Bearings Prognostics based on Blind Sources Separation and Robust
Correlation Analysis
Tarak Benkedjouh
1
, Noureddine Zerhouni
2
and Said Rechak
3
1
EMP, Laboratoire M´ecaniques des Structures, Bordj Elbahri Algiers, Algeria
2
FEMTO-ST Institute UMR CNRS 6174, UFC/ ENSMM/ UTBM/ AS2M Dept, 24, rue Alain Savary, Besanon, France
3
ENP, Laboratoire G´enie M´ecanique, Elharrach Algiers, Algeria
Keywords:
Blind Sources Separation, Empirical Modes Decomposition, Robust Correlation, Prognostics, bearings, RUL.
Abstract:
Prognostics and Health Management (PHM) for condition monitoring systems have been proposed for pre-
dicting faults and estimating the remaining useful life (RUL) of components or subsystem. For gaining impor-
tance in industry and decrease possible loss of production due to machine stopping, a new intelligent method
for bearing health assessment based on Empirical mode decomposition (EMD) and Blind Source Separation
(BSS). EMD is one of the most powerful time-frequency analysis decompose the signal into a set of orthogonal
components called intrinsic mode functions (IMFs). BSS method used to separate IMFs of one-dimensional
time series into independent time series. The health indicator based on the robust correlation coefcient is
proposed based on a weighted average correlation calculated from different combinations of the original data.
The correlation coefficients between separated IMFs used to estimate the health of bearing; The correlation
coefficient used for comparison between the estimated sources with differents degradation levels. The corre-
lation coefficient values are then fitted to a regression to obtain the model for Remaining Useful Life (RUL)
estimation. The method is applied on accelerated degradations bearings called PRONOSTIA. Experimental
results show that the proposed method can reflect effectively the performance degradation of bearing.
1 INTRODUCTION
Bearings performance degradation assessment plays
an important role in various rotating machines fault
prognostics to avoid catastrophic accidents (Yan,
2015). Several researches have been made to develop
methods for machine condition monitoring. Qiu et al
(Qiu et al., 2003) used using Self OrganizingMap and
neural network for developing a robust technique for
performance degradation assessment of REB. Liao et
al (Liao and Lee, 2009) used Support vector machine
based on wavelet packet analysis and Gaussian mix-
ture model for assessment of machine performance
degradation. Xiaoran et al (Zhu et al., 2013) proposea
method based on support vector data description; The
proposed solution can effectively reflect the health of
bearing’s, some limitation of this technique for gener-
alized performance the problem for different operat-
ing condition.
For improving prognostics it is necessary that the
collected raw signals from differentsensors be ’clean’
enough that small changes in in the raw signal can re-
flect the severity defect; But this problem is compli-
cated in complex machines because the combination
between different sources measurementsuch as vibra-
tions or acoustics effect the signal energy produced
by different components in the machine in addition to
the noise. In this area Blind Source Separation (BSS)
proposed in the literature for recovering the various
independent sources exciting the system given only
the outputs of the system (S´anchez A, 2002). BSS
has become a mature field of research with many
technological applications in areas such as medical,
image processing, communications, ...etc (Naik and
Wang, 2014). Several researches for machines con-
dition monitoring proposed in this area; Roan et al
(Roan et al., 2002) Proposed an application for in-
formation maximisation based on BSS algorithm for
tooth failure detection and analysis. Serviere et al
(Serviere and Fabry, 2004) proposed a new estima-
tor of the whitening matrix and the signal subspace
for the separation of rotating machine signals.
Recently, Haile et al (Haile and Dykas, 2015) ap-
plied the blind source separation for demixing vi-
bration signals from defective bearings, by compar-
ing five well-known algorithms using experimental
658
Benkedjouh, T., Zerhouni, N. and Rechak, S.
Bearings Prognostics based on Blind Sources Separation and Robust Correlation Analysis.
DOI: 10.5220/0006472006580663
In Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2017) - Volume 1, pages 658-663
ISBN: 978-989-758-263-9
Copyright © 2017 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
data collection from degraded and healthy bearings.
