213 
 

 American Scientific Research Journal for Engineering, Technology,  and Sciences  (ASRJETS) 
ISSN (Print) 2313-4410, ISSN (Online) 2313-4402 

© Global Society of Scientific Research and Researchers  
http://asrjetsjournal.org/  

 

Rotating Machinery Signal Analysis Method Based on 

EEMD and Spectrum Correction 

Han Xiaojuna, Liu Xiaoyongb, Rong Fengc, Li Dechongd 

a,b,c,dElectronic and Information Engineering and Tianjin Key Laboratory of Optoelectronic Detection 

Technology and Systems, Tianjin Polytechnic University, 30387 Tianjin, China 
aEmail: hanxiaojun@tjpu.edu.cn 

bEmail: A_romance@163.com 
cEmail: 471913480@qq.com 
dEmail: dechongli@163.com 

 

 

Abstract 

Aiming at the problems of low accuracy of non-stationary signal spectrum analysis in rotating machinery 

vibration, this paper puts forward a kind of rotating mechanical signal analysis method based on EEMD and 

spectrum correction. Firstly, ensemble empirical mode decomposition (EEMD) is used to obtain the intrinsic 

mode functions (IMF) of the original signal; secondly, do correlation analysis for each IMF component and the 

original signal separately, and find out the IMF component with the largest correlation coefficient and calculate 

the frequency spectrum of the IMF; finally, spectrum correction algorithm is employed to get accurate spectrum 

for quantitative analysis. A practical vibration signal of rotor vibration platform is applied to testing the method 

of this paper, the EMD method and wavelet analysis method separately. The results show that the proposed new 

method can improve the precision of spectrum analysis for rotating mechanical signal significantly; therefore, it 

has a good application prospect. 

Key words: EEMD; spectrum correction; Intrinsic mode; signal analysis. 

1. Introduction  

At present, there are many methods for the analysis of vibration signal of rotating machinery, such as wavelet 

analysis, empirical mode decomposition (EMD), analytical modal method, envelope demodulation method, etc.  

------------------------------------------------------------------------ 

* Corresponding author.  

http://asrjetsjournal.org/


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For the wavelet analysis method [1], because of its own sensitivity to parameters, it is difficult to break down 

the characteristic signal adaptively, and the time-frequency resolution accuracy is not high, especially for the 

non-stationary signal. For the EMD method [2], although it can be adaptively decompose the basic model 

components from the time scale of the original signal itself, but the EMD method itself has such problems as the 

mode mixing, the end effect, the overshoot or the under impulse, which will affect the final analysis results. For 

analytical modal method [3], although the time used in analysis process is greatly reduced, the premise is to 

determine the signal in the various frequency components, so it is very difficult to realize fault diagnosis in 

mechanical systems with unknown characteristic frequency. 

The EEMD is a noise assisted data analysis method that Wu and Huang proposed. This method not only inherits 

the advantages of empirical mode decomposition but can effectively inhibit the impact of noise in the original 

signal to prevent aliasing mode, so as to separate the natural modal components with real physical meaning from 

the original signal. The different components corresponding to different characteristic frequency for some 

rotating machinery, and the fault will be accompanied by some kind of modulation phenomenon. In this paper, 

the EEMD method is used to separate the original signal adaptively. Then, the correlation analysis of each IMF 

component and the original signal is carried out to find out the largest correlation coefficient of the IMF 

component. If there is a failure in the mechanical equipment, the characteristic frequency of this component is 

inevitable. Finally, due to the limitation of frequency resolution in the frequency domain analysis, it is difficult 

to locate the frequency domain. In order to get accurate spectrum information, spectrum correction algorithm is 

used to correct the spectrum to improve the accuracy of the spectrum. 

2. EEMD and the principle of spectrum correction 

2.1. Principle of EEMD 

If the original signal is x(t), then the decomposition of the EMD algorithm can be expressed as 

1
( ) ( ) ( )

n

i n
i

x t c t r t
=

= +∑                                                 (1) 

Where ci (t) the intrinsic mode function (IMF), and rn (t) is the remainder of the decomposition. 

