A classifier fusion system for bearing fault diagnosis


Expert Systems with Applications 40 (2013) 6788–6797
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Expert Systems with Applications

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e s w a
A classifier fusion system for bearing fault diagnosis
0957-4174/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.eswa.2013.06.033

⇑ Corresponding author. Tel.: +1 (514) 396 8932; fax: +1 (514) 396 8595.
E-mail addresses: luana.bezerra@gmail.com (L. Batista), bechirbadri@yahoo.fr

(B. Badri), robert.sabourin@etsmtl.ca (R. Sabourin), marc.thomas@etsmtl.ca
(M. Thomas).
Luana Batista, Bechir Badri, Robert Sabourin ⇑, Marc Thomas
École de Technologie Supérieure, 1100, rue Notre-Dame Ouest, Montreál, QC H3C 1K3, Canada

a r t i c l e i n f o a b s t r a c t
Keywords:
Bearing fault diagnosis
Vibration analysis
Machine condition monitoring
Support vector machines
Iterative Boolean Combination
ROC curves
Classifier fusion
In this paper, a new strategy based on the fusion of different Support Vector Machines (SVM) is proposed
in order to reduce noise effect in bearing fault diagnosis systems. Each SVM classifier is designed to deal
with a specific noise configuration and, when combined together – by means of the Iterative Boolean
Combination (IBC) technique – they provide high robustness to different noise-to-signal ratio. In order
to produce a high amount of vibration signals, considering different defect dimensions and noise levels,
the BEAring Toolbox (BEAT) is employed in this work. The experiments indicate that the proposed strat-
egy can significantly reduce the error rates, even in the presence of very noisy signals.

� 2013 Elsevier Ltd. All rights reserved.
1. Introduction

Although the visual inspection of time- and frequency-domain
features of measured signals is adequate for identifying machinery
faults, there is a need for a reliable, fast and automated procedure
of diagnosis (Samanta et al., 2004). Due to the increasing demands
for greater product quality and variability, short product life-cy-
cles, reduced cost, and global competition, automatic machine con-
dition monitoring (MCM) has been gaining importance in the
manufacturing industry (Liang et al., 2004). MCM systems allow
for a significant reduction in the machinery maintenance costs,
and, most importantly, the early detection of potential faults
(Guo et al., 2005). Mass unbalance, rotor rub, shaft misalignment,
gear failures and bearing defects are exemples of faults that may
lead to the machine’s breakdown (Samanta et al., 2004).

Besides the detection of the early occurence and seriousness of
a fault, MCM systems may also be designed to identify the compo-
nents that are deteriorating, and to estimate the time interval dur-
ing which the monitored equipment can still operate before failure
(Lazzerini and Volpi, 2011). These systems continuously measure
and interpret signals (e.g., vibration, acoustic emission, infrared
thermography, etc.), that provide useful information for identifying
the presence of faulty symptoms.

The focus of this work is in rotating machines, which usually
operate by means of bearings. Since they are the place where the
basic dynamic loads and forces are applied, bearings represent a
critical component. A defective bearing causes malfunction and
may even lead to catastrophic failure of the machinery (Tandon
and Choudhury, 1999). Vibration analysis has been the most em-
ployed methodology for detecting bearings defects (Thomas,
2011). Each time a rolling element passes over a defect, an impulse
of vibration is generated. On the other hand, if the machine is oper-
ating properly, vibration amplitude is small and constant (Alguin-
digue et al., 1993). Another methodology successfully applied to
this problem has been the acoustic emission (AE) (Elmaleeh and
Saad, 2008; Tandon and Choudhury, 1999).

Automatic bearing fault diagnosis can be viewed as a pattern
recognition problem, and several systems have been designed
using well-known classification techniques, such as Artificial Neu-
ral Networks (ANNs) and Support Vector Machines (SVM). When
these systems employ real vibration data obtained from bearings
artificially damaged, they have to cope with a very limited amount
of samples. Furthermore, with exception of a few works (Guo et al.,
2005; Jack and Nandi, 2002) – which consider a validation set, be-
sides the training and test sets –, the choice of the system’s param-
eters, including the feature selection step, too often has been done
by using the same datasets employed to train/test the classifiers.
This may lead to biased classifiers that will hardly be able to gen-
eralize on new data. Another important aspect that has been little
investigated in the literature is the presence of noise, which dis-
turbs the vibration signals, and how this affects the identification
of bearing defects (Lazzerini and Volpi, 2011).

