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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 13, Number 9 (2018) pp. 6579-6586
© Research India Publications. http://www.ripublication.com
6579
SVM Multi-Classification of Induction Machine's bearings defects using
Vibratory Analysis based on Empirical Mode Decomposition
Karima Amara Korba, Fayçal Arbaoui
Faculty of Engineering, Department of Electronics, Badji Mokhtar University, Annaba Laboratory of Automatic and Signals, Annaba, BP.12, Annaba, 23000, Algeria.
Abstract
The rolling defect is one of the main causes of dysfunctions in
induction machines, resulting in a significant economic loss.
The main purpose of this study is an automated diagnosis of
bearing defects based on vibratory analysis.
The work was carried out on the Case Western Reserve University database, where the signals were acquired in
different modes and operating conditions (healthy and faulty
cases, speed variations, load and defect severity variations).
A vector of indicators known as vector form, composed of
statistical and spectral indicators for optimal performance, is
extracted from the original vibration signals via processed
signals using Empirical Mode Decomposition (EMD).
In the classification phase, the Multi-Class Support Vector
Machine (SVM) was chosen.
A comparison of the results with empirical modal
decomposition using one and three relevant Intrinsic Mode
Functions (IMFs) was performed; the obtained results show
the effectiveness of this approach.
Furthermore, a comparative study was achieved on two other
types of classifiers, namely, Artificial Neural Network (ANN)
and Neuro-Fuzzy Network (NFN). A better efficiency in
terms of time and classification rate goes to the multi-class
SVM compared to the ANN and the NFN.
Keywords: Support Vector Machines (SVM); Statistical
parameters;Empirical Mode Decomposition(EMD);Rolling
failure, Vibration signal.
INTRODUCTION
Time-frequency domain techniques are mainly used to process
non-stationary vibratory signals. We can distinguish theShort-
Time Fourier Transform (STFT), the Wigner-Ville
Distribution (WVD), the Wavelet Analysis (WA), Wavelet
Packet Decomposition (WPA), the Empirical Mode
Decomposition (EMD) and the Hilbert-Huang Transform
(HHT). The short Fourier transform segments the signal into
time windows and then applies the Fourier Transform (FT) on
the obtained windows; however, the size of the windows is
difficult to choose.
Concerning the distribution of Wigner-Ville, it sometimes
leads to the appearance of cross-terms, which can lead to
erroneous analyzes.
Wavelet packet decomposition is an extended form of wavelet
decomposition (WD) and consists of using a pair of high-pass
and low-pass filters. These filters allow realizing a division of
the frequency contents of the raw signal in two components
(or packets), one contains high frequencies and other one low
frequencies. Then, these packages are successively injected in
filters in order to separate them again into the frequency
space. This operation allows reaching rather fine levels of
decomposition which allow followingthe evolution of the
frequencies, while keeping a good resolution for the fast and
slow phenomena thanks to the use of a wavelet mother and
parameters of scale and translation. The WPD can be used for
the detection and the follow-up of damages, but its efficiency
depends strongly on the quality of the signals being processed
[1].
One of the most efficient methods for the preprocessing of
non-stationary signals is the Hilbert-Huang transform; which
consists of applying two techniques: the EMD and the Hilbert
Transform. The EMD identifies the intrinsic oscillatory
modes, i.e., the Intrinsic Mode Functions (IMFs) of the signal
then the Hilbert Transform is applied to each IMF to extract
the instantaneous frequencies and amplitudes. As a result, a
three-dimensional representation (amplitude, frequency, time)
of each oscillatory mode of the signal is obtained [2].
It has been proved that SVM has well established theoretical
background and intuitive geometrical interpretation. It is
widely applied and has even served as the baseline in
computer vision, pattern recognition, information retrieval,
and data mining, etc. [5].
The aim in our approach is to prove especially that SVM
method used as classification technique and associated with
the empirical mode decomposition for bearing faults diagnosis
is a discerning choice. The resulting combination is a well-
adapted and efficient technique in term of time and data size
using a minimum number of samples.
