MEV


 

 

J. Mechatron. Electr. Power Veh. Technol 07 (2016) 21-26 
 

Journal of Mechatronics, Electrical Power, 
and Vehicular Technology 

 
e-ISSN:2088-6985 
p-ISSN: 2087-3379 

 

 

 

www.mevjournal.com 
 

© 2016 RCEPM - LIPI All rights reserved. Open access under CC BY-NC-SA license. doi: 10.14203/j.mev.2016.v7.21-26. 
Accreditation Number: (LIPI) 633/AU/P2MI-LIPI/03/2015 and (Ministry of RTHE) 1/E/KPT/2015. 

APPLICATION OF EMPIRICAL MODE DECOMPOSITION METHOD 
FOR CHARACTERIZATION OF RANDOM VIBRATION SIGNALS 

 
Setyamartana Parman a, Edwar Yazid b,* 

aMechanical Engineering Departement, Universiti Teknologi Petronas 
Bandar Seri Iskandar, 31750 Tronoh, Perak, Malaysia 

bResearch Center for Electrical Power and Mechatronics, Indonesian Institute of Sciences 
Jl. Sangkuriang Komplek LIPI Gedung 20, 40135 Bandung, Indonesia 

 
Received 13 March 2016; received in revised form 27 April 2016; accepted 28 April 2016 

Published online 29 July 2016 
 

Abstract 
Characterization of finite measured signals is a great of importance in dynamical modeling and system 

identification. This paper addresses an approach for characterization of measured random vibration signals where 
the approach rests on a method called empirical mode decomposition (EMD). The applicability of proposed 
approach is tested in one numerical and experimental data from a structural system, namely spar platform. The 
results are three main signal components, comprising: noise embedded in the measured signal as the first 
component, first intrinsic mode function (IMF) called as the wave frequency response (WFR) as the second 
component and second IMF called as the low frequency response (LFR) as the third component while the residue is 
the trend. Band-pass filter (BPF) method is taken as benchmark for the results obtained from EMD method. 

 
Keywords: EMD; BPF; IMF; vibration signals. 

 
I. INTRODUCTION 

Modeling and system identification either 
based on input-output or output-only models 
require finite measured signals. Characterization 
of signals is a great of importance in selecting 
identification models. In practice, there are three 
main components in raw signals; namely noise, 
dynamical characteristics of the system and trend. 
Noise with certain level of SNR distributes in 
Gaussian and non-Gaussian functions. If the 
noise has Gaussian function, zero-mean with 
finite variance and statistically uncorrelated 
variables, then it is called as Gaussian white 
noise. This type of noise is embedded in mostly 
random vibration signals in addition to non-
Gaussian and non-white noise. Noise with high 
level of SNR has significant effect in time and 
frequency domains. In time domain, noise tends 
to lower the modeling accuracy. Further, in 
frequency domain, noise tends to hide the 
predominant frequency bands. Dynamical 
characteristics of the system cover the linear and 
non-linear behaviors. The latter appears in signals 

in terms of sub harmonics, super harmonics and 
frequency interactions [1-2]. If the behaviors 
change with respect to time, then the system is 
linear and non-linear time-varying systems. 
Identification models must accommodate the 
non-stationary of the system in terms of time-
varying model coefficients. Recent researches in 
this area can be found in [3-4].  

Trend is characterized as a long-term 
movement in signals. It has an upward or 
downward tendency and rate of change in a time 
series. In many cases, this trend leads to a direct 
component (DC) term in signals. These three 
main components must be characterized as a 
preliminary stage for modeling and system 
identification of system dynamic. The results can 
be taken as consideration for choosing the 
suitable model structure and model coefficient 
estimation method for identification models. 

This paper proposes the application of 
empirical mode decomposition (EMD) method in 
de noising, de trending, and decomposing the 
measured random vibration signals into the three 
main components. The method is applied in one 
numerical and experimental data. * Corresponding Author. Tel: +6222-2503055 E-mail: edwar.putra@gmail.com 

http://dx.doi.org/10.14203/j.mev.2016.v7.21-26


S. Parman and E. Yazid / J. Mechatron. Electr. Power Veh. Technol 07 (2016) 21-26 
 

 

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II. EMPIRICAL MODE 
DECOMPOSITION 

