Journal of Robotics, Networking and Artificial Life, Vol. 5, No. 1 (June 2018) 10–14___________________________________________________________________________________________________________Advanced Rolling Bearing Fault Diagnosis Using Ensemble Empirical Mode Decomposition,Principal Component Analysis and Probabilistic Neural Network
Caixia Gao*, Tong Wu, Ziyi Fu

School of Electrical Engineering and Automation, Henan Polytechnic University
Jiaozuo 454000, China
E-mail: gcx81@126.com, 249419152@qq.com, Fuzy@hpu.edu.cn
http://www.hpu.edu.cn/www/index.html

Abstract
Aiming at the problem that the vibration signal of the incipient fault is weak, an automatic and intelligent fault
diagnosis algorithm combined with ensemble empirical mode decomposition (EEMD), principal component
analysis (PCA) and probabilistic neural network (PNN) is proposed for rolling bearing in this paper. EEMD isapplied to decompose the vibration signal into a sum of several intrinsic mode function components (IMFs), which
represents the signal characteristics of different scales. The energy, kurtosis and skewness of first few IMFs areextracted as fault feature index. PCA is employed to the fault features as the linear transform for dimension
reduction and elimination of linear dependence between the fault features. PNN is applied to detect rolling bearing
occurrence and recognize its type. The simulation shows that this method has higher fault diagnosis accuracy.
Keywords: Rolling bearing, fault recognition, ensemble empirical modal decomposition, principal component
analysis, probabilistic neural network.

method combined with LMD to extract fault
information. In Ref.4, discrete wavelet transform isproposed to extract the feature, but the adaptability ofwavelet analysis is not as strong as EMD and EEMD
when dealing with non-stationary signals. It can be seenfrom the above bibliographies that how to better distill
the fault features from non-stationary and noisy bearing
signal is the key to fault diagnosis of rolling bearings.
In the operation of rotating machinery, the vibration
signal usually has non-stationary and nonlinearity
characteristics, so it is difficult to obtain good effect infeature extraction by using traditional Fourier transformas the theoretical basis. And the collected signal isaccompanied by a certain degree of noise. Therefore,EEMD is applied to decompose the vibration signal intoa sum of several intrinsic mode function components

1. Introduction
Rolling bearings are common and vulnerable parts inrotating machinery. According to statistics, 30% of therotating machinery faults are caused by the bearing
failure, so the condition of the rolling bearing is closely
related to the operation of the machinery, and it is ofgreat importance to detect and diagnose the fault ofrolling bearings.1
At present, there are many scholars studying thefault diagnosis of rolling bearings. The Ref.1 uses amethod of combining EMD decomposition withsingular value difference spectrum. The Ref.2 uses thefast independent component analysis to extract the fault
feature, but it does not extract the fault information indepth, and the Ref. 3 uses the wavelet packet de-noising

Corresponding author: Caixia Gao (1981- ), female, associate professor, master tutor, fault diagnosis research. Tel (Tel.): 0391-3987580. E-mail:gcx81@126.com.
*Copyright © 2018, the Authors. Published by Atlantis Press.
This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
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Journal of Robotics, Networking and Artificial Life, Vol. 5, No. 1 (June 2018) 10–14___________________________________________________________________________________________________________(IMFs), which represents the signal characteristics ofdifferent scales. The energy, kurtosis and skewness offirst few IMFs are extracted as fault feature index. Then
PCA is employed to the fault features as the linear
transform for dimension reduction and elimination of
linear dependence between the fault features. Finally,
PNN is applied to detect rolling bearing occurrence andrecognize its type, the generalized algorithm for rolling
bearing is shown in Fig1.

Ref.1.Use EMD to decompose the bearing signal, taking
a number of high-frequency components andabandoning the last several IMF components which are
generally low-frequency noise-based.1
2.2. The principle of EEMD
The EEMD algorithm is a new signal decomposition
method based on the traditional EMD algorithm. In
order to overcome the algebraic phenomenon ofabnormal events (such as pulse interference) intraditional EMD decomposition, the ensemble empiricalmode decomposition algorithm, that is EEMD algorithm,
is proposed. In the traditional EMD decomposition ofthe signal, the algebraic generation of the signal isrelated to the selection of the extreme value of the signal.
If the interval of the extreme points of the signal is not
uniform, the fitting error of the upper and lower
envelope will occur, resulting in mode mixing. By
adding different amplitude of the Gaussian white noise
to the signal to change the extreme value of thecharacteristics of the signal, offsetting the IMF and thewhite noise, the EEMD algorithm can get accurate IMF
and eliminate the noise, which can better suppress thealienation of the abnormal event pattern and the inherent
pattern of signal vibration and better highlight the real
signal characteristics.
The specific decomposition process changes to thefollowing steps：(i) Adding a given amplitude white noise to theanalysis signal X (t ) and then normalizing the signal。
(ii) EMD decomposition of the signal after adding
white noise.
(iii) Repeating the above two steps N times, eachtime adding random white noise sequence.
(iv) Average calculating operation for thecorresponding decomposed ensemble IMF to offset theeffect of multiple Gaussian white noise on the real IMF.
Finally, the IMF component and the remainder of theEEMD decomposition can be obtained.
Use EEMD to decompose the bearing signal,
taking a number of high-frequency components andabandoning the last several IMF components which aregenerally low-frequency noise-based [1].

