In this paper, we propose a new method for detecting bearing faults using vibration signals. The proposed method is based on support vector machines (SVMs), which treat the harmonics of faultrelated frequencies from vibration signals as fault indices. Using SVMs, the crossvalidations are used for a training process, and a twostage classification process is used for detecting bearing faults and their status. The proposed approach is applied to outerrace bearing fault detection in threephase squirrelcage induction motors. The experimental results show that the proposed method can effectively identify the bearing faults and their status, hence improving the accuracy of fault diagnosis.
1. Introduction
Induction motors are widely used as major electrical machines in a variety of industrial applications. Induction motor failures that are due to environmental stress and load conditions can result in severe damage to the motor itself as well as to motorrelated industrial applications. It is well known that bearings are among the most common sources of motor faults in induction motors. Further, bearing faults represent 4050% of the various types of induction motor faults
[1
,
2]
. The major source of bearing faults is damage on the inner or outer races of the bearing due to thermal or mechanical stresses
[2
,
3]
.
For bearing fault detection, various types of sensors and conditionmonitoring systems have been employed
[2

9]
. Vibration measurements are commonly used to identify bearing faults
[2
,
5

9]
. The amplitude at the bearing faultrelated frequency is used as the fault index in the vibration spectrum
[2
,
6
,
13]
. In addition, there are also harmonic frequencies in the vibration spectrum in motors with faulty bearings
[3
,
5
,
9]
. The spectral analysis of vibration signals is performed using the fast Fourier transform (FFT) method, which is the basic tool used together with some other approaches such as machine learning and statistical analysis.
To increase the accuracy of bearing fault detection, various machine learning and statistical analysis have been developed
[10

13]
. Neuralnetworkbased fault diagnosis has been proposed for rolling bearing faults using timefrequency domain vibration analysis
[10]
. The fuzzy classifier has been adopted to diagnose roller bearing faults using simple fuzzy rules and membership functions
[11]
. A support vector machine (SVM) was employed using timedomain and frequencydomain features for multiple faults diagnosis of induction motors
[12]
. Quadratic discriminant analysis and SVM have been used for multiple fault (airgap eccentricity, bearing damages, and their combinations) detection using multiple sensors such as acoustic, vibration, and current sensors
[13]
. However, the effects of variations of the motor speed and fault severity have not been examined for SVMbased bearing fault detection
[12
,
13]
.
This paper considers bearing faults that are due to outerrace damages to the bearing in induction motors. In order to detect bearing faults, we implemented a twostage diagnosis method for fault and faultseverity detections based on the FFT and SVMs. The first SVM classifier distinguishes faulty motors from healthy motors, while the second SVM classifier is used to discriminate between different bearing fault severities. The proposed fault detection method focuses on the spectra of vibration signals at faultrelated frequency harmonics, and uses the values of the peaktomean ratio at harmonic frequencies as fault indices. Using the crossvalidation for the SVM, the fault indices and SVM parameters are optimized from experiment results for different load conditions. The proposed diagnostic method can distinguish a faulty motor from a healthy motor with a probability of 100% of correct detection and a 0% likelihood of obtaining a false alarm under different load conditions. It can also discriminate between different severities with an average detection probability of 98.67% and a false alarm probability of 0% under different load conditions.
2. Outerrace Rolling Bearing Faults
In this section, we present characteristic frequencies that are due to outerrace faults of rolling bearings and an experimental setup for rolling bearing fault detection.
 2.1 Characteristic frequencies
The outerrace defect of rolling bearings induces a specific vibration frequency as shown below:
[2
,
9]
where
N
represents the number of rolling elements,
f_{r}
is the mechanical rotational frequency,
D_{BD}
is the rolling element diameter,
D_{PD}
is the pitch diameter, and
ϕ
is the contact angle. Moreover, when the defective area is large, the harmonics of
f_{OD}
will also lead to the vibration spectrum as in
[3
,
5
,
10]
where
k
= 1, 2, 3, ⋯ is the harmonic index.
