Bearings are widely used in rotating machines. Its health status is a significant index to indicate whether machines run continually or not. Detecting the bearing defects timely is very important for the maintenance decision making. In this paper, a novel bearing defects detection method based on EMD and Fractal Dimension is developed. The original data is decomposed into a set of intrinsic mode functions (IMFs) using EMD, and the fractal dimension of IMFs which contains bearing fault characteristic information are calculated, and these characteristic parameters are used to identify bearing fault types. The effectiveness of this methodology is demonstrated using experimental data

Chen Chen

Haiping Li

Hongzhi Teng

Jianmin Zhao

English

Vibroengineering PROCEDIA

 120 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. DEC 2016, VOL. 10. ISSN 2345-0533  
A novel method for detecting bearing defects based on 
EMD and fractal dimension 
Jianmin Zhao1, Haiping Li2, Hongzhi Teng3, Chen Chen4 
1, 2Mechanical Engineering College, Shijiazhuang, 050003, China 
3Lanzhou Equipment Maintenance Center, Lanzhou, 730060, China 
4Baicheng Ordnance Test Center of China, Baicheng, 137001, China 
2Corresponding author 
E-mail: 1jm_zhao@hotmail.com, 2hp_li0929@163.com, 3tenghzh@126.com, 4chench@126.com 
(Received 22 August 2016; accepted 23 August 2016) 
Abstract. Bearings are widely used in rotating machines. Its health status is a significant index to 
indicate whether machines run continually or not. Detecting the bearing defects timely is very 
important for the maintenance decision making. In this paper, a novel bearing defects detection 
method based on EMD and Fractal Dimension is developed. The original data is decomposed into 
a set of intrinsic mode functions (IMFs) using EMD, and the fractal dimension of IMFs which 
contains bearing fault characteristic information are calculated, and these characteristic parameters 
are used to identify bearing fault types. The effectiveness of this methodology is demonstrated 
using experimental data. 
Keywords: bearing, defects detection, EMD, fractal dimension. 
1. Introduction 
Researchers pay great attention to rolling element bearings because they are key components 
of mechanical systems and always play important roles in mechanical transmission. Proper 
functioning of mechanical systems depends on the smooth and normal running of the bearings. 
Therefore, bearing fault diagnosis is very important to prevent the machine failure and save costs. 
Generally, two techniques are commonly used to diagnose the bearing faults: model-based 
methods, and data-driven methods. In model-based methods, the goal of signal models (such as 
wavelet analysis [1], morphological theory [2], etc.) are to find the fault frequencies of different 
locations (like inner race, out race, ball, and cage). In practice, it is impossible to store all the 
vibration signals for vibration analysis. On the contrary, data-driven methods can diagnose the 
bearing faults using features extracted from the vibration signals without the demand to store a 
large amount of data. 
Boutros and Liang [3] developed a discrete Hidden Markov Model (HMM) to determine the 
fault location and classify the fault severity. In this paper, energies of five frequency bands were 
used as the fault features. Kang and Zhang [4] used a continuous HMM to detect the incipient 
faults. Like HMM, Support Vector Machine (SVM) [5-7] and Artificial neural network (ANN) 
[8, 9] were widely used in bearing fault diagnosis. In these models, fault features are the key 
factors affecting the model performance. Therefore, in bearing fault diagnosis, extracting good 
features is a more important thing than model selection. Recently, many researchers pay main 
attention to the fault feature extraction methods. For bearing fault diagnosis, the research goal is 
to enhance the impulsive contents in the signal and depress the noise. Many novel methods such 
as Spectral Kurtosis [10, 11], Minimum Entropy Deconvolution (MED) [11], etc. were developed 
for bearing fault diagnosis. Recently, an adaptive morphological gradient lifting wavelet was 
proposed in [12] for detecting the bearing defects. In this paper, the updating filters can be 
appropriately selected based on the local features in the signal. This enabled the fault characteristic 
frequency of bearing can be detected effectively. Morphology theory was used to diagnose the 
bearing fault and attracted considerable attention for a long time. Raj and Murali [13] proposed a 
new algorithm in which the structuring elements was selected based on kurtosis. This enabled the 
morphological operators more robust for bearing fault diagnosis.  
However, features extracted using above mentioned methods are very effective to determine 
A NOVEL METHOD FOR DETECTING BEARING DEFECTS BASED ON EMD AND FRACTAL DIMENSION.  
JIANMIN ZHAO, HAIPING LI, HONGZHI TENG, CHEN CHEN 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. DEC 2016, VOL. 10. ISSN 2345-0533 121 
the fault location under the assumption that training sets and test sets are collected form the same 
fault severity bearing produced by the same factory. In engineering practice, there will have many 
severity levels fault bearings waiting to be classified. Therefore, the training sets and test sets will 
be different. Some traditional feature extraction methods will be ineffective in this circumstance. 
In order to solve this dilemma, this paper developed a new fault diagnosis method based on 