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 13, Number 9 (2018) pp. 6579-6586
© Research India Publications. http://www.ripublication.com
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REVIEWS OF EMD AND SVM THEORY(THEORETICAL
BACKGROUND)
A. EMPIRICAL MODE DECOMPOSITION ALGORITHM.
The EMD process ofasignal x(t) can be described as follows:
(1) Initialize: 𝑟0 = 𝑥(𝑡), 𝑎𝑛𝑑 𝑖 = 1.
(2) Extract the ith IMF.
(a) Initialize: ℎ𝑖(𝑘−1) = 𝑟𝑖 , 𝑘 = 1.
(b) Extract the local maxima and minima of ℎ𝑖(𝑘−1).
(c) Interpolate the local maxima and the minima by cubic
Spline lines method to form upper and lower envelops
of ℎ𝑖(𝑘−1).
(d) Calculate the mean 𝑚𝑖(𝑘−1) of the upper and lower
Envelops of ℎ𝑖(𝑘−1).
(e) Let ℎ𝑖𝑘 = ℎ𝑖(𝑘−1) − 𝑚𝑖(𝑘−1).
(f) If ℎ𝑖𝑘 is an IMF the n set 𝐼𝑀𝐹𝑖 = ℎ𝑖𝑘 , else go to step(b)
with k = k+1. Standard Deviation (SD) of two adjacent
h(t) isusually used as a criterion to stop the
iteration,SD>0.3and it is defined as
𝑆𝐷 = ∑ |ℎ𝑘−1(𝑡) − ℎ𝑘(𝑡)|2 ℎ𝑘2(𝑡)⁄
𝑇
𝑡=0
where, T, is the signal length.
(3) Define 𝑟𝑖+1 = 𝑟𝑖 − 𝐼𝑀𝐹𝑖.
(4) If 𝑟𝑖+1 still has at least 2 extrema then go to step (2)else
decomposition process is finished and 𝑟𝑖+1 is the residue of
the signal.
At the end of the procedure we have a residue 𝑟𝑖 and a
collection of l IMFs 𝑥(𝑡) = ∑ ℎ𝑖 𝑙𝑖=1 (𝑡) + 𝑟(𝑡)[3].
The performances of the system of diagnosis depend on the
robustness of the method in presence of noise, disturbance and
modeling errors. The data preprocessing can significantly
improve the diagnostic performances. New methods offer the
possibility of reducing the noise and extracting only the
relevant information. One can mention, for example:
The EEMD: (Ensemble EMD)
A method of analyzing noisy data, Noise Assisted Data
Analysis (NADA).
The EEMD consists of "sifting" a white noise added to the
signal.
The white noise is calculated on average with a sufficient
number of tests, the only persistent part that survives the
process of averaging is the signal, which is then treated as the
true and most significant physical response. In addition, the
EEMD represents a substantial improvement over the original
EMD[24,3].
The CEEMDAN :(Complete Ensemble EMD with Adaptive Noise)
A Complete Ensemble EMD with Adaptive Noise is a
variation of the EEMD algorithm that provides an exact
reconstruction of the original signal and a better spectral
separation of IMFs with less noise and more physical
information [23].
B. MULTI-CLASS SVM CLASSIFICATION
The multi-class SVM is an algorithm for finding the nonlinear
separating hyper plane modeled as a constraint optimization
problem of a Multi labeled dataset. It is based on two key
ideas, the maximum margin and the kernel function; we can
construct a multi-class classifier by combining several binary
classifiers. Several methods have been proposed, some of
them are: “one-against-one”, “one-against-all” [25,4]. In the
one-against-all methods, to classify N classes, N classifiers
are trained to separate one class from the rest. For the Nth bi-
class classifier, all training data needs to be involved; the
positive result is the data point in the N class, and the negative
result is the data point in the other N-1 classes.
Each of the two-class classifiers is trained to find the decision
function, and then all the decision functions are combined to
obtain the final decision function for the multi-class
classification problem [26, 27]. In figure 1, a four classes One
against All multi-SVM classification is depicted. Some of
other previous works using Multi-Class SVM of bearing
defects by several preprocessing methods are listed in table 1.