In (1) and (2), the frequencies that are commonly used as a diagnostic measure for bearing fault detection in
[2
,
3
,
5
,
9
,
10]
, and vary depending on the load conditions.
Table 1
lists the mechanical rotation frequency
f_{r}
and the outerrace defect frequency
f_{OD}
for test motors under different load conditions.
Mechanical rotation frequencyfrand outerrace defect frequencyfODfor test motors
Mechanical rotation frequency f_{r} and outerrace defect frequency f_{OD} for test motors
 2.2 Experimental setup
Experimental tests were performed with 75kW squirrelcage induction motors, where the rated voltage is 3300 V, the rated current is 16.3 A, the supply frequency
f_{s}
is 60 Hz, the speed is 1780 rpm, and the number of poles is 4. As shown in
Fig. 1
, the rolling bearing outerrace faults were simulated by making a hole in the outer race. This artificial fault cannot occur while a bearing is operating in a motor, but it is important to understand this fault in order to analyze the effects of bearing outerrace faults
[3
,
14]
. For motor conditions, three types of test motors were used: a healthy motor, a motor with faulty bearing with an 8mm hole, and a motor with faulty bearing with a 12mm hole. In this paper, the two latter motors are labeled as “bearing 1” and “bearing 2,” respectively.
Outerrace faults of roller bearings (bearing 1 and bearing 2).
Fig. 2
shows the induction motor test system, which is composed of a test motor, a load motor, an inverter, and a data acquisition system (DAS)
[15]
. The test motor is equipped with a type NU318E roller bearing with
N
= 13 rollers (
D_{BD}
and
D_{PD}
are 28 and 145 mm, respectively). An acceleration sensor (AS022 from B&K Vibro) is used, and is mounted on the test motor with
ϕ
= 0 . The inverter is connected to the load motor to control the load condition of the test motor. In the experimental tests, we considered for different load conditions of test motors, i.e., no load, 50%, and 100% load. For the vibration measurement experiments, the discrete time signals
x_{S}
[
n
] with
N_{S}
= 2
^{22}
were measured at a sampling frequency of 200
F_{S}
= kHz using the DAS, and the acquisition time was calculated as
T_{acq}
= 20.972 s .
Experimental setup.
3. Proposed Diagnostic Method for Bearing Fault Detection
To diagnose bearing faults using the spectra of the vibration signal, we propose a new detection method that is based on the SVM, which is a type of machinelearning technique based on the statistical learning theory. In the proposed approach, the objective of the SVM is to diagnose motor bearing faults using optimal fault indices from the faultrelated harmonics of the most important components present in the spectrum of the vibration signals. In this section, we first introduce the SVM, emphasizing its use as a diagnostic tool for the vibration spectrum. Second, we propose an SVMbased twostage diagnostic method that includes the feature calculation, feature selection, training, and classification, in order to detect the outerrace faults of rolling bearings.
 3.1 Background of SVM
The basic idea that is introduced in this paper was thoroughly developed based on the statistical learning theory
[16

19]
. The basic SVM deals with twoclass problems separating two classes by a hyperplane, which is defined by a number of support vectors.