Empirical Mode Decomposition and Fractal Dimension. 
The remaining sections of this paper are organized as follows. In Section 2, framework of the 
proposed method is introduced. Section 3 describes the experiment and applies the proposed 
method to bearing defects detecting. Finally, conclusions are given in Section 4. 
2. Framework of the proposed method 
2.1. Empirical mode decomposition 
Hilbert Huang Transform (HHT) is a new signal processing method which developed by 
Huang et al. [14, 15]. It contains two parts: EMD and Hilbert spectrum analysis method. As the 
kernel of HHT, EMD has been developed and widely used in fault diagnosis of rotating machinery 
recently. Using EMD, the complex signal can be decomposed into a set of complete, simple and 
almost orthogonal components named intrinsic mode functions (IMF). The IMFs represent the 
natural oscillatory mode embedded in the signal and work as the basis functions, which are 
determined by the signal itself. And the IMFs should satisfy the following two conditions: (1) In 
the whole data set, the number of extreme and the number of zero-crossings must either be equal 
or differ at most by one; and (2) At any point, the mean value of the envelope defined by local 
maxima and minima must be zero. Namely, local signal is symmetrical about the time axis. 
EMD is developed based on the assumption that any signal consists of many different IMFs. 
The procedures of decomposing a given signal ݔ(ݐ) to different IMFs can be categorized into the 
following steps. First, identify all the local extreme from the given signal and then connect them 
with a cubic spline line as the upper envelope ݈௠௔௫(ݐ). Second, repeat the first step for the local 
minima to produce the lower envelope ݈௠௜௡(ݐ). The upper and lower envelopes should cover the 
entire signal between them. Third, compute their mean as ݉ଵ(ݐ) and the difference between the 
signal ݔ(ݐ) and ݉ଵ(ݐ) is ℎଵ(ݐ): 
݉ଵ(ݐ) =
݈௠௔௫(ݐ) + ݈௠௜௡(ݐ)
2 , ℎଵ(ݐ) = ݔ(ݐ) −݉ଵ(ݐ). (1)
Ideally, after the sifting operation of Eq. (1), ℎଵ(ݐ) should be the first IMF. The construction 
of ℎଵ(ݐ) described above seems to satisfy all the requirements of IMF. However, during the 
practical process, the theoretical upper envelope ݈௠௔௫(ݐ) and lower envelope ݈௠௜௡(ݐ) are very 
difficult to calculate. In addition, any little inflection points of the monotonous signal can be 
transformed to new extrema. And these new extremas should be contained by the next sifting 
operation. To solve this dilemma, Huang et al. repeated the sifting process of Eq. (1) as many 
times as required to reduce the extracted signal to an IMF. Therefore, the fourth step is to repeat 
the sifting process by treating ℎଵ(ݐ) as the original signal as follows: 
݉ଵଵ(ݐ) =
݈ଵ௠௔௫(ݐ) + ݈ଵ௠௜௡(ݐ)
2 , ℎଵଵ(ݐ) = ℎଵ(ݐ) − ݉ଵଵ(ݐ). (2)
The sifting process will be repeated ݇ times until ℎଵ௞(ݐ) becomes a true IMF, that is: 
ℎଵ௞(ݐ) = ℎଵ(௞ିଵ)(ݐ) − ݉ଵ(௞ିଵ)(ݐ). (3)
Then, make ܿଵ(ݐ) = ℎଵ௞(ݐ), and can be seemed as the first IMF. Remove ܿଵ(ݐ) from the signal 
A NOVEL METHOD FOR DETECTING BEARING DEFECTS BASED ON EMD AND FRACTAL DIMENSION.  
JIANMIN ZHAO, HAIPING LI, HONGZHI TENG, CHEN CHEN 
122 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. DEC 2016, VOL. 10. ISSN 2345-0533  
ݔ(ݐ), namely: 
ݎଵ(ݐ) = ݔ(ݐ) − ܿଵ(ݐ). (4)
And generate the residue signal ݎଵ(ݐ). Treating ݎଵ(ݐ) as a new original signal and repeating the 
same sifting process above, the second IMF can be got. Similarly, a series of IMFs (ܿ௜(ݐ)  
(݅ = 1, 2,…, ݊)) can be obtained until the final residue ݎ௡(ݐ) is monotonous. Then the original 
signal ݔ(ݐ) can be reconstructed as: 
ݔ(ݐ) = ෍ ܿ௜(ݐ) + ݎ௡(ݐ)
௡
௜ୀଵ
. (5)
The IMFs ܿଵ, ܿଶ,…, ܿ௡ represent different frequency bands ranging from high to low. The 
frequency components contained in each frequency band are different and they change with the 
variation of the original signal ݔ(ݐ), and ݎ௡(ݐ) represents the central tendency of signal ݔ(ݐ). 
2.2. Fractal dimension 
The vibration signals of mechanical equipment always have non-linear. Fractal theory is an 
effective means to deal with this dilemma. As an essential parameter in fractal theory, fractal 
dimension (FD) has been widely used in many areas of science, including the capability of 
quantitative measurement for fractal characteristics of nonlinear systems and the ability of 
space-filling capacity measurement for signals. In mechanical fault diagnosis, the influences of 
nonlinear factors for mechanical vibration signals are different under diverse fault status. Fractal 
dimension describes the fault features of mechanical system and recognizes the fault status of 
mechanical device effectively. In the field of vibration signal processing, fractal box dimension 
and correlation dimension are two parameters that usually used by researchers. However, the 
calculate process of correlation dimension is very complicated. So this paper mainly studies the 
fractal box dimension. 
Assume that ܻ ⊂ ܴ௡, ܻ ≠ Φ, if there are ܰ(ߝ) hypercube can cover ܻ, then: 
ܦ஻(ܻ) = limఌ→଴
lnܰ(ߝ)
ln(1/ߝ). (6)
Eq. (6) is the definition of fractal box dimension. 
2.3. The bearing defects detecting method 
The flow chart of the method based on EMD and FD which proposed in this paper is shown in 
Fig. 1. It consists of the following procedural steps. (1) Obtain several IMFs by EMD 
decomposition. (2) Compute out the FD of each IMF. (3) Gain the detecting result. 
0 1 2 3 4 5 6-2
0
2
0 1 2 3 4 5 6-0.2
0
0.2
0 1 2 3 4 5 6-0.1
0
0.1
0 1 2 3 4 5 6-0.05
0
0.05
0 1 2 3 4 5 6-0.05
0
0.05
0 1 2 3 4 5 6
4
4
6
8
10 x 10
-3
0 1 2 3 4 5 6-5
0
5
 