In this paper, a classification system based on the fusion of dif-
ferent SVMs is proposed to detect early defects on bearings in the
presence of high noise levels. Each SVM classifier is designed to
deal with a specific noise configuration and, when combined to-
gether – by using the Iterative Boolean Combination (IBC) tech-
nique (Khreich et al., 2010) – they provide high robustness to
different noise-to-signal ratio.

In order to produce a high amount of bearing vibration signals,
considering different defect dimensions and noise levels, the BEAr-
ing Toolbox (BEAT) is employed in this work. BEAT is dedicated to
the simulation of the dynamic behaviour of rotating ball bearings

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L. Batista et al. / Expert Systems with Applications 40 (2013) 6788–6797 6789
in the presence of localized defects, and it was shown to provide
realistic results, similar to those produced by a sensor during
experimental measurements (Sassi et al., 2007).

This paper is organized as follows. Section 2 presents the state-
of-the-art in automatic bearing fault diagnosis. Section 3 describes
the experimental methodology, including datasets, measures used
to evaluate the system performance, and the IBC technique. Finally,
the experiments are presented and discussed in Section 4.
2. The state-of-the-art in automatic bearing fault diagnosis

Fig. 1 illustrates the general structure of a bearing. It is com-
posed of six components: housing, outer race (OR), inner race
(IR), rolling elements (RE) (i.e., rollers or balls), cage and shaft
(Guo et al., 2005). As previously mentioned, the interaction of de-
fects in rolling element bearings produces impulses of vibration. As
these shocks excite the natural frequencies of the bearing ele-
ments, the analysis of the vibration signal in the frequency-do-
main, by means of the Fast Fourrier Transform (FFT), has been an
effective method for predicting the health condition of bearings
(Tandon and Choudhury, 1999).

Each defective bearing component produces frequencies, which
allow for localizing different defects occurring simultaneously.
BPFO (Ball Pass Frequency on an Outer race defect), BPFI (Ball Pass
Frequency on an Inner race defect), FTF (Fundamental Train Fre-
quency) and BSF (Ball Spin Frequency) – as well as their harmonics,
modulating frequencies, and envelopes – are examples of fre-
quency-domain indicators, calculated from kinematic consider-
ations – that is, the geometry of the bearing and its rotational
speed (Sassi et al., 2007).

It is worth noting that the shock amplitude is directly related to
the defect dimension: the bigger the defect, the bigger the shock.
Fig. 1. Typical roller bearing, showing different component parts. Adapted from
Jack and Nandi (2002).

Fig. 2. Example of a hypothetical defect located in the rolling element (a) and its corresp
frequency). Adapted from Sassi et al. (2007).
Fig. 2 presents an example of a defect located in the outer race
and its corresponding vibration signal.

Not only frequency- but also time-domain indicators have been
widely employed as input features to train a bearing fault diagno-
sis classifier. Time-domain indicators are adimensional, and allow
for representing the vibration signal through a single scalar value.
For instance, peak is the maximum amplitude value of the vibra-
tion signal, RMS (Root Mean Square) represents the effective value
(magnitude) of the vibration signal and Kurtosis describes the
impulsive shape of the vibration signal. Table 1 presents the effec-
tiveness (advantages and disadvantages) of some time-domain
indicators in describing the presence (or absence) of faulty symp-
toms (Kankar et al., 2011; Sassi et al., 2008; Tandon and Choudhu-
ry, 1999).

A bearing fault diagnosis system may be designed to provide
different levels of information about the defect (s). The first and
simpler issue investigated in the literature is the detection of the
presence or absence of a defect (Jack and Nandi, 2002; Samanta
et al., 2004). The second issue is the determination of the defect
location, which may occur in different components of a bearing
(Alguindigue et al., 1993; Bhavaraju et al., 2010). Often, the type
of defect is considered along with the defect location. For instance,
some authors consider the following classes: sandblasting of IR/OR,
indentation on the roll, unbalanced cage (Lazzerini and Volpi,
2011; Volpi et al., 2010), crack on IR/OR, spall on IR/OR, spalls on
rollers (Widodo et al., 2009), generalized fault of two balls (Alguin-
digue et al., 1993), etc.