The essence of empirical mode decomposition 
is to decompose signal into its oscillatory mode, 
called intrinsic mode function (IMF). This is 
achieved by sifting process. The overall EMD 
algorithm has been well documented in reference 
[5-8]. Details are available in those references, 
but it is revisited in this paper for a more concise 
notation. A step by step procedure of EMD 
method can be summarized as follows: 
1. Identify all the local extreme, maxima and 

minima of, and then connect the local maxima 
and minima using the cubic spline to obtain 
the upper and lower envelope, respectively. 
Those envelopes should cover all the data of. 
Their mean is designated as, and the 
difference between 𝒚(𝒏)  and 𝒎𝟏  is defined 
by: 

𝐻1(𝑡) = 𝑦(𝑛) − 𝑚1 (1) 

 Ideally, 𝒉𝟏 should be an IMF if it satisfies two 
conditions: i) in all data of 𝒚(𝒏), the number 
of extrema and zero crossings must be either 
be equal or differ at most by one; and ii) at 
any point, the mean value of the envelope 
defined by the local maxima and minima is 
zero. 

2. If 𝒉𝟏 does not satisfy the conditions, set 𝒉𝟏 as 
the original data and repeat the process in step 
1 until the conditions are fulfilled and the first 
IMF is achieved.  

3. Residue is then subtracted from step 2, taken 
as original signal and sifting process is 
repeated to obtain another IMF. The process is 
repeated until 𝒎  IMF is obtained, where 
relationship between IMFs and the original 
data 𝒚(𝒏) may be expressed as: 

𝑦(𝑛) = ∑ 𝐶1 (𝑛) +  𝑟𝑚 (𝑛)
𝑚
𝑖=1   (2) 

 Term 𝐶𝑖(𝑛)  contains the IMFs of the 𝑦(𝑛) , 
from high to low frequency components. Each 
𝐶𝑖(𝑛)  also contains a different frequency 
component, while 𝑟𝑚(𝑛) is the residual which 
is the trend of the data or a constant. 
For an easy interpretation, all steps are 

depicted in Figure 1. The square dot (…) denotes 
the upper envelope while the dash line (---) 
denotes the lower envelope and the mean 
envelope is denoted with long dash dot line (-.-.). 
Since the residue (lower panel of Figure 1) is not 
a monotonic function, sifting process is then 
performed following step 1 until step 3. 

In practice, sifting process produces an IMF 
which contains more than one natural frequency 
component. This is called as a mode mixing, 

because of some drawbacks in the EMD 
algorithm. The mode mixing must be avoided for 
the purpose of this paper. Rilling et al. [9] 
proposed intermittent frequency to avoid the 
mode mixing. In their work, the intermittency is 
based on the period length to separate the signals 
into different modes. 

The criterion frequency is set as the upper 
limit of the period that can be included in any 
given IMF component, so that the resulting IMF 
will not contain any natural frequency 
components smaller than the intermittent 
frequency. However, the intermittent frequency 
as an additional criterion might not always 
guarantee the final expected results, since 
choosing the intermittent frequency is a 
subjective task. Rato et al. [10] solved this 
problem by proposing some modifications on the 
EMD algorithm. Their finding results show that 
some issues related to the drawbacks of EMD 
algorithm can be solved, such as mode mixing 
and tail effect. Hence, their EMD algorithm is 
adopted in this paper for decomposing the 
vibration signals. 

 
III. NUMERICAL DATA 

To validate the application of EMD method in 
filtering, detrending, and decomposing vibration 
signals, a deterministic discrete vibration signal is 
simply selected and described by Eq. (3), 

𝑦(𝑛) = 𝐴1 sin(2𝜋𝑓1𝑛) + 𝐴2 sin (2𝜋𝑓2𝑛), (3) 

where 𝐴 and 𝑓 are amplitude and frequency, 
respectively. The chosen system parameters for 
Eq. (3) are as follows: 𝐴1 = 1,  𝐴2 = 2,  𝑓1 =
8 𝐻𝑧 and 𝑓2 = 4 𝐻𝑧, respectively. 

The signal is corrupted with a Gaussian noise 
having SNR of 40 dB and a polynomial trend. 
The results are depicted in Figure 2. It is seen in 
Figure 2(a) that the noise can be accordingly 
extracted with SNR of 41.05 dB and has 
Gaussian distribution. Sinusoidal signal with 
respective frequency of 𝑓1 = 8𝐻𝑧 and 𝑓2 = 4𝐻𝑧 

 
 

Figure 1. Process of EMD method 



 S. Parman and E. Yazid / J. Mechatron. Electr. Power Veh. Technol 07 (2016) 21-26 
 

 

23 

can be also extracted with insignificant 
discrepancy between the actual result and that of 
EMD method (Figures 2(b) – 2(c)). Similar result 
also can be observed for extracted polynomial 
trend as shown by Figure 2(d). Overall results in 
Figure 2 show that the decomposition process 
results in signals from high frequency to low 
frequency. This finding result is also reported in 
the previous researches [7-8]. 