The EMD algorithm can decompose the signal into the IMF based on the time characteristics scale of the signal. 

But there are several problems, such as the computation of the overshoot and the impact of the extreme 

envelope, the mode mixing [4], the end effect, etc. And the phenomenon of mode mixing is the most serious, 

namely the IMF of EMD decomposition contains a number of time scale components. 

To overcome the problem of mode mixing, EEMD [5] was introduced based on the statistical properties of 

white noise, which shows that the EMD method is an effective self-adaptive dyadic filter bank when applied to 

the white noise, and the noise could help data analysis in the decomposition of EMD. When a signal is added to 

this uniformly distributed white noise background, the components in different scales of the signal are 

automatically projected onto proper scales of reference established by the white noise in the background. But the 



American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2016) Volume 26, No  1, pp 213-223 

 

215 
 

noise in each trial is different in separate trials. Thus it can be decreased or even completely cancelled out in the 

ensemble mean of enough trials. So after several empirical mode decomposition (EMD) trials, the ensemble 

mean is treated as the true solution and can effectively suppress the noise of the original signal [6].Then the 

mode mixing phenomenon can be well suppressed in EMD. 

EEMD decomposition steps are as follows: 

•  Initialize the number of trials in the ensemble, M, the amplitude of the added white noise, and the trial 

number m= 1; 

•  Perform the m-th trial on the signal added with white noise, 

a. Generate a white noise series with the initialized amplitude and add it to the investigated signal x (t), where 

nm (t) indicates the m-th added white noise series, and xm (t) represents the noise-added signal of the m-th trial; 

( ) ( ) ( )m mx t x t k n t= + ⋅                                               (2) 

b. Decompose the noise-added signal xm (t) into IMFs cjm (j=1,2,3…I) using the EMD method, where cjm 

denotes the j-th IMF of the m-th trial, and I is the number of IMFs; 

c. If the trial number is smaller than the number required, i.e. m<M ,then go to step(a) with m=m+1. Repeat 

steps(a) and (b) again, but with a new randomly generated white noise series each time; 

•  Calculate the ensemble mean jc
 of the M trials for each IMF,  

,
1 ( 1, 2,3... ; 1, 2,3... )

M

j m
m

j

c
c j I m M

M
== = =
∑                           (3) 

•  Report the mean jc
 of each of the I IMFs as the final IMFs. 

2.2. principle of spectrum correction 

Considering each IMF component of EEMD decomposition includes only a fundamental mode oscillation, and 

no complicated superposition of wave exists, energy centrobaric correction method is adopted to meet the 

accuracy requirements of the practical application of spectrum analysis. It is characterized by using discrete 

spectrum energy center of window function limitlessly approach origin of coordinate for discrete spectrum 

correction. Although the energy center method theory of discrete frequency correction are suitable for all 

symmetric window function[7], the Hanning window has a higher accuracy than the university. Due to the 

spectral energy centrobaric correction method can correct multi segment average spectrum directly, it is widely 

used in single frequency component signals or signals contain multiple frequency components with larger 

intervals for it is simple and with high accuracy [8]. 



American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2016) Volume 26, No  1, pp 213-223 

 

216 
 

The Hanning [9] window energy centrobaric method is used in this paper, and its basic principle can be 

expressed as 

( ) ( ) 0
n

i n
G x i x x i

=−

+ + =∑ �                                             (4) 

Where G (x) is the power spectrum function of the window function, and the formula (4) shows that the energy 

center of the Hanning window is close to the center of the energy. Considering power spectrum values of the 

side lobe of window function is very small, if let x [-0.5, 0.5], it can be used to accurately find the center 

coordinates of the winner valve by a few lines with a larger power spectrum according to the characteristics of 

the energy center, expressed as 

0 ( ( ) / )
n n

i s i
i n i n

x Y m i f N Y
=− =−

= +∑ ∑� �                            (5) 