Start
Vibration
signalDecomposition
vibration signals
using EEMD
Extracting Features fromIMFs
Reducing Dimension UsingPAC
Recognizing Fault Type
Using PNN
Start

Fig.1. Rolling bearing fault diagnosis algorithm

2. Fault Feature Extraction Using EEMD
Empirical Mode Decomposition (EMD) is a new
method for analyzing non-linear and non-stationary timeseries proposed by Huang N.E. in 1998.
2.1. The principle of EMD
EMD is a self-adapting time-frequency analysis
method, which is different from the wavelet analysis inthat is that there is no basis function system, that is,when analyzing the series, the original sequence isdivided into a limited number of intrinsic functions
rather than with certain basis functions, and eachcomponent shows uniqueness and reflects theinformation at each unique time scale in the signal. The
decomposed signal is a stationary signal. In essence,EMD is a method to turn non-stationary signals intostationary ones. The main calculation procession sees

2.3. Multi-feature Extraction Using EEMD
The method of extracting characteristic parametersof signals with multiple characteristic parameters is11

Journal of Robotics, Networking and Artificial Life, Vol. 5, No. 1 (June 2018) 10–14___________________________________________________________________________________________________________

improved on the basis of intrinsic mode energy method.
As a single energy method is the overall energy
calculation for each component of IMF, it may lose
some useful fault information for the extracted featuresignal. Therefore, this paper adds two feature quantities,
namely, the kurtosis and skewness of the signal5.
The kurtosis index is a dimensionless parameter
which bears no relationship to the speed, size and loadof the bearing and is particularly sensitive to theimpulse signal, so it is quite suitable for pitting damage
fault of the surface. Generally the normal bearing
kurtosis index is close to 3.
The skewness index reflects the asymmetry of thevibration signal, indicating the degree of deviation of
the center of the signal probability density function fromthe standard normal distribution and reflecting theasymmetry of the signal amplitude distribution
compared with its ideal mean. Except the machinerywith quick-return characteristics, if there is friction or
collision in a certain direction, it will cause theasymmetry of the vibration waveform so that the degreeof bias index increases.
They are calculated as follows:nEnergy： Ei 1

(1)
Kurtosis： K(2)

nn 1i 11nn 1i 1(3)3. Reducing Feature Dimensions Using PCA
In the process of modern production industry, generally
a lot of process variables will be collected to detect andcontrol the process. Principal component analysis is acommonly used analytical method in multivariate
statistical analysis, and there’s a fundamental difference
between this method and the mentioned Fourier system
based method or other time-domain and frequencydomain analysis methods. It is characterized by thesimultaneous processing of multiple dimension
variables data from which finds the hidden statisticalinformation characteristics and can eliminate thecorrelation between different dimensions well, so that a
number of related variables can be turned into a few
independent variables, that is, a new feature index ofless dimensions rather than the original feature index
reflects most of the information that should be originallyavailable. And the principal component analysis caneliminate the noise and redundancy in the fault data andimprove the accuracy. The main calculation procession
sees Ref. 6.

X i21

Skewness： K

A sum of several intrinsic mode function
components of the fault vibration signal are obtained
after EEMD decomposition, their frequencies arearranged from high to low, the first few IMFs which aregenerally high-frequency are employed for featureextraction, the last several IMFs which are generally
low-frequency noise-based are abandoned, so the first n
IMF components are taken after EEMD decomposition,then the number of dimension of the final extraction ofthe feature index is 3n.

(XiX )4 /4(XiX )3 /3The flow chart of multi-feature extraction is shownin Fig2.

4. Fault Type Recognition Using PNN
PNN was first proposed by Dr. Specht, and it can get
the Bayesian optimal results when used for patternclassification. It has the following advantages: ① Easy
for training with fast convergence; ② strong faulttolerant characteristics; ③ network nodes are up to thenumber of training samples and the number of patterns
to decide.
The structure of the PNN network is divided into
four layers, namely the input layer, hidden layer, sum oflayers and the output layer. The raw data is processed asa PNN diagnostic model after a series of previousprocessing. The main calculation procession sees Ref. 7.

signalEEMD

IMF1

E1

K1

S1

IMF2

E2

K2……

S2……

IMFn

En

KnSnFig.2. The flow chart 1 of multi-feature extraction.