Fig. 1. Flowchart of the proposed method 
A NOVEL METHOD FOR DETECTING BEARING DEFECTS BASED ON EMD AND FRACTAL DIMENSION.  
JIANMIN ZHAO, HAIPING LI, HONGZHI TENG, CHEN CHEN 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. DEC 2016, VOL. 10. ISSN 2345-0533 123 
3. Case study 
3.1. Experimental setup and data acquisition 
A mechanical test bed in the RCM laboratory of Mechanical Engineering College is used in 
this research to validate the effectiveness of the proposed method in this paper. The gearbox is 
driven by a 4 KW three phase asynchronous drive motor. In addition, the speed and torque sensors 
are used to acquire the speed and torque information, a magnetic powder brake is utilized to 
provide load. These components are connected by couplings, as shown in Fig. 2. The sampling 
frequency of this experimental system is 20 kHz. 
Bearings are defected after experiment. This paper chooses four states to analyzing. The four 
states are normal state, ball defect, inner face defect and outer face defect, as Fig. 3 shows. 
 
Fig. 2. The test rig 
 
Fig. 3. The states of bearings 
3.2. Results analysis and discussion 
The vibration signal acquired from the test rig is utilized to analyzing according to the method 
proposed in Section 2.3. Fig. 4 is the detecting results using the method proposed in this paper. It 
can be seen from the figure that the classification result is very obvious. 
1 2 3 4 5 6 71.65
1.7
1.75
1.8
1.85
Sample NO.
Fr
ac
tal
 D
im
en
sio
n
 
 
Normal State
Ball Defect
Inner Face Defect
Outer Face Defect
 
Fig. 4. Detection results using the proposed method 
A NOVEL METHOD FOR DETECTING BEARING DEFECTS BASED ON EMD AND FRACTAL DIMENSION.  
JIANMIN ZHAO, HAIPING LI, HONGZHI TENG, CHEN CHEN 
124 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. DEC 2016, VOL. 10. ISSN 2345-0533  
In order to validate the necessity of EMD, this paper analyzes the data but without processed 
by EMD and the results can be seen in Fig. 5. The detecting results of normal state, inner face 
defect and outer face defect are confused. So, the necessity of EMD can be validated. 
In order to validate the effectiveness of method proposed in this paper, a method based on 
wavelet and fractal dimension is utilized. It can be seen from Fig. 6 that all of the four states are 
confused seriously. So, the effectiveness of the method can be validated. 
1 2 3 4 5 6 71.72
1.73
1.74
1.75
1.76
1.77
1.78
1.79
1.8
Sample NO.
Fr
ac
tal
 D
im
en
sio
n
 
 
Normal State
Ball Defect
Inner Face Defect
Outer Face Defect
 
Fig. 5. Detection results without EMD 
1 2 3 4 5 6 71.685
1.69
1.695
1.7
1.705
1.71
Sample NO.
Fr
ac
tal
 D
im
en
sio
n
 
 
Normal State
Ball Defect
Inner Face Defect
Outer Face Defect
 
Fig. 6. Detection results using wavelet and FD 
4. Conclusions 
In this paper, the dilemmas of bearing defects detection are point out firstly. Then a novel 
method based on EMD and FD is proposed to solve this problem. In the proposed method, IMFs 
are obtained after the original vibration signal processed by EMD first. Then compute the fractal 
dimensions of IMFs. Finally, gain the detecting results through compare all the fractal dimensions 
of four states. A gearbox test rig is established and four kinds of states are utilized. Furthermore, 
the effectiveness of the proposed method and the necessity of EMD are validated by experimental 
data. 
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A novel method for detecting bearing defects based on EMD and fractal dimension

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A novel method for detecting bearing defects based on EMD and fractal dimension

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