IV. EXPERIMENTAL DATA 
The experimental scheme is shown in Figure 3. 

Details of setup have been described in [4] and 
briefly summarized here. The model test was 
tested in the wave tank, excited with excitation 
function (random waves) and measured with 
wave probes. The motion response in horizontal 
plane was measured by an optical tracking 
camera. 

 
A. Raw Data Processing 

Raw time series of motion response as a 
random vibration signal is displayed in Figure 
4(a). By observing the motion response in Figure 
4(a), it can be seen that the amplitudes 
distribution appears to be drifted upward. Its 
probability density is unsymmetrical distributed, 
suggesting that the motion response is non-linear 
random waves and non-Gaussian-type. This 
result is validated by using normality test under 
Kolmogorov-Smirnov test, Lillie test, and Jarque-
Bera test. The motion response is also non 
stationary which is confirmed by Kwiatkowski-
Phillips-Schmidt-Shin test, Phillips-Perron test, 

 
(a) 

 

(b) 

 
(c) 

 
(d) 

Figure 2. EMD results for numerical data (a) noise; (b) 
𝑓1 = 8 𝐻𝑧; (c) 𝑓2 = 4 𝐻𝑧; (d) trend 

 
 

Figure 3. Experimental scheme 



S. Parman and E. Yazid / J. Mechatron. Electr. Power Veh. Technol 07 (2016) 21-26 
 

 

24 

and Augmented Dickey-Fuller test. As additional 
information, the motion response is non-white 
noise as validated with Ljung-Box Q-statistic. 

The signal is then converted into frequency 
domain with FFT length of 1024. It can be 
observed in Figure 4(b) that the motion response 
has two principal frequency peaks. The first peak 
(low frequency response, LFR) is hidden around 
the low frequency. The second peak (wave 
frequency response, WFR) is clearly around 
0.077 Hz, corresponds to the frequency of 
random waves. It is seen that the first peak is 
hidden and is difficult to be identified although 
the FFT length is higher than 1024 and only 
produces ripples. These results suggest that the 
signal of measured motion response is 
contaminated with noise and it might be due to a 
polynomial trend as proved by the next section. 
Modeling and system identification using this 
data will lead to a biased estimation. Hence, 
EMD method is applied for characterization 
purpose so that noise and trend can be 
accordingly extracted from the signal. 

 
B. Application of EMD Method 

Based on result in Figure 4(b), EMD method 
is applied to the raw signal of motion response in 
the Figure 4(a). This method simultaneously 
performs denoising, decomposition, and 

detrending in time domain. Results in time 
domain are then converted into frequency domain 
using FFT and depicted in Figures 5-8. The first, 
second and third components are successfully 
decomposed by using FFT length of 1024 for all 
components. As benchmark for the EMD method, 
band-pass filter (BPF) method is chosen. 

As seen in those figures, decomposition 
results can be classified into noise, two IMFs and 
a trend. Each can be interpreted as follows: 
i) The first component is identified as 

measurement noise embedded in the raw 
signal of motion responses confirmed by FFT 
result.  

ii) The first component is the first IMF, 
identified as WFR as confirmed by FFT result. 
The frequency is similar with the second peak 
in the lower panel of Figure 4. 

iii) The second component is the second IMF, 
identified as LFR as confirmed by FFT result. 
The frequency is around 0.005 Hz and looks 
clearer than the first peak in the lower panel 
of Figure 4. 

iv) The last component is the trend of the motion 
response, which is found as a polynomial 
trend. The polynomial trend obtained from 

 
(a) 

 
(b) 

Figure 4. Raw data of motion response (a) time series; (b) 
spectrum 

 
(a) 

 
(b) 

Figure 5. Decomposition result: noise (a) time series; (b) 
spectrum 



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25 

both methods has similar pattern where both 
trends increase with respect to time. 
When BPF method is applied as filter for the 

measured signal, the noise embedded in the 
signal is comparable with the first component, 
followed by the first and second IMFs. Minor 
differences are found between those two methods 
due to different resolution bandwidth. This 
finding result confirms that the EMD method 
may be used as an alternative filter and 
decomposition tool for noisy signals besides the 
conventional BPF method. Scale separation of 
EMD method is adjusted to decompose the signal 
into the WFR and LFR according to the results 
shown in Figure 4(b). With some trials, it is 
found that the best resolution for the separation 
scale is found to be around 7 - 10 dB. For BPF 
method, after several trials, it is found out that the 
suitable band pass is between 0.04 Hz and 0.1 Hz 
for the WFR and between 0.001 Hz and 0.03 Hz 
for the LFR. 