Eq. (5) is the general formula of energy correction frequency, where x0 is main valve center, Yi is the i-th line 

spectrum value of the power spectrum, m is peak spectral line number of the main valve, and fs is sampling 

frequency, n is the spectral points. Let Kt be the energy recovery coefficient (Hanning window for 8/3), then the 

correction amplitude is 

n

t i
i n

A K Y
=−

= ∑�                                                               (6) 

Let the correction rate of the normalized correction frequency be ∆x, and it can be got by Eq. (5), 

0( / ) / ( / )s sx x mf N f N∆ = −                                  (7) 

According to the characteristic of the phase of the symmetric window, the correction of the phase is 

xϕ π∆ = −∆ �                                                                (8) 

According to Eq. (8), phase correction of the energy method is 

( / )k karctan I Rϕ ϕ= + ∆                                         (9) 

Where Ik and Rk are respectively the imaginary part and the real part of the FFT corresponding to the spectral 

line number k. 

3. Rotating machinery signal analysis method based on the EEMD and spectral correction  

Aiming at the non-stationary vibration signal of rotating machinery, there are many analysis methods, such as 



American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2016) Volume 26, No  1, pp 213-223 

 

217 
 

wavelet analysis method, empirical mode decomposition (EMD), analytical modal method, etc. But there are 

some drawbacks, which affect the final results of the analysis. In order to accurately locate the fault 

characteristic frequency in the spectrum analysis, this paper proposes a signal analysis method based on EEMD 

and spectrum correction. 

The specific steps of the method are as follows: 

•  The original vibration signal is decomposed by EEMD, and get IMFs; 

•  Correlation analysis between the IMF component and the original signal is obtained, and find out the 

IMF component with larger correlation coefficient and seek its frequency spectrum; 

( ) ( )2 2

2 2

X Y
XY

NR
X Y

X Y
N N

−
=

− −

∑ ∑∑

∑ ∑∑ ∑
                        (10) 

•  The IMF component spectrum with larger correlation coefficient is processed to get the correct 

spectrum; 

•  According to the frequency components and spectral amplitude of the corrected spectrum to determine 

the operating state of the rotating machinery, and find out whether there is a fault and the fault degree. 

Original signalOriginal signal

EEMD is used to obtain the  IMFi� i=1� 2�
3...n�

EEMD is used to obtain the  IMFi� i=1� 2�
3...n�

i<=n?i<=n?

Correlation analysis between the Ith  
IMF and the original signal

Correlation analysis between the Ith  
IMF and the original signal

Y� i=i+1�

Find out the IMF component with larger 
correlation coefficient and seek its frequency 

spectrum

Find out the IMF component with larger 
correlation coefficient and seek its frequency 

spectrum

According to the frequency and amplitude of the 
correction spectrum, the state or fault degree of 

equipment is analyzed

According to the frequency and amplitude of the 
correction spectrum, the state or fault degree of 

equipment is analyzed

EndEnd

b

Correction algorithm for 
spectrum

Correction algorithm for 
spectrum

 

Figure 1: Flow chart of signal analysis of rotating machinery 



American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2016) Volume 26, No  1, pp 213-223 

 

218 
 

4. Experiment and analysis 

The analysis object is a large rotor platform, and the original data is collected by BENTLY3500 vibration probe. 

Sampling frequency fs= 2k. The number of rotating shaft of the rotor platform is two, and the main and 

subordinate rotating shafts are N1 and N2, respectively, and their gear teeth are Q1=9, Q2=54. Set rotational 

speed R= 1285 r/min, so the theoretical calculation value of the N1 rotation frequency is f1=21.42 Hz, N2 

rotation frequency f2=3.57Hz, and meshing frequency f3=192.75Hz. To capture the 2.5s data from the 

acquisition data as the original data, and the original signal is shown in Figure. 2. 