In a linear separable case, there exists a separating hyperplane whose function is
where the vector
w
defines the boundary,
x
is the input vector of dimension
d
, and
b
is a scalar threshold. The optimal hyperplane can be obtained as follows
[17]
:
where
is the Euclidean norm of
w
,
i
= 1, ⋯,
l
is the number of training sets, and labels
y_{i}
= 1 and
y_{i}
= − 1are for positive and negative classes, respectively. The solution can be obtained by
where
α_{i}
≥ 0 are Lagrange multipliers and
x_{i}
are support vectors obtained from training. After training, the decision function for the linear SVM is obtained as follows:
In a linear nonseparable case, SVMs can create a hyperplane, which allows linear separation in the higher dimension, to perform a nonlinear mapping. The nonlinear mapping by the kernel function converts the input vector
x
from a
d
dimensional space into a higher dimensional feature space. In nonlinear SVMs, kernel functions such as the polynomial, sigmoid, and radial basis functions (RBF) may be selected to obtain the optimal classification results
[18]
. In this study, the RBF kernel is used for nonlinear SVM and is defined by
where
γ
> 0 is the RBF kernel parameter. For the nonlinear SVM, the decision function is obtained by
 3.2 Feature calculation
The peaktoaverage ratio (PR) has been proposed as an indicator to identify bearing faults in the spectrum
[20]
. The PR is defined as the sum of the peak values of the defect frequency and harmonics over the average value of the spectrum, and is defined as
[20
,
21]
where
P_{k}
is the amplitude of the maximum peak located at the frequency band that is centered at the
k
th defect frequency harmonic,
f_{OD,k}
, with a bandwidth
BW
,
S_{ j}
is the amplitude at any frequency,
J
is the number of points in the spectrum, and
K
is the number of harmonics in the spectrum. In (9), the PR will contain the information at all harmonics contained in the vibration signal; however, only some of them will be significant depending on load rates. Therefore, the peak values of the defect frequency or harmonics are used as fault diagnostic indices, respectively, and are defined by
where
k
is the harmonic index,
W_{k, j}
is the amplitude of frequency component at the frequency band centered at
f_{OD, k}
with
BW
, and
M
is the number of frequencydomain sample points in
BW
.
 3.3 Feature selection
After feature calculation, a sequential forward search (SFS) creates candidate feature subsets using (2) for feature selection
[13]
. For each candidate feature subset, using
υ
 fold crossvalidation, the SFS examines the performance of a linear SVM when separating the data for healthy motors from those for faulty motors. In
υ
fold cross validation, the training set is divided into subsets of equal size and a subset is sequentially tested using the classifier trained on the remaining
υ
−1 subsets. Based on experimental results, the motor speed can be calculated using the vibration signal
[10]
, and therefore, feature selection gives the optimal feature subsets depending on variable load rates.
 3.4 Training and classification
Based on the SVM algorithm, a twostage classification is used to detect the motor fault and its severity. From the selected feature subset on the each load rate, the whole test data set is classified by the first SVM for the bearing fault detection. Then, some of the test data, which were classified as faulty motors by the first SVM, are classified by the second SVM to distinguish the severity of the bearing faults. The whole training set is used for the training of the first SVM, while the second SVM classifier exploits training data for faulty motors.
In the SVM training processes, to optimize the parameters
C
for linear SVM or {
C
,
γ
} for nonlinear SVM, we use the
υ
fold crossvalidation to test all values of
C
for the linear SVM or all of the pairs of {
C
,
γ
} for the nonlinear SVM, where
C
> 0 is the penalty parameter of the error term for SVMs,
υ
= 5 ,
C
= {2
^{−15}
, 2
^{−14.9}
, ⋯, 2
^{15}
} for the linear SVM, and
C
= {2
^{−10}
, 2
^{−9.5}
, ⋯, 2
^{10}
} and
γ
= {2
^{−10}
, 2
^{−9.5}
, ⋯, 2
^{10}
} for the nonlinear SVM
[19]
. Using the training set,
υ
fold crossvalidation accuracies are obtained by the grid search, where the crossvalidation accuracy is the percentage of data that are correctly classified. The values corresponding to the best crossvalidation accuracies are then selected. With the optimal parameters, the entire training dataset was trained again to define hyperplane for SVM classifiers. The process employed for the proposed fault diagnosis algorithm is illustrated in
Fig. 3
.
Block diagram of the proposed fault diagnosis system.
4. Classification Results
To validate the proposed method, we performed experimental tests using the rolling bearings of squirrelcage induction motors. The experiments were performed in the steadystate condition and the measured vibration signals were analyzed using the FFT. The Hanning window was used to minimize frequency leakage for the FFT
[22]
and the frequency resolution for the spectrum analysis was Δ
f
= 0.0477 Hz. For feature calculation in (9), we set the following values:
K
= 3 and
J
=
N _{S}
/2 . The bandwidth
BW
was 8 Hz for feature calculation in (10). Experiments were performed 50 times in each load condition.