Finally, the severity of a bearing defect is the last and perhaps
the most difficult information to be predicted. Through this infor-
mation, it may be possible to estimate the duration during which
the equipment can still operate safely. In the literature, this issue
has been partially investigated, by associating a different class to
each defect dimension (Cococcioni et al., 2009a, 2009b; Widodo
et al., 2009). Cococcioni et al. (2009a), for example, have employed
three classes for describing the seriousness of an ‘‘indentation on
the roll’’, namely, light (450lm), medium (1.1 mm) and high
(1.29 mm). The drawback of this strategy is that other defect
dimensions are not considered by the classifier. A more suitable
solution would be the estimation of defect dimensions as a regres-
sion problem.

Table 2 presents a summary of different systems reported in the
literature, with their respective employed classification tech-
niques, types of signal, descriptors (features), types of defects
and datasets. It is important to mention that the bearing defects
may be categorized as distributed or local. Distributed defects
are due to unavoidable manufacting imperfections, such as surface
roughness, waviness, misaligned races and off-size rolling ele-
ments (Sassi et al., 2007), whereas localized defects include cracks,
onding shock impulses (b), where FTF is the Fundamental Train Frequency (or cage



Table 1
Time-domain indicators.

Indicator Advantage Disadvantage

Peak May indicate the presence of a defect even at the initial stage The signal source is unknown; May create a false alarm
Root Mean Square (RMS) Toward the end of the bearing life, the RMS level increases dramatically Low sensitivity to indicate a defect at the initial stage; The signal source is unknown
Kurtosis Low sensitivity to the variations of load and speed; Well suited for detecting a defect at the

initial stage
When the defect is at an advanced stage, the Kurtosis value comes down to a value of an
undamaged bearing; The signal source is unknown

Crest Factor (CF) Impulse Factor (IF) Like Kurtosis, CF and IF are well suited for detecting a defect at the initial stage Same problems as Kurtosis
Thikat (Sassi et al., 2008) May indicate the presence of a defect at any rotational speed Same problems as Kurtosis; No physical meaning; Needs the initial RMS value
Talaf (Sassi et al., 2008) The talaf value constantly increases with the defect dimension; A slope change is an

indication of impending failure; Indicates 4 levels of degradation
The signal source is unknown; No physical meaning; Needs the initial RMS value

Table 2
Survey of bearing fault diagnosis systems. (AE = Acoustic Emission, MLP = Multi-Layer Perceptron, SVM = Support Vector Machine, CHC = Convex Hull Classifier, PNN = Probabilistic Neural Network, RNN = Recirculation Neural Network,
RBF = Radial Basis Function, GA = Genetic Algorithms, HMM = Hidden Markov Model, MFCC = Mel-Frequency Complex Cepstrum, SOM = Self-Organizing Maps, RVM = Relevance Vector Machine, QDC = Quadratic Discriminant Classifier,
LDC = Linear Discriminant Classifier, PCA = Principal Component Analysis, ICA = Independent Component Analysis, EoC = Ensemble of Classifiers.)

Refs. Classifiers Signals Features Defect classes Datasets

Kankar et al. (2011) SVM
MLP
SOM

real vibration signals,
artificial defects

5 different speeds

kurtosis, skewness, std
(from wavelet coefficients)
number of loaders, speed

faultless bearing,
IR fault, OR fault, RE fault,
fault in all components

150 samples
10-fold cross-validation

Bhavaraju et al. (2010) MLP
SOM

real vibration signals,
artificial defects,
5 different speeds

kurtosis, skewness, std
(from wavelet coefficients),
number of loaders, speed

faultless bearing,
IR fault, OR fault, RE fault,
fault in all components

150 samples
50% training,
50% test

Lazzerini and Volpi (2011) ensembles of
MLPs

real vibration signals,
artificial defects,

10 different noise levels

FFT parameters
(performed forward
feature selection)

faultless bearing, indentation on IR,
indentation on the roll, sandblasting of IR,

unbalanced cage

12740 samples
70% training, 30% test
(100 trials)

Volpi et al. (2010) one-class
CHC

real vibration signals,
artificial defects

FFT parameters
(performed forward
feature selection)

faultless bearing unbalanced cage,
indentation on IR (450 lm),
sandblasting of IR, indentation on the roll
(450 lm, 1.1 mm and 1.29 mm)

12740 samples
training with ‘‘fautless’’ class,
test with all classes
(30 trials)

Widodo et al. (2009) RVM
SVM

real AE and vibration signals,
artificial defects,
considered only low-speeds
(e.g., 20 and 80 rpm)

statistical, time- and
frequency-domain features
selected with PCA/ICA

faultless bearing, crack on IR (0.1 mm),
spall on IR (0.6 mm), crack on OR (0.1 mm),

spall on OR (0.7 mm),
spalls on rollers (1 mm and 1.6 mm)