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-150

-100

-50

0

50

100

150

Sampling sequence/N

A
m

pl
itu

de
/m

V

Original signal time domain waveform

 

Figure 2: Time domain waveform of the original signal 

Wavelet analysis method is used to get the original signal decomposition waveform and wavelet spectrum as 

shown in Figure. 3 and Figure. 4, respectively. Although the wavelet method can suppress the random noise and 

pulse interference, the final decomposition waveform distortion is serious. And  the method can not extract the 

true signal characteristics, which can be seen from the decomposition results. In addition, there are many 

frequency components and features are not related. This is due to the theoretical basis of the wavelet analysis is 

the Fourier transform, which cannot exactly describe the signal  whose frequency changes with time. So in the 

analysis of non-stationary signals, it is easy to produce false signals and false frequency and other faults. 

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-20

0
20

d1

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-20

0
20

d2

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-50

0
50

d3

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-50

0
50

d4

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-100

0
100

d5

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-200

0
200

d6

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-100

0
100

d7

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-100

0
100

d8

Sampling sequence/N

 

Figure 3: Wavelet decomposition of the original signal 



American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2016) Volume 26, No  1, pp 213-223 

 

219 
 

0 50 100 150 200 250
0

5

10

15

20

25

30

35

40

X: 22.8
Y: 1.264

Wavelet spectrum

Frequency/Hz

A
m

pl
itu

de
/m

V

 

Figure 4: Wavelet spectrum 

Using EMD to decompose the signal, and obtain 9 IMF components and one remainder. The decomposition 

waveform is shown in Figure. 5. 

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-50

0
50

im
f1

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-100

0
100

im
f2

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-200

0
200

im
f3

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-100

0
100

im
f4

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-50

0
50

im
f5

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-20

0
20

im
f6

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-10

0
10

im
f7

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-10

0
10

im
f8

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-5
0
5

im
f9

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-15
-10
-5

re
s

Sampling sequence/N

 

Figure 5: Results of EMD decomposition of the original signal 

The results from the EMD decomposition can hardly see any significant signals. After the correlation analysis of 

the IMF components and the original signal, the correlation coefficients of each IMF are obtained and is shown 

in table 1. It can be seen from the table that the correlation coefficient is larger for the imf3 component, and its 

frequency spectrum is obtained. The results are shown in Figure. 6. Due to the impact of the intermittent signal 

or noise, the mode mixing is generated when the EMD is decomposed, and the useful signal is submerged in 

other time scale components. And all these factors make the imf3 spectrum contains more frequency 



American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2016) Volume 26, No  1, pp 213-223 

 

220 
 

components, and make it difficult to distinguish the characteristics of signal frequency. 

Table 1: Correlation coefficients of each component after EMD decomposition 

component imf1 imf2 imf3 imf4 imf5 imf6 imf7 imf8 imf9 

correlation coefficient 0.0116 0.0225 0.9219 0.2795 0.0063 0.1086 0.0265 0.0623 0.0606 

 

0 50 100 150 200 250
0

5

10

15

20

25

30

35

40

45

X: 22
Y: 3.599

imf3 spectrum

Frequency/Hz

A
m

pl
itu

de
/m

V

 

Figure 6: The IMF component spectrum with the larger correlation coefficient in EMD decomposition 

The original signal is analyzed and processed by the method proposed in this paper. Firstly, the original signal is 

decomposed by EEMD and obtained 12 IMF components and a remainder, and the results are shown in Figure. 

7. It can be seen from the EEMD decomposition results that IMF1 and IMF6 have complete time scale, and they 

all have certain physical meanings. In order to make a quantitative analysis, the correlation analysis between the 

EEMD decomposition and the original signal is done, and the results are shown in Table 2. 