Figure 1. SVM classification "One Vs All"
METHODOLOGY ADOPTED FOR THE DIAGNOSIS
OF BEARINGS FAULTS DETECTION.
The proposed methodology involves three main steps: feature
extraction, feature selection and classification. The block
diagram of fault classification system is shown in Figure 2.
Figure 2. Block diagram
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 13, Number 9 (2018) pp. 6579-6586
© Research India Publications. http://www.ripublication.com
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The approach consists, after vibratory signals acquisition, in
the application of the empirical mode decomposition which
generates the IMFs of the vibratory signal and highlights the
three most relevant ones obtained according to the highest rate
of correlation with original vibratory signal as depicted in
Figure 4.
Afterwards, the strategy consists in extracting temporal and
spectral features from this most relevant IMFs which is shown
in Figure6. The selected features are evaluated on the base of
specifications of the defect vibratory signal signatures; they
are shown in table 2.
The resulting data will be divided into two categories: one for
multi-SVM learning step and the constitution of the
classification model and the other for multi-SVM
classification tests.
The classification was carried out using three classifiers;
explicitly the support vector machines as the main classifier,
artificial neural networks, and fuzzy neural networks for
comparison purposes.
The classification rate and the estimated classification time
are used as a metrics to compare performances of each classif
A. NON-STATIONARY TIME-FREQUENCY SERIES
ANALYSIS:
Aiming at the non stationary and nonlinear characteristics
of bearing vibration signals as well as the complexity of
condition-indicating information, a study was carried out for
all the features extracted in time and frequency domains
shown in Figure5 which proved that the vibration signals
extracted are non stationary. therefore, this justifies the
application of one of the most efficient methods analysing non
stationary signals, that is the empirical mode decomposition.
Figure 3. Adopted methodology
Figure 5. X3006 Ball’s Non-stationary time-frequency
features analysis
Figure 4. Extraction of the three most relevant IMFs
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 13, Number 9 (2018) pp. 6579-6586
© Research India Publications. http://www.ripublication.com
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Table I. Some published works using SVM based on CWRU Data
Article
ref
No. of
Classes
No. of
train(bins)
Or width
window
No. of
test
(BINS)
Classifier
Type
Preprocessing Methods ACCURACY %
&/or
Classification Time
[10] 04 SVM (OAO)
one-against-
ones
Time Synchronous Averaging
TSA as a signal processing tool with Independent
Component Analysis (ICA)
Drive End bearing
Ball 88.9%, IR 94.4%, OUR
97.62%
[11] 04 120 SVMs Combination CoD and InD /3 features
Combination FDF and TDF/3 features
99.579
100
[12] 04 30/120
30
120
ANN
SVM
32 features are used and 8 are selected:
RMS, STD, SHF, CLF, KURTOSIS
Normalized Energy 5 /3 /14
85%-97%
training time (s)
0.083-0.062
91%-98%
0.045-0.012
[13] 20/6000 20 KNNC
NBC
LS-SVM
(MFDs) based on morphological cover (MC) 100
~99
100
[14] 04 2048
10/20/30/40/50
200
SVM
One
Versus
one
multiscale permutation ENTROPY (MPE)
~91%
~74%
~98%
~99%
[15] Case1 :426
Case2 :1706
LSSVM EMD-Principal Component Analysis (PCA), 96.92
95.53
[16] 16/ 4096 16 SVM Particle Swarm Optimization (PSO) algorithm
based on the combining of the DWT preprocessor
and the Kurtosis for feature extraction.
100
[17] 10 15 35 SVM 1. EMD and Intrinsic Mode Function (IMF)
envelope with sample entropy (SampEn)
2. EMD-IMF-SampEn
98
90
[18] 06 6/500
12
30
60
120
240
300
576
54
104
270
540
1080
2160
2700
5184
MSVM FFT
Multi –class Support Vector Machine
Artificial Neural Network
84.48% with run time0.007s
85.63-0.009
99.26-0.014
99.63-0.017
99.91-0.043
99.95-0.135
99.88-0.201
100-1.460s
[19] 04 30 30 two-layer
SVRMs
SVR with the selected parameters and
optimization.