For comparison purposes, the bearing fault detection with one feature was examined based on the signal detection theory
[23]
. Each fault index
A
and the corresponding threshold parameter
A_{th}
were determined for each load condition using the combination criterion
[15]
,
[24]
, where
A
∈{
PR
,
PR
_{1}
,
PR
_{2}
, ⋯,
PR
_{5}
}. The optimal fault index
A
^{*}
and optimal threshold
for the classifier with one feature is obtained by
where the detection probability
P_{D,A}
and the false alarm probability
P_{FA, A}
are defined as
[23]
respectively,
H
_{1}
is the bearing faulty motor hypothesis, and
H
_{0}
is the healthy motor hypothesis.
Fig. 4
shows the cumulative distributive functions (CDFs) of
PR
and
PR
_{1}
under the noload condition. For each fault index, the optimal threshold was determined based on the combination criterion. For the fault index
PR
, bearing 1 can be easily detected, but the difference between the healthy motor and bearing 2 is unclear. The fault index
PR
_{1}
is more evident than
PR
, and performs optimally when separating healthy motor from faulty motors. However,
PR
_{1}
does not perform optimally when discriminating between bearing 1 and bearing 2 under noload conditions.
CDFs for the fault detection with one feature under 0% load condition: (a) PR and (b) PR_{1}.
For the fault detection with one feature,
A
^{*}
and
are summarized in
Table 2
. The optimal fault index for noload and 50% load conditions is
PR
_{1}
. In particular,
PR
_{3}
, which is obtained from the third harmonic of the vibration signal, is the optimal fault index under 100% load condition. For the bearing fault detection with one optimal feature, the detection probability decreases as the load rate increases.
Figs. 5(a)
and
5(b)
show the CDFs of
PR
_{1}
and
PR
_{3}
under 50% and 100% load conditions, respectively. The amplitudes of
PR
_{1}
for bearing 2 are lower than those for bearing 1 under the 50% load condition, while the amplitudes of
PR
_{3}
for bearing 2 are larger than those for bearing 1 under the 100% load condition. This is because the severity of the bearing faults induces the large harmonic of the fault frequency
[3
,
5
,
10]
; therefore,
PR
_{3}
is the dominant feature for bearing 2. As shown in this figure, fault detection with one optimal feature cannot guarantee an optimal performance for classifying a healthy motor, bearing 1, or bearing 2.
Fault detection performance for the classifier with one feature under different load condition
Fault detection performance for the classifier with one feature under different load condition
CDFs for the fault detection with an optimal feature: (a) PR_{1} under 50 % load condition and (b) PR_{3} under 100 % load condition.
For the proposed scheme, using the SFS method, a subset of features {
PR
_{1}
,
PR
_{2}
, ⋯,
PR
_{5}
} is determined as the best feature set depending on the load rate.
Fig. 6
illustrates the first classifier with the linear SVM using the best feature set {
PR
_{1}
,
PR
_{3}
} on the 50% load rate. The parameter
C
= 2
^{14.9}
is determined from the fivefold crossvalidation analysis during the training process.
Fig. 6
indicates that the healthy motors can be easily separated from the motors with faulty bearings (bearing 1 and bearing 2). For the 50% load condition, the proposed scheme is better than the previous fault detection method with one feature, as shown in
Fig. 5(a)
.
The 1^{st} classifier with linear SVM for faulty motor detection under 50 % load condition.
For the 100% load rate, the best feature set can be obtained by {
PR
_{1}
,
PR
_{3}
} using the SFS method for the first classifier with both the linear and nonlinear SVMs. As shown in
Fig. 7(a)
, for the first classifier with the linear SVM, the detection probability is 0.98 and the false alarm probability is 0, where
C
= 2
^{2}
.