Theodore et al (Popescu, 2010) purpose a new ap-
proach for machine vibration analysis and health
monitoring combining blind source separation (BSS)
and change detection in source signals.
The purpose of this research is to propose a
method combining EMD and BSS is applied in bear-
ing degradation performanceassessment. The method
consists of three processing stages. In stage one;
EMD is used to decompose the collected signal in to
intrinsic mode functions (IMFs) ; In stage two ,the
BSS used to separate the IMFs signals into indepen-
dent components sources signal, and hence to com-
plete the BSS process. In addition, .Finally, the health
state of bearing identified by the calculation of the
correlation between separated signals.
2 Description of the Proposed
Method
Various prognostic researches have been con-
ducted for improving the RUL prediction. In figure
1 three steps procedure can be achieved in Bearing
prognostics process :
Preprocessing
- Filtering
- Features extraction
- Selection
Prognostic
- Prediction
- Health Assessment
- RUL estimation
Decision
DATA Acquisition &
processing
Raw signal
- Force
- Vibrations
- Temperature
Figure 1: Steps of the proposed method.
Data acquisition step is to collect the data related
to system health; Data preprocessing is to analyze the
acquired signals Including centering, filtering to re-
move the offset in the measured signals. In prepro-
cessing step, a EMD used to IMFs that contains infor-
mation about sources as the input signal for BSS; the
correlation coefficients value of independent sources
based regression used for the health assessment; in
maintenance decision-making step, effective mainte-
nance policies will be obtained based on information
analysis.
2.1 Empirical Mode Decomposition
The EMD method was first developed by (Huang
et al., 1998). It decomposes the time signal into a
set of intrinsic mode functions (IMFs). In EMD, two
conditions should be satisfied:
1. the number of extrema and zero crossings may
differ by no more than one;
2. the local mean is zero.
Figure 2 show the sensors measurements of the
normal condition and degradation bearing . The de-
composed results of vibration signal with degraded
cutter by using EMD are given in Figure. 4 that has 9
IMFs .
Time (s)
0 500 1000 1500 2000 2500
Acceleration (m/s
2
)
-1
-0.5
0
0.5
1
Time (s)
0 500 1000 1500 2000 2500
Acceleration (m/s
2
)
-5
0
5
Figure 2: Sensors measurement for normal condition (top)
and degradation bearing (bottom).
IMF4RIEHDULQJYLEUDWLRQVLJQDO
9LEUDWLRQVLJQDO
8SSHUHQYHORSSH
/RZHUHQYHORSSH
5HVLGX
7LPHV
Figure 3: The EMD results of vibration signal.
2.2 Description of the BSS Techniques
Blind Source Separation (BSS) is a method for recov-
ering the signal produced by individual sources from
their mixtures. In the simplest case, m mixed signals
fromm different sensors x
i
(k) are assumed to be linear
combinations of unknown mutually statistically inde-
pendent signals from n vibrating components s
j
(k)
Bearings Prognostics based on Blind Sources Separation and Robust Correlation Analysis
659
0 500 1000 1500 2000 2500
IMF1
-1
0
1
0 500 1000 1500 2000 2500
IMF2
-1
0
1
0 500 1000 1500 2000 2500
IMF3
-1
0
1
0 500 1000 1500 2000 2500
IMF4
-0.5
0
0.5
0 500 1000 1500 2000 2500
IMF5
-0.2
0
0.2
0 500 1000 1500 2000 2500
IMF6
-0.1
0
0.1
0 500 1000 1500 2000 2500
IMF7
-0.1
0
0.1
0 500 1000 1500 2000 2500
IMF8
0.025
0.03
0.035
Figure 4: The EMD decomposed results of vibration signal.
with noise. This can be stated as:
X(t) = A.S(t) + N (1)
1
s
2
s
1
x
2
x
1
s
ˆ
m
s
ˆ
2
s
ˆ
{
{
Estimated
TPVSDFT
{
Mixed
TJHOBMT
Sources
m
x
n
s
8QEDODQFH
0LVDOLJQPHQW
%HDULQJGHIHFW
*HDUPHVK
%OLQG
6RXUFH
6HSDUDWLRQ
*OUFSGFSFODFOPJTF
.JYJOH
TJHOBMT
$SJUJDBMDPNQPOFOUT
Figure 5: Blind source separation model.