105 samples
cross-validation

Cococcioni et al. (2009b) LDC, QDC,
MLP,

RBF NN

real vibration signals,
artificial defects,
10 different noise levels

FFT parameters
(performed forward
feature selection)

faultless bearing, indentation on IR,
indentation on the roll
(450 lm, 1.1 mm and 1.29 mm),

sandblasting of IR, unbalanced cage

12740 samples
70% training, 30% test
(100 trials)

Cococcioni et al. (2009a) LDC, QDC,
MLP, EoC

real vibration signals,
artificial defects,
5 frequency ranges

FFT parameters
(performed forward
feature selection)

faultless bearing, indentation on IR,
indentation on the roll
(450 lm, 1.1 mm and 1.29 mm),

sandblasting of IR, unbalanced cage

12740 samples
70% training, 30% test
(10 trials)

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Table 3
Survey of bearing fault diagnosis systems (continuation).

Refs. Classifiers Signals Features Defect classes Datasets

Sreejith et al. (2008) MLP real vibration signals,
artificial defects

time-domain
features

fautless bearing,
RE fault,
OR fault, IR fault

80 samples from CWRU
bearing data center (Case Western

Reserve University)
60% training, 40% test

Teotrakool et al. (2008) SVM motor current signals,
artificial defects,
4 different speeds

RMS values from
wavelet packet coefficients
(feature selection with GA)

faultless bearing vs. OR fault;
faultless bearing vs. cage fault

–

Lei et al. (2008) improved
fuzzy
c-means

real vibration signals
from locomotive

roller bearings

time-domain
features

fautless bearing
slight rub faults on OR,

serious flaking faults on OR

150 samples
for clustering

Sugumaran et al. (2008) one-class &
multi-class

SVMs

real vibration signals,
artificial defects,
3 different speeds

Kurtosis and statistical
features (selected with a
decision tree)

faultless bearing,
OR fault, IR fault,
OR fault + IR fault

–

Sugumaran et al. (2007) SVM,
proximal
SVM

real vibration signals,
artificial defects,
3 different speeds

Kurtosis and statistical
features (selected with a
decision tree)

faultless bearing,
OR fault, IR fault,
OR fault + IR fault

600 samples
83% training,
17% test

Abbasion et al. (2007) SVM real vibration signals,
artificial defects

Weibull negative
log-likelihood function
of time-domain signals

faultless bearing,
IR-drive fault, IR-fan fault,
RE-drive fault, RE-fan fault,
OR-drive fault, OR-fan fault

63 samples for test

Rojas and Nandi (2006) SVM real vibration signals,
speeds

FFT parameters
and statistical

features

faultless bearing, worn bearing,
OR fault, IR fault,
RE fault, cage fault

1920 samples
50% training,
50% test

Guo et al. (2005) MLP,
SVM

real vibration signals,
defects artificially introduced,
16 different speeds

statistical, frequency-
and time-domain features
selected with GA

fautless bearing,
worn bearing, cage fault,

IR fault, OR fault,
RE fault

2880 samples
1/3 training,

1/3 test 1/3
validation,

Table 4
Survey of Bearing Fault Diagnosis Systems (continuation).

Refs. Classifiers Signals Features Defect classes Datasets

Purushotham et al. (2005) HMMs
(one per class)

real vibration signals,
artificial defects,
considered multiple faults

MFCC coefficients
(wavelet analysis)

2 faults on IR + 1 fault on RE,
2 faults on OR + 1 fault on RE,

one fault in each component

training,
test
(4 different splits)

Samanta et al. (2004) MLP,
RBF NN,
PNN

real vibration signals,
artificial defects

statistical and
time-domain features
selected with GA

fautless bearing vs.
faulty bearing (OR fault)

288 samples
50% training,

50% test
Samanta et al. (2003) MLP

SVM
real vibration signals,
artificial defects

statistical and
time-domain features
selected with GA

fautless bearing vs.
faulty bearing (OR fault)

288 samples
60% training, 40% test

Samanta and Al-Balushi (2003) MLP real vibration signals,
artificial defects

statistical and
time-domain features

fautless bearing vs.
faulty bearing (OR fault)