Fig. 7(b)
shows the performance of the first classifier with the nonlinear SVM, where the kernel parameters
C
= 2
^{7}
and
γ
= 2
^{8}
are used for the RBF kernel. The first classifier with the nonlinear SVM gives the optimal performance under a 100% load rate. Therefore, the proposed approach can correctly differentiate all motors with faulty bearings from healthy motors using the linear SVM under the 50 % load condition, and nonlinear SVM under the 100% load condition.
Table 3
summarizes the performance and parameters of the first classifier with linear and nonlinear SVMs. With the proper parameter
C
and kernel parameter
γ
, the linear SVM obtains the optimal detection probabilities under 0% and 50% load conditions, and the nonlinear SVM gives the optimal detection probability under the 100% load condition. For linear and nonlinear SVMs, proper kernel parameter selection is important to obtain good classification results; therefore, a grid search of
C
or {
C
,
γ
} is needed to obtain the proper SVM parameters.
The 1^{st} SVM classifier for faulty motor detection under 100% load condition: (a) Linear SVM and (b) nonlinear SVM with RBF kernel.
1stSVM classification results for fault detection
1^{st} SVM classification results for fault detection
Finally, in
Table 4
, we present the fault classification using the 2
^{nd}
classifier for bearings 1 and 2. It can be seen that almost all bearing fault types have been classified correctly under different load conditions. The feature set selected for the 2
^{nd}
classifier is based on the use of the data obtained from faults involving bearings 1 and 2.
Fig. 8
shows that both bearings 1 and 2 are in two separate clusters with the feature set of {
PR
_{1}
,
PR
_{3}
} for the 50% load rate, where
C
= 2
^{4.9}
. Compared to
Fig. 6
, the normalization set for the 2
^{nd}
classifier is different from that for the 1
^{st}
classifier, and therefore, the sample points in
Fig. 8
are different from those in
Fig. 6
. Furthermore, the classification for bearing fault types on the 100% load rate has a high detection probability and low false alarm rate (
P_{D}
= 0.96 and
P_{FA}
= 0).
2ndSVM classification results for fault type detection
2^{nd} SVM classification results for fault type detection
The 2^{nd} SVM classifier used to separate bearings 1 and 2 under 50 % load condition.
5. Conclusion
In this paper, we proposed a new diagnosis method for rolling bearing faults in induction machines. The proposed method is based on the FFT and SVM methods, and consists of the two SVM classifiers to detect outerrace rolling bearing faults and their severity under different load conditions. The harmonics of faultrelated frequency of vibration signal, which can be extracted from the vibration signal, serve as new bearing fault signatures. The optimization of the fault index subsets and hyperplanes was investigated using SVM crossvalidation based on experimental data depending on the load conditions. An analysis of the experimental results shows that the proposed method has the higher detection probability and lower false alarm probability than the classifier with one feature under different load conditions. Experimental results show that the proposed twostage classifier significantly improved the detection performance of bearing faults and their severity conditions. The proposed method will be useful in other bearingrelated faults detections such as innerrace, cage, and ball faults modifying interested frequency bands.
Acknowledgements
This work was supported in part by the “Development of Motor Diagnosis Technology for the Electric Vehicle” project of Korea Electrotechnology Research Institute (KERI) and in part by the Human Resources Development program (No. 20134030200310) of the Korea Institute of Energy Technology Evaluation and Planning(KETEP) grant funded by the Korea government Ministry of Trade, Industry and Energy.
BIO
DonHa Hwang received B.S., M.S., and Ph.D. degrees in Electrical Engineering from Yeungnam University in 1991, 1993, and 2003, respectively. He is currently a principal researcher at Korea Electrotechnology Research Institute (KERI), Changwon, Korea. His main research interest are design, analysis, monitoring, and diagnosis of electric machines.
YoungWoo Youn received B.S. and M.S. degrees in Communication Engineering from Information and Communication University, Daejeon, Korea, in 2005 and 2007, respectively. He is currently a researcher at power apparatus research center at Korea Electrotechnology Research Institute (KERI), Changwon, Korea. His research interests are in condition monitoring and signal processing.