The sources must satisfy two conditions: statisti-
cal independenceand the Non-Gaussianity (Haile and
Dykas, 2015). The problem of BSS is reduced to a
mathematical optimization problem, for which a mul-
titude of techniques are reported in the literature. Five
algorithms implemented in this paper selected from
the most used in the fault diagnosis (Peter et al., 2006)
such as : FastICA , Second Order Blind Identifica-
tion, COMBI, Algorithm for Multiple Unknown Sig-
nals Extraction and EWASOBI.
In order to obtain an accurate and quantitative
measure of the performance of the algorithms, several
techniques used in the literature for the performance
measurement of distortion are given in (Chen et al.,
2013). The performance measuring criteria used are
crosstalk, performance index (PI) and signal to inter-
ference ratio (SIR).
2.3 Robust Correlation Analysis
Correlation is a signal matching method. It is a key
component of many systems such as: sonar, radar and
digital communications. In this study, the application
of digital correlation to blind sources separation was
addressed.
The least median of square (LMS) estimation
(Simpson, 1997). is one of the most robust methods
for estimating correlation; The LMS regression coef-
ficients minimize the median of the squared residu-
als. The advantages of the LMS estimator can give
reliable results (Niven and Deutsch, 2012).
The some well known correlation coefficients,
namely, Pearson’s, Spearman’s and Kendall’s, are ex-
amined (Nivenand Deutsch, 2012). The results shows
that these correlation coefficients are sufficiently ro-
bust against a substantial number of outliers, The cor-
relation coefficient based on the LMS is proposed.
II is given a higher breakdown point than the well
known correlation coefficients.
In this section we present the correlation between
the estimated sources obtained by BSS technique us-
ing vibrations signals, more advanced prognostics in-
terested on performance degradation assessment, so
that failures can be predicted and prevented. As soon
as, the concept of correlation coefficients for accu-
rately assessing the bearing performance degradation
is a critical step toward realizing an online tool condi-
tion monitoring platform.
Correlation =
n
∑
i=1
(x
i
− ¯x)(y
i
− ¯y)
n
∑
i=1
(x
i
− ¯x)
2
n
∑
i=1
(y
i
− ¯y)
2
(2)
In this study; The correlation coefficients of each
level used in regression for performances degradation
assessment. In this combination strategy, the raw sig-
nal is first decomposed in different scales by EMD.
Accordingly, it is expected that the proposed EMD-
BSS model can more accurately model and compen-
sate the performance degradation of the raw signal
characteristic.
The correlation coefficients values has been used
for follow-up the level or the system severity. In ex-
perimental setup, this value is used to monitor the
overall signal force level. The RMS value of the sig-
nal force is a very good temporal descriptor of the
overall condition for the other monitor signal figure
10 .
2.4 Experimental System and Signals
Acquisition
An accelerated bearing life test platform called
PRONOSTIA (Figure.6) used in this paper to verify
the prognostics of proposed technique. PRONOSTIA
is an experimental platform dedicated to test, verify
and validate developed methods related to bearing life
acceleration, diagnostic and prognostic. The four data
shown in Table 1 for the different operating condi-
tions.
Table 1: Bearings dataset from PRONOSTIA experimental
setup.
Tests duration Loading (N) Speed (RPM)
6h50 (410 minutes) 4000 1800
3h25 (205 minutes) 6000 1500
1h30 (90 minutes) 8000 1500
ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics
660
Bearing tested Accelerometers
Torquemeter
Speed sensor
AC Motor
NI DAQ card Pressure regulator
Speed reducer
Force sensor
Thermocouple
Coupling
Cylinder Pressure
Figure 6: Platfrom pronostia.