200 samples
60% training, 40% test

Lou and Loparo (2004) neuro-fuzzy real vibration signals,
artificial defects,

4 different load values

std of wavelet
coefficients

fautless bearing,
IR fault,
RE fault

24 samples
50% training,
50% test

Jack and Nandi (2002) SVM,
MLP

real vibration signals,
artificial defects,
16 different speeds

statistical and
frequency-domain features
selected with GA

faultless (brand new bearing,
worn bearing) vs. faulty (OR fault, IR fault,
RE fault, cage fault)

2880 samples
1/3 training, 1/3 test,
1/3 validation

Jack and Nandi (2001) SVM,
MLP

real vibration signals,
artificial defects,
16 different speeds

statistical and
frequency-domain features

faultless bearing,
worn bearing, OR fault, IR fault,

RE fault, cage fault

960 samples
1/3 training, 1/3 test,
1/3 validation

Alguindigue et al. (1993) RNN,
MLP

real vibration signals,
real and artificial defects

high- and low-
frequency
features

faultless bearing, fault on IR,
generalized fault on IR, fault on OR,
generalized fault on OR, artificial
fault of a ball, generalized fault of two balls,
generalized fault of all the components

the test set
contained samples from
the training set

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Table 6
Classes of defects.

OR IR RE

class 0 0 0 0
class 1 1 0 0
class 2 0 1 0
class 3 0 0 1
class 4 1 1 0
class 5 1 0 1
class 6 0 1 1
class 7 1 1 1

Table 7
Data partitioning for each DB(nc) (1 6 nc 6 6).

Positive class Negative class

trn 3500 3500
vld 1750 1750
tst (per noise level) 1750 1750

Table 8
ROC AUC on validation data.

System AUC

S(nc=1) 1
S(nc=2) 0.9999
S(nc=3) 0.9999
S(nc=4) 0.9996
S(nc=5) 0.9992
S(nc=6) 0.9989

Fig. 3. DET curves of the selected systems S(nc), 1 6 nc 6 6, using their respective
validation sets (vld).

6792 L. Batista et al. / Expert Systems with Applications 40 (2013) 6788–6797
pits and spalls on the rolling surfaces (Tandon and Choudhury,
1999). In Tables 2–4, only localized defects are considered.

Some authors have worked with signals obtained from multiple
rotational speeds. With exception of Widodo et al. (2009) and
Sugumaran et al. (2007) – which developed a different system
for each rotational speed –, the classifiers have been trained/tested
with data corresponding to several speeds simultaneously (Guo
et al., 2005; Jack and Nandi, 2002; Rojas and Nandi, 2006; Teotra-
kool et al., 2008), and, sometimes, the rotational speed is employed
as input-feature (Bhavaraju et al., 2010; Kankar et al., 2011). How-
ever, these systems consider either non-rotating loads or no-load
conditions, which means that the shock amplitudes are not af-
fected if the rotational speed changes. So far, no work investigated
the case where a same system has to deal with different speeds un-
der a rotating load.

Regarding non-rotating loads, few works have considered sig-
nals obtained from multiple load conditions. While (Bhavaraju
et al., 2010; Kankar et al., 2011) employed the number of loaders
(which goes from 0 to 2) as input-feature, (Lou and Loparo, 2004)
acquired vibration data from four load values (0, 1, 2 and 3 Horse
Power (HP)). In both cases, the signals regarding the different load
conditions were employed to train/test a same classifier.

3. Methodology

The objective of this work is to detect the presence or absence of
bearing defects by taking into account six levels of noise, i.e., sig-
nal-to-noise ratio ranging from 40 to 5 db. Noise robustness is
achieved through the incorporation of noisy data during the train-
ing phase, along with the fusion of different SVMs, each one is de-
signed to deal with a specific noise configuration.

The BEAT simulator (Sassi et al., 2007) is employed to generate
vibration signals coming from the operation of a ball bearing type
SKF 1210 ETK9. The rotational speed is 1800 RPM, subjected to a
non-rotating load of 3000 N. From the simulated data, the follow-
ing time-domain indicators are calculated: RMS, peak, Kurtosis,
crest factor, impulse factor and shape factor. As frequency-domain
indicators, BPFO, BPFI, 2BSF, as well as their first two hamonics are
calculated. It is worth noting that the frequency-domain indicators
employed in this work are normalized with respect to the rota-
tional speed. Regarding the time-domain indicators, they are inde-
pendent of the rotational speed when the load is non-rotating.

The rest of this section describes the datasets and the perfor-
mance evaluation methods employed in the experiments, as well
as the Iterative Boolean Combination technique.