JongHo Sun received B.S., M.S., and Ph.D. degrees in Electrical Engineering from Pusan National University in 1986, 1988, and 2001, respectively. Currently, he is a principal researcher at Korea Electrotechnology Research Institute (KERI), Changwon, Korea. His interests are diagnosis techniques for electric power equipments.
KyeongHo Choi received B.S., M.S., and Ph.D. degrees in Electrical Engineering from Yeungnam University in 1991, 1995, and 2002, respectively. Currently, he is a professor in the departement of railroad electricity at Kyungbuk College, Korea.
JongHo Lee received the B.S. degree in electrical engineering and the M.S. and Ph.D. degrees in electrical engineering and computer science from Seoul National University, Seoul, Korea, in 1999, 2001, and 2006, respectively. From 2006 to 2008, he was a Senior Engineer with Samsung Electronics, Suwon, Korea. From 2008 to 2009, he was a Postdoctoral Researcher with the Georgia Institute of Technology, Atlanta, GA, USA. From 2009 to 2012, he was an Assistant Professor with the Division of Electrical Electronic and Control Engineering, Kongju National University, Cheonan, Korea. Since 2012, he has been with the faculty of the Department of Electronic Engineering, Gachon University, Seongnam, Korea. His research interests are in the area of wireless communication systems and signal processing for communication with current emphasis on multiple antenna techniques, multihop relay techniques, physical layer security, and fullduplex wireless.
YongHwa Kim received a B.S. in electrical engineering in 2001 from Seoul National University, Seoul, Korea, and a Ph.D. in electrical and computer engineering from Seoul National University, Seoul, Korea, 2007. From 2007 to 2011, he was a senior researcher with the Korea Electrotechnology Research Institute (KERI), Geonggido, Korea. From 2011 to 2013, he was an assistant professor at the Division of Maritime Electronic and Communication Engineering, Mokpo National Maritime University, Korea. Since March 2013, he has joined the faculty with the Department of Electronic Engineering at Myongji University, Korea. His general research interests include communication systems, motor drives and diagnosis, and digital signal processing. Currently, he is particularly interested in communications and digital signal processing for Smart Grid.
Thomson W. T.
,
Fenger M.
2001
“Current signature analysis to detect induction motor faults,”
IEEE Ind. Appl. Mag.
7
(4)
26 
34
Bellini A.
,
Filippetti F.
,
Tassoni C.
,
Capolino G.A.
2008
“Advances in diagnostic techniques for induction machines,”
IEEE Trans. Ind. Electron.
55
(12)
4109 
4126
DOI : 10.1109/TIE.2008.2007527
Schoen R. R.
,
Habetler T. G.
,
Kamran F.
,
Bartheld R. G.
1995
“Motor bearing damage detection using stator current monitoring,”
IEEE Trans. Ind. Appl.
31
(6)
1274 
1279
DOI : 10.1109/28.475697
Zhou W.
,
Habetler T.
,
Harley R.
2008
“Bearing fault detection via stator current noise cancellation and statistical control,”
IEEE Trans. Ind. Electron.
55
(12)
4260 
4269
DOI : 10.1109/TIE.2008.2005018
Li B.
,
Goddu G.
,
Chow M.Y.
1998
“Detection of common motor bearing faults using frequencydomain vibration signals and a neural network based approach,”
Proc. of the 1998 American Control Conference
June 2426
2032 
2036
Chow T. W. S.
,
Hai S.
2004
“Induction machine fault diagnostic analysis with wavelet technique,”
IEEE Trans. Ind. Electron.
51
(3)
558 
565
DOI : 10.1109/TIE.2004.825325
Stack J. R.
,
Harley R. G.
,
Habetler T. G.
2004
“An amplitude modulation detector for fault diagnosis in rolling element bearings,”
IEEE Trans. Ind. Electron.
51
(5)
1097 
1102
DOI : 10.1109/TIE.2004.834971
Stack J. R.
,
Habetler T. G.
,
Harley R. G.