The platform PRONOSTIA composed of two
main parts: The first part related to the speed varia-
tion and a second part dedicated to load profiles gen-
eration. The speed variation part is composed of a
synchronous motor, a shaft, a set of bearings and a
speed controller. The synchronous motor develops a
power equalto 1.2 kW and its operational speed varies
between 0 and 6000 rpm.
A pair of ball bearings is mounted on one end
of the shaft to serve as the guide bearings and a
NSK6307DU roller ball bearing is mounted on the
other end to serve as the test bearing. The transmis-
sion of the movement between the motor and the shaft
drive is done by a rub belt.
Two accelerometers (DYTRAN3035B) mounted
horizontallyand vertically on the housing of the tested
bearing to pick up the horizontal and the vertical ac-
celerations (Table. 2). In addition, the monitoring
system includes one temperature probe and a torque
sensor (Figure 6). The sensors are connected to a data
acquisition card .
The data acquisition software is programmed by
using a LabView interface. Each record is stored in
a matrix format where the following parameters are
defined: the time, the horizontal acceleration, the ver-
tical acceleration, the temperature, the speed and the
torque.
Table 2: Experimental data acquisition.
Measurement Type
Acceleration DYTRAN3035B
Temperature PT100
Torque DR2269
Force AEPC2S
Acquisition card NIDAQCard− 9174
Sampling frequency 25600Hz
Motor speed 6000rpm,1.2 kW
With this experimental platform, several types of
profile can be created by varying the operating condi-
tions (speed and load). The bearing’s behavior is cap-
tured during its whole degradation process by using
the dedicated sensors shown in (Table. 2) . The tested
bearing have the characteristics shown in Table3.
Table 3: Tested Bearing.
Bearing type NSK6804DD
⊘ Outside 32 mm
⊘ Inside 20 mm
Number of Balls 8
⊘ Ball 3.5 mm
3 RESULTS AND DISCUSSION
In order to confirm the validity of the proposed
method EMD-BSS. The correlation values between
different sources obtained by IMFs separation are
shown in Table. 4 for the vibrations signal.
Table 4: The Correlation Values Between Sources.
Source ˆs
1
ˆs
2
ˆs
3
ˆs
4
ˆs
5
ˆs
6
IMF1 0.95 0.23 0.00 0.00 0.00 0.00
IMF2 0.28 0.97 0.00 0.00 0.00 0.00
IMF3 0.06 0.01 0.99 0.02 0.00 0.00
IMF4 0.05 0.02 0.04 0.99 0.01 0.00
IMF5 0.04 0.01 0.01 0.04 0.99 0.02
IMF6 0.04 0.00 -0.01 0.03 0.01 0.99
Separated signals based on EWASOBI are shown
in Figure 7 have high dependent, the other BSS tech-
nique have not a good separation of the original
source signals, but the proposedapproach based IMFs
can separate the desired signals properly and given a
good correlation.
0 500 1000 1500 2000 2500
-2
0
2
Source 1
0 500 1000 1500 2000 2500
-1
0
1
Source 2
0 500 1000 1500 2000 2500
-0.5
0
0.5
Source 3
0 500 1000 1500 2000 2500
-0.5
0
0.5
Source 4
0 500 1000 1500 2000 2500
-0.2
0
0.2
Source 5
0 500 1000 1500 2000 2500
Time (sample)
-0.2
0
0.2
Source 6
Figure 7: Sources estimation.
The proposed EMD-BSS algorithm can separate
the signals properly. Next, for comparison between
different BSS algorithms along the criteria statistical
whose performance, the results shown in Table 1.
In order to confirm the validity of the proposed
method EMD-BSS . The independence between esti-
mated sources can be measured by using some per-
Bearings Prognostics based on Blind Sources Separation and Robust Correlation Analysis
661
formances criteria shown in Table 5 of various algo-
rithms .
Table 5: Performance criteria for various BSS algorithms.