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-200

0
200

IM
F1

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-10

0
10

IM
F2

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-10

0
10

IM
F3

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-50

0
50

IM
F4

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-100

0
100

IM
F5

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-200

0
200

IM
F6

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-20

0
20

IM
F7

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-20

0
20

IM
F8

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-10

0
10

IM
F9

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-5
0
5

IM
F1

0

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-5
0
5

IM
F1

1

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-1
0
1

IM
F1

2

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-40
-20

0

RE
S

Sampling sequence/N

 

Figure 7: Results of EEMD decomposition of the original signal 



American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2016) Volume 26, No  1, pp 213-223 

 

221 
 

Table 2: Correlation coefficients of each component after EEMD decomposition 

compone

nt 
IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 IMF7 IMF8 IMF9 

IMF1

0 

IMF1

1 

IMF1

2 

correlati

on 

coefficie

nt 

0.989

6 

0.002

7 

0.001

3 

0.015

7 

0.106

9 

0.895

9 

0.493

2 

0.045

2 

0.172

2 

0.117

2 

0.066

5 

0.067

9 

 

Find the spectrum of the component with larger correlation coefficient, as shown in Figure. 8, whose energy is 

mainly concentrated in 0Hz, 21Hz, 43Hz, 64Hz, 86Hz. The 21Hz spectrum space contains the largest energy, 

and 0 Hz represents the DC component of the original signal, so the 0Hz component is not considered. And then 

the spectrum correction is carried out on the basis of Fig. 6. The results are shown in Figure. 9. 21.34 Hz, 42.72 

Hz, 64.05 Hz and 85.44 Hz components are obtained, and corresponding to the fundamental frequency, two 

times frequency, three times frequency and four times frequency respectively. Thus we can know that the 

rotation frequency of the main shaft of the rotor platform is 21.34Hz (0.16 Hz deviation is produced by the 

motor drive and other factors). Hence there is a fault in the main shaft of the rotor platform, and the degree of 

fault can be quantified by the amplitude of the characteristic frequency in the frequency spectrum. In practical 

application, a threshold value can be set, and the fault or fault severity can be judged if the amplitude exceeds 

the threshold value in the frequency spectrum. 

0 50 100 150 200 250
0

200

400

600

800

1000

1200

1400

1600

1800

X: 43
Y: 65.94

Frequency/Hz

A
m

pl
itu

de
/m

V

The figure of frequency and amplitude before correction

X: 21
Y: 1691

X: 64
Y: 31.82

X: 86
Y: 16.86

 

Figure 8: The spectrum of IMF1 component with a larger correlation coefficient in EEMD decomposition 



American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2016) Volume 26, No  1, pp 213-223 

 

222 
 

0 50 100 150 200 250
0

10

20

30

40

50

60

70

80

90

100

X: 21.34
Y: 89.24

Frequency/Hz

A
m

pl
itu

de
/m

V

The figure of frequency and amplitude after correction

X: 42.72
Y: 17.04 X: 64.05

Y: 11.38

X: 85.44
Y: 9.734

 

Figure 9: The spectrum after spectrum correction 

In summary, the analysis results of different spectrum analysis methods are shown in Table 3. 

Table 3: Spectral analysis results of different methods 

 Theoretical value /Hz Measured value /Hz Absolute error /Hz 

Wavelet method 

21.42 

22.8 1.38 

EMD method 22 0.58 

Paper method 21.34 0.08 

 

5. Conclusion 

Aiming at the problem that the spectrum analysis of the non-stationary signal is not high, this paper proposes a 

new analysis method of rotating machinery signal based on EEMD and spectrum correction after analyzing the 

principle of EEMD and spectrum correction. The method proposed in this paper, the EMD method and wavelet 

analysis method are respectively used on the same large rotor system vibration signal for processing and testing, 

and the results show that the new method can accurately analyze the characteristic frequency of the original 

signal, and the results can accord with the actual circumstance. Compared with wavelet analysis and EMD, the 

frequency components of the vibration signal spectrum obtained by this paper proposed method are more clear, 

and the spectral accuracy is significantly improved. 

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