svm multi-classification of induction machine's …the empirical mode decomposition for bearing...

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.

mailto:[email protected]



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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



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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



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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



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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)



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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 / /



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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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