Based on results in Figures 5-8, statistics of 
the signal are performed and listed in Table 1. 
Overall, it is shown that the mean, variance 
skewness and kurtosis values decrease after 
signal are treated with EMD method. 

Table 2 shows the properties of signal before 
and after EMD method is applied. It can be seen 
that properties of signal are still preserved in this 

 
(a) 

 
(b) 

Figure 6. Decomposition result: the LFR (a) time series; (b) 
spectrum 

 
(a) 

 
(b) 

Figure 7. Decomposition result: the WFR (a) time series; (b) 
spectrum 

 
Figure 8. Decomposition result: trend 

Table 1. 
Basic statistics of experimental data 

Data Mean Variance Skewness Kurtosis 

Motion 
Response 

*0.054 
**0.728 

*1.31 
**1.33 

*0.256 
**0.335 

*2.89 
**3.16 

*denoised, decomposed and detrended,  
**raw 
 
Table 2. 
Properties of experimental data 

Data Property 

Motion 
Response 

*Non- 
Gaussian 

*Non-stationary 
*Non- white 

noise 
**Non- 

Gaussian 
**Non-stationary 

**Non- white 
noise 

*denoised, decomposed and detrended,  
**raw 



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26 

case, only its statistics change. It is noted that all 
the statistical tests are run under Matlab statistics 
toolbox. 

 
V. CONCLUSION 

EMD method is able to decompose random 
vibration signals in terms of noise, IMFs, and 
trend. BPF method as benchmark produces 
comparable results with minor differences due to 
different resolution bandwidth. Selection of pass 
band range for decomposition process indicates 
that the EMD method is more flexible than the 
BPF method. The noise and the trend can be 
included or excluded according to the purpose of 
identification process. As such, identification 
models in terms of model structure and model 
coefficient estimation method can be accordingly 
selected. As a recommendation, current work can 
be extended to the experimental modal analysis 
by combining the EMD method with respective 
modal analysis method. 

 
ACKNOWLEDGEMENT 

The authors are thankful to Cheng Yee Ng 
from Universiti Teknologi PETRONAS for 
providing the experimental data. 

 
REFERENCES 
[1] F. He et al., “Spectral analysis for 

nonstationary and nonlinear systems: a 
discrete time model based 
approach,“ Biomedical Engineering, Vol. 
60(8), pp. 2233-2241, 2013. 

[2] E. Yazid et al., ”Identification of slow drift 
motions of a truss spar platform using 
parametric Volterra model,“ Journal of 
Ocean Engineering, Vol. 109, pp. 654-668, 
2015.  

[3] E. Yazid et al., “Improving the modeling 
capacity of Volterra model using 
evolutionary computing methods based on 
Kalman Smoother adaptive filter,” Journal 
of Applied Soft Computing, Vol. 35, pp. 695-
707, 2015.  

[4] E. Yazid et al., “Identification of transfer 
functions from surge motion response of a 
semisubmersible platform using time-
varying NARX model,“ Journal of Applied 
Ocean Research, Vol. 54, pp. 53-66, 2016.  

[5] C. Guo et al., “Application of empirical 
mode decomposition to a Jeffcott rotor with 
a breathing crack,“ Journal of Sound and 
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[6] S.I. Mc. Neill, “Decomposing a signal into 
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339, 2016.  

[7] L.Lu et al., “Dominant feature selection for 
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[8] F.Jiang et al., “Fault identification of rotor 
bearing system based on ensemble empirical 
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[9] G. Rilling et al., “On empirical mode 
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[10] R.T. Rato et al., “On the HHT, its problems, 
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	I. Introduction
	II. Empirical Mode Decomposition
	III. Numerical Data
	IV. Experimental Data
	Raw Data Processing
	Application of EMD Method

	V. Conclusion
	Acknowledgement
	References