figure 11(b), Figure 12(b), and Figure 13(b).Table 4 shows the correlation coefficients between theraw vibration signal and the extracted low-frequencymotor signal, the latter of which is IMF3 obtained byEEMD or EIMF2 obtained by the enhanced EEMD.The results in Table 4 demonstrate that the extractedlow-frequency motor signal (EIMF2) obtained by theenhanced EEMD has higher correlation coefficient withthe raw vibration signal dominated by the low-frequency component of 920 Hz than the extractedlow-frequency motor signal (IMF3) obtained byEEMD. Therefore, the proposed enhanced EEMD suc-cessfully extracts both signal components generated bythe faulty bearing and the motor and has better decom-position performance than EEMD. The enhancedEEMD provides a solution to the problems of BCS.

5. Conclusions

Based on the concept of blind component separation,an enhanced EEMD was developed in this paper to

adaptively extract periodic components and randomtransient components from a single-channel vibrationsignal mixture. First, a multi-component signal wasdecomposed into some IMFs by using EEMD. Then,a revised spectral coherence was defined to quantify thelinear spectral dependence between two successiveIMFs. The closer the revised spectral coherence wasto one, the stronger the spectral dependence of twosuccessive IMFs was. Accordingly, a series of localminima of the revised spectral coherence were identi-fied. A fusion rule based on locations of these minimawas proposed to combine the IMFs with similar spec-tral characteristics into one enhanced IMF. The per-formance of the developed enhanced EEMD methodwere verified by using two vibration signal mixturesincluding simulated and real single-channel vibrationsignal mixtures. Experimental results demonstratedthat the developed method generates more satisfactorydecomposition results. By using the enhanced EEMD,periodic components and random transient compo-nents are adaptively extracted from a single-channelvibration signal mixture, respectively; whereas, byusing EEMD, one signal with a similar scale is distrib-uted in some successive IMFs, which makes the phys-ical meaning of IMFs unclear. As for one limitation ofthe BCS concept, it is only concerned with two subsets:periodic components and random transient compo-nents. In order to obtain finer results, fast Fouriertransform for periodic components and, time-frequencyanalysis and cyclic spectral analysis (frequency-frequency analysis) for random transient componentsare recommended to be used further.

Funding

This work was supported by two grants from the Research

Grants Council of the Hong Kong Special AdministrativeRegion, China (project number CityU_122513) and theFundamental Research Funds for the Central Universities(project number ZYGX2013J094). The authors thank the

anonymous reviewers for their valuable comments and sug-gestions for improving this paper.

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Table 4. Correlation coefficients between the identified low-

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