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Journal of Robotics, Networking and Artificial Life, Vol. 5, No. 1 (June 2018) 10–14___________________________________________________________________________________________________________

5. Simulation and the experiment analysis

147.5

47.5

5.1. Description of the experiment

23

24.5
7.6

72.0
79.6

4

4.8

84.4

56

4.5
3.9

88.9
92.8

7395.8In order to verify the effectiveness of the diagnostic
method in this paper, the data is taken from theDepartment of Electrical Engineering and Computer
Science, Case Western Reserve University, USA.8
The analyzed data is obtained with the motor in 2
horsepower, and there are the inner ring fault data, outerring fault data, rolling element failure data, and normal
bearing data. The above four kinds of data form theoriginal data of this experiment. Select 1024 data as agroup from the original data and 40 groups for eachstate from the above four states, totally 160 groups ofdata, of which 10 groups randomly selected for eachstate as the training group and the remaining 30 groups
as the test group.

In general, the cumulative contribution rate of themain component analysis up to 85% can keep most of
the original signal information. 6As can be seen from theabove table, starting from the 7th main element, thecumulative contribution rate reaches 95.8%, meeting therequirement of dimensionality reduction for the original
data index.
5.3. Pattern recognition using PNN
This paper is based on the EEMD intrinsic mode energy
method to improve. First, the energy of the first 5 IMF
is calculated and then input into PNN, and the
diagnostic accuracy is 85.33%; and then adds the othertwo features to form a 15-dimensional feature index,
enter the PNN, the diagnostic accuracy is 91%. It can beconcluded that after adding two features, PNN will
increase the diagnostic accuracy.
Finally, the data analyzed by the principal
component analysis are input to the PNN in turn forpattern recognition.

5.2. Feature extraction and principal component
analysis
In this experiment, EEMD is used to decompose theabove-mentioned vibration signals, and then each IMF
component is calculated for the energy, kurtosis andskewness. Next, PCA method is used to reduce thedimension, and finally input into PNN for stateclassification. The classification flow chart is as follows.

signalEEMD

Multifeature

Principal
component
analysis

PNN

resultFig.3. Troubleshooting flowchart.

Five IMF components are obtained after EEMD foreach group of data, forming five-dimensional data, andthen calculate each IMF component for the energy,
kurtosis, and skewness, getting 15-dimensional data toform a multi-feature data index.
Then, the principal component analysis is performedon the multi feature data index, and the following
principal component analysis table 1 is obtained
Fig.4. The number of different principal components todiagnose the correct rate.

Tab.1. Part of the main component contribution table.
Main component
numberContribution
rate %

Cumulative
contribution
rate %

As can be seen from the figure above, when thenumber of principal components reaches five, the13Journal of Robotics, Networking and Artificial Life, Vol. 5, No. 1 (June 2018) 10–14___________________________________________________________________________________________________________correctness rate reaches 95%, and the cumulative
contribution rate at this time is 88.9%. Then as thenumber of principal components increases, thecumulative contribution rate increases. The correct rateof accuracy fluctuates about 95%. Therefore, taking fivemain elements is the final solution, which can ensure theaccuracy and efficiency. The comparison of the threemethods is shown in Table 2.

(iii)When the principal component analysis is used
to reduce the dimensionality of the data, the higher thecontribution rate is, the higher the accuracy is, but it
remains within a certain range after reaching a certain
limit.
Acknowledgements
Fund Project: National Key Research and Development
Program (2016YFC0600906)

Tab.2. Comparison of three methods for correct diagnosis.
MethodAccuracy

Energymethod85.33%

Multi - feature
method91%

References

Multi - feature
PCA
95%

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diagnosis method based on EMD and difference spectrum
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3. W. Sun, B. S. Xiong and J. P. Huang. Fault diagnosis of arolling bearing using Wavelet packet de-noising andLMD, Vib. Shock. 31(18) (2012) 153-156.
4. J. Chebil, M. Rairi and N. Bushikhah. Signal analysis ofvibration measurements for condition monitoring ofbearings, Australian J. Basic and Applied Sci. 5(1) (2011)70-78.
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8. K. A. Loparo ． Bearings Vibration Data set, (Case
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It can be seen that the accuracy of the energy
method is low, and the accuracy is improved effectively
when two features are added. It is thus obvious that thekurtosis and skewness of vibration signal can be used tomake up the deficiency of energy feature in fault
information completeness. Finally, on the basis ofmulti-feature method, the PCA is processed to further
improve the fault diagnosis accuracy, which proves that
PCA can effectively remove the noise and redundancy
in the vibration signal.
6. Conclusion(i) The proposed feature index combined with theenergy, kurtosis and skewness of first few IMFs, canrecognize the fault type of rolling bearing.
(ii) The feature index of the principal component
analysis has higher accuracy rate than that of the featureindex without main component analysis, whichindicates that the principal component analysis caneliminate the redundancy and noise in the information toa certain extent.

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