2006
“Faultsignature modeling and detection of innerrace bearing faults,”
IEEE Trans. Ind. Appl.
42
(1)
61 
68
DOI : 10.1109/TIA.2005.861365
Bianchini C.
,
Immovilli F.
,
Cocconcelli M.
,
Rubini R.
,
Bellini A.
2011
“Fault Detection of Linear Bearings in Brushless AC Linear Motors by Vibration Analysis,”
IEEE Trans. Ind. Electron.
58
(5)
1684 
1694
DOI : 10.1109/TIE.2010.2098354
Li B.
,
MoYuen C.
,
Tipsuwan Y.
,
Hung J. C.
2000
“Neuralnetworkbased motor rolling bearing fault diagnosis,”
IEEE Trans. Ind. Electron.
47
(5)
1060 
1069
DOI : 10.1109/41.873214
Sugumaran V.
,
Ramachandran K.
2011
“Fault diagnosis of roller bearing using fuzzy classifier and histogram features with focus on automatic rule learning,”
Expert syst. Appl.
38
(5)
4901 
4907
DOI : 10.1016/j.eswa.2010.09.089
Widodo A.
,
Yang B. S.
,
Han T.
2007
“Combination of independent component analysis and support vector machines for intelligent faults diagnosis of induction motors,”
Expert Syst. Appl.
32
(2)
299 
312
DOI : 10.1016/j.eswa.2005.11.031
Esfahani E. T.
,
Wang S.
,
Sundararajan V.
2014
“Multisensor wireless system for eccentricity and bearing fault detection in induction motors,”
IEEE/ASME Trans. Mechatronics
19
(3)
818 
826
DOI : 10.1109/TMECH.2013.2260865
Frosini L.
,
Bassi E.
2010
“Stator current and motor efficiency as indicators for different types of bearing faults in Induction motors,”
IEEE Trans. Ind. Electron.
57
(1)
244 
251
Kim Y.H.
,
Youn Y.W.
,
Hwang D.H.
,
sun J.H.
,
Kang D.S.
2013
“Highresolution parameter estimation method to identify broken rotor bar faults in induction motors,”
IEEE Trans. Ind. Electron.
60
(9)
4103 
4117
DOI : 10.1109/TIE.2012.2227912
Vapnik V. N.
1999
The Nature of Statistical Learning Theory
Springer
New York
Burges C. J. C.
1998
“A Tutorial on Support Vector Machines for Pattern Recognition,”
Data mining and Knowledge Discovery
12
121 
167
Scholkopf B.
,
Smola A. J.
2002
Learning with Kernels:Support Vector Machines, Regularization, Optimization, and Beyond
The MIT Press
Hsu C. W.
,
Chang C. C.
,
Lin C. J.
2007
“A Practical Guide to Support Vector Classification”
[Online], Available:
Shiroishi J.
,
Li Y.
,
Liang S.
,
Kurfess T.
,
Danyluk S.
1997
“Bearing condition diagnostics via vibration and acoustic emission measurements,”
Mechanical Systems and Signal Processing
11
(5)
693 
705
DOI : 10.1006/mssp.1997.0113
Kim Y. H.
,
Tan A. C. C.
,
Mathew J.
,
Yang B. S.
2006
“Condition monitoring of low speed bearings: A comparative study of the ultrasound technique versus vibration measurement,”
Proc. of WCEAM 2006
182 
191
Jung J.H.
,
Lee J.J.
,
Kwon B.H.
2006
“Online diagnosis of induction motors using MCSA,”
IEEE Trans. Ind. Electron.
53
(6)
1842 
1852
DOI : 10.1109/TIE.2006.885131
Kay S. M.
1993
Fundamentals of Statistical Signal Processing: Detection Theory
PrenticeHall
Englewood Cliffs, NJ
Peterson W.
,
Birdsall T.
,
Fox W.
1954
“The theory of signal detectability,”
Proc. IRE Prof. Group Inf. Theory
4
(4)
171 
212
DOI : 10.1109/TIT.1954.1057460