Comparisons with other SVM and ANN methods.
1rst layer 98-100
2nd layer
98-100
[20] 04 20
78
58
12
50
38
SVM-OAA
(One against
all)
Derived bi-spectrum features from the bearing
vibration signals+ Principal component analysis
(PCA) to reduce the feature dimensionality
95 /n- selected
100/selected f
[21] 04 SVM
IMASFD: EMD- IMF + ant colony optimization
(ACO) to optimize the parameters of SVM model
94.93%,96.04%,99.74%
and 100.00%.
[22] Load0
Load1
Load2
Load3
Euclid
distance
discriminance
1. FFT are processed with two-dimensional
principal component analysis (2DPCA) to reduce
the dimensions
2. minimum distance applied to classify
PCA
2DPCA
75~100
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 13, Number 9 (2018) pp. 6579-6586
© Research India Publications. http://www.ripublication.com
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Figure 6. Time domain features extracted from the first IMF
under different conditions,(a) inner race defect X169-0.014”,
(b) outer race defect X130-0.07”,(c) ball defectX3006-
0.028”,(d) healty signal
Table II. Selected features
Time domain Features
Symbol & Formula Symbol & Formula
Mean ∶ xm = ∑ x(n) N⁄
N
n=1
Variance ∶ xvar
= ∑ (x(n)_xm)2N
n=1N⁄
Kurtosis xkur
= ∑ (x(n) − xm)4N
n=1(N − 1)σ4⁄
Clearance factor ∶ CLF
= xmax (1
N∑ √|x(n)|
N
n=1)
2
⁄
Clearance factor ∶
CLF = xmax (1
N∑ √|x(n)|
N
n=1)
2
⁄
Mean absolute deviation ∶
MAD = ∑|∑ (x(n) − xm)N
n=1 |
N
N
n=1
Range ∶ xrange = |xmax − xmin| Standard Deviation ∶
σ = √∑ (x(n) − xm)2N
n=1
N
Frequency domain Features
Symbol & Formula Symbol & Formula
Mean Frequency
𝑓𝑚𝑒𝑎𝑛 =∑ In. fn
Nn=1
∑ InNn=1
Mean power frequency
MNF = Cs =∑ Pn. fn
Nn=1
∑ PnNn=1
Power Spectral Density
DSP =∑ Pn
Nn=1
N
Spectral Entropy
Ens = − ∑ Pn log Pn
N
n=1
Short time Energy
∑[𝑥[𝑚] 𝑊[𝑛 − 𝑚]]2
𝑁
𝑛=1
x (n) / (n = 1, ..., N) is the amplitude at sampling point n and N is the
number of sampling points. xm is the mean of x, and σ its standard
deviation.
fn and In are the frequencies and amplitudes at the n-point of the
spectrum of the signal.
Pn is the spectral power of the signal at point n.
Spectra produce peaks at identified fault; these peaks
represent the indicated fault. An evaluation of the bearing’s
defect frequencies according to the CWRU drive end
bearing’s tests rig specifications is highlighted according the
following values :
Frequency of inner race fault is 160~162.1Hz.
Frequencyof outer race fault is 106~ 107.3Hz.
Frequency of balls fault is 139~141.1Hz. [28,29].
(a)
(b)
(c)
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 13, Number 9 (2018) pp. 6579-6586
© Research India Publications. http://www.ripublication.com
6584
Table III. Results of the applied methods
EXPERIMENTAL SET UP AND VIBRATION DATA
Figure 7. The bearing tests rig from Case Western Reserve
University (CWRU) [6].
All the rolling element bearing vibration signals used for
analysis were downloaded from CaseWestern Reserve
University Bearing Data Center [6]. The whole experimental
rig consists of a two-horsepowerdrive, three-phase induction
motor(IM), a torque transducer and a dynamometer as shown
in Fig 7,on the motor’s shaft at the drive end, a ball bearings
6205-2RS JEM SKFis placed,on which accelerometers with a
bandwidth up to 5000Hz was installed.The data was sampled
at a frequency of 12 kHz.