Algorithms Performance Signal to Interference
Index (PI) Ratio (SIR)
SOBI 0.28 18.45
JADE 0.25 33.15
FastICA 0.27 29.54
COMBI 0.23 9.46
FPICA 0.98 12.60
EWASOBI 0.02 35.31
Table 5 shown the performance evaluation of
sources separation, the value of PI is less than 5%
and the technique Efficient Weights Adjusted SOBI
(EWASOBI) (Tichavsk`y and Yeredor, 2009) given
a good separation with a small time computing ,
whereas JADE, FastICA and SOBIRO and COMBI
has the lowest performance.
3.1 RUL Estimation
The experimental data sets are generated from
PRONOSTIA run-to-failure tests under constant load
conditions . In order to prove the effective prediction
of the EMD-BSS method 4 data sets was used with the
same operating condition. The failure threshold lim-
ited by using the international standards (ISO 13381-
1, ISO 10816 and ISO 7919). The ISO standards lim-
ited in vibration signals energy (the root mean square
RMS of vibration signal), and for different indicators
are used (AFNOR, 2005). An illustration of RUL pro-
gression is shown in Figure 8.
Time
Equipment condition
Potential Failure Detected
Monitoring
Time for prediction
Time for decision
Failure !!!
Condition
monitored
Condition
predicted
Figure 8: Illustration of remaining useful life.
The regression results are presented in Table 6 in
terms of the factors of determination R
2
for the dif-
ferent training models. The R values, indicating the
fraction of the total variance that could be explained
by the model, are very high. From the results, it is
seen that all the predictors perform very well. The
objective is to apply the best power fit on the degra-
dation model obtained by equation 4.
f(t) = a.t
b
+ c (3)
RUL(t) = t
final
− HI
−1
(t) (4)
Where t
f
inal is the time when the fault occurs
and HI
1
the inverse of the health indicator HI(t) used
to get the current cycle or time (t). The validation
of these results shown in table 6 by computing of
the sum square error (SSE), R square and root mean
square error (RMSE).
0 50 100 150 200 250 300 350 400
Time (minute)
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
Health Indicator
Real data
Regression: f(t) = 0.0903.t
0.2774
+0.4887
Figure 9: Health indicator for the bearing (6H50).
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Time (s)
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Health indicator
Tested Beaing 1H30
Figure 10: Health indicator for the bearing (90 minutes).
Table 6: Prediction performance.
Bearings SSE RMSE R
2
1H30 0.3959 0.03562 0.9453
3H25 0.0750 0.01550 0.9974
6H50 0.1933 0.0225 0.9570
The goal of this technique is to analyze prediction
capabilities by using EMD-BSS. A comparativestudy
between different algorithms used in BSS on reliabil-
ity performance analysis was summarized in Table 1.
The RUL estimation is the distance between the cur-
rent time and the time for which the regression model
given in equation (3). The threshold or the accept-
able limit of the vibration magnitude (AFNOR, 2005)
of each degradation in bearings, corresponds to the
end of each experiment. The power fitting of the
smoothed health indicator is shown in Figure 9.
4 CONCLUSION
This paper presented a new approach of using the
EMD-BSS based correlation. The study of bearing
degradation assessment is done by using vibrations
ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics
662
0 50 100 150 200 250 300 350 400 450 500
Time (minute)
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
RUL (%)
Tested Bearing 6H50
Maximum of correlation
Figure 11: RUL estimation for the tested bearing (6H50).
signals. The proposed models were developed based
on the acceleration signal. The potential of EMD-
BSS based correlation shown in this paper for perfor-
mance degradation assessment. The health indicator
calculated in this contribution by using a correlation
between the nominal and degraded bearing signal of
estimated sources. The method is applied on vibra-
tions signals acquired from the experimental platform
PRONOSTIA. The proposed technique based on ro-
bust correlation coefficient is shown to have a higher
accuracy than either Pearsons and Spearmans correla-
tion. It is expected that with additional development,
EMD-BSS can drastically improve the accuracy of
RUL estimation based bearing condition monitoring
across the full range of working. The accuracy of the
estimated results was tested using validation experi-
ments,showing a good results.
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Bearings Prognostics based on Blind Sources Separation and Robust Correlation Analysis
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