Experiments were conducted for end bearing with normal
case, inner race fault, outer race fault and ball fault with the
defect severity as follows:
Inner race defect diameter: 0.007 "and 0.014".
Outer race defect diameter: 0.007 "and 0.014".
Ball defect diameter 0.028 ".
4 or16 is the Number of samples used for the test.
Example: Number of samples x windowing = 28000 x 16 =
448000 samples used at a frequency of 12 K Hz.
0.016 or 0.047 Classification Time: the CPU time spent
performing the classification function.
N.B.: All of the experiments were done on intel core ™ i7-
4500U 2.4GHz CPU with 8GoRAM.
RESULTS AND DISCUSSION
We applied the learning and test phases to the previously
detailed CWRU database. the table 3 shows the good
classification rates as well as the different calculation times.
the statistical attributes are calculated on the 3 most relevant
IMFs obtained by the application of the EMD, namely having
the highest correlation factor with the original signal, the
classification rate reaches 96.88%. But, by selecting only the
most relevant IMF, this classification rate increases to 100%.
The best result obtained with the neuronal classifier is 96.87
with 3IMFs and number of samples four times more than the
previous results.
However, classification rates are close for both SVM and
Neuro-fuzzy methods with a slight lead for the SVM.
These results show the pertinence of the procedure based on a
selection of the IMFs and the statistical parameters as well as
the need to combine with the EMD for the speed of the
convergence and the efficiency of the support vector machine
with wide margin compared to the other classification
methods. Other divergences appeared in this study are
illustrated in table 4.
Number Of features
Vectors
EMD / one IMF +SVM
EMD/ 1IMF+ANN
EMD/1IMF+NF
N
EMD/3 IMFs +SVM
EMD/3IMFs+AN
N
EMD/3IMFs
+NFN
Accuracy Rate (%)
(AR)
Classification time(s)
(CT)
AR&CT
AR AR CT AR AR
Win
do
ws
wid
th
28
00
0 b
ins 09 / / / /
10 / / 96.88/16 / 90/16 96.87/16
11 100/4 0.016 25-0.015 100 93.75/4 0.030 75/4 81.25/4
12 / / 93.75/4 0.023 68.75/4 81.25/4
13 / / 93.75/4 0.028 75/4 75/4
Win
do
ws
wid
th
28
00
bin
s 09 / / / /
10 / /
11 100/4 0.047 25-0.014 100 / /
13 / / / /
Win
do
ws
wid
th
28
0 b
ins 09 / / / /
10 / / / /
11 / / / /
13 87.5/4 0.0001 56.25-0.013 62.5 / /
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 13, Number 9 (2018) pp. 6579-6586
© Research India Publications. http://www.ripublication.com
6585
A. CAMPARATIVE STUDY
Several methods have been introduced for the mechanical
diagnosis of failures; among the most commonly used are
artificial neural networks, support vector machine and fuzzy
neural networks with various efficiency [7,8,9].
However, they can be complementary such a SVM and ANN
combinations. For example, one can use multiple ANN layers
and have the latest classification via SVM at the output layer.
SVM without kernel is a single neural network neuron but
with different cost function. If you add a kernel function, then
it is comparable with a 2-layer neural network. The first layer
is able to project data into some other space and next layer
classifies the projected data.
Table IV. SVM VS ANN & NFN
EMD+ SVM EMD+ANN EMD+NFN
Reduced number of samples for training. A large number of samples for training. Reduced number of samples for
training
Theory based on statistical learning retro propagation of the gradient Based on the inference logical rules
Accuracy is highly determined by selection of
optimal parameters.
Accuracy rate depends on large size data
training.
Good convergence rate.
Sensitivity to noisy data robustness in relation to disturbances robustness in relation to
disturbances
Fast in classification Slow in classification Fast in classification
good generalization ability even with a few
training samples
a poor generalization ability if trained
with few training samples
incapable to generalize, it only
answers to what is written in its
rule base
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