3.1. Datasets

Six noise configurations (nc = 1,2,3,4,5,6) are considered in this
paper, as indicated in Table 5. For each noise configuration, there
is a specific database, that is, DB(nc). Each sample in the databases
is composed of a set of frequency and temporal indicators, plus
the defect diameter, ddef, related to each bearing component, i.e.,
ddef(OR), ddef(IR) and ddef(RE). Eight classes of defects are defined in Ta-
ble 6. The flag = 1 indicates that there is a defect in the correspond-
ing component, while flag = 0 indicates the absence of defect. For
Table 5
Noise configurations (nc).

nc Training/validation Test

1 40 db 40, 30, 20, 15, 10, 5 db
2 40, 30 db 40, 30, 20, 15, 10, 5 db
3 40, 30, 20 db 40, 30, 20, 15, 10, 5 db
4 40, 30, 20, 15 db 40, 30, 20, 15, 10, 5 db
5 40, 30, 20, 15 10 db 40, 30, 20, 15, 10, 5 db
6 40, 30, 20, 15, 10, 5 db 40, 30, 20, 15, 10, 5 db
instance, class 6 corresponds to two different defects occuring
simultaneously: one in the outer race, and another in the ball.
For the non-defective components, ddef goes from 0 mm to
0.016 mm. Regarding the defective components, ddef goes from
0.017 mm to 2.8 mm.

Since the objective of this work is to indicate the presence or
absence of a bearing defect, regardless its location, only two clas-
ses are considered, i.e, faultless and faulty. The faultless class
corresponds to the class 0 (see Table 6) and, in order to have
two balanced classes, the faulty class contains subsets of samples
from classes 1 to 7. Table 7 presents the way the samples are
partitioned.



Fig. 4. DET curves of the selected systems S(nc), 1 6 nc 6 6, using the test sets (tst).

L. Batista et al. / Expert Systems with Applications 40 (2013) 6788–6797 6793
3.2. Performance evaluation methods

The ROC (Receiving Operating Characteristics) curve – where
the true positive rates (TPR) are plotted as function of the false po-
sitive rates (FPR) – is a powerful tool for evaluating, comparing and
combining pattern recognition systems (Khreich et al., 2010).
Several interesting properties can be observed from ROC curves.
First, the AUC (Area Under Curve) is equivalent to the probability
that the classifier will rank a randomly chosen positive sample
higher than a randomly chosen negative sample. This measure is
useful to characterize the system performance through a single
scalar value. In addition, the optimal threshold for a given class



Table 9
Average EER ±r (%) on test data over 10 trials.

tst S(nc=1) S(nc=2) S(nc=3) S(nc= 4) S(nc=5) S(nc=6)

40 db 0.02 ± 0.02 0.05 ± 0.05 0.10 ± 0.07 0.17 ± 0.10 0.38 ± 0.17 0.57 ± 0.27
30 db 1.40 ± 1.09 0.00 0.01 ± 0.01 0.09 ± 0.07 0.14 ± 0.10 0.32 ± 0.16
20 db 5.38 ± 0.81 7.51 ± 1.01 0.07 ± 0.06 0.06 ± 0.06 0.08 ± 0.08 0.10 ± 0.06
15 db 20.98 ± 7.4 34.12 ± 6.7 � 0.11 ± 0.03 0.16 ± 0.07 0.15 ± 0.06
10 db � � � � 0.27 ± 0.09 0.68 ± 0.26
5 db � � � � � 0.36 ± 0.08

10
−1

10
0

10
1

10
2

10
−1

10
0

10
1

10
2

FPR (%)

FN
R

 (%
)

DET curves (vld)

IBC
MRDET
Individual Systems

4 5
6

8
7

3

Fig. 5. DET curve obtained with IBC using a validation set containing all noise
levels. The DET curves of the 6 individual systems and the Maximum Realizable DET
curve (MRDET) are shown as well.

Table 10
Operating points of IBC DET curve.

Operating point FNR (%) FPR (%) Average (%)

1 100.00 0.00 50.00
2 0.89 0.00 0.45
3 0.65 0.06 0.36
4 0.48 0.24 0.36
5 0.42 0.42 0.42
6 0.24 1.13 0.69
7 0.18 2.68 1.43
8 0.12 6.25 3.19
9 0.00 15.65 7.83
10 0.00 100.00 50.00

Table 11
Decision thresholds associated to the EER
operating point.

Classifier Threshold

c1 0.9919
c2 0.9816
c3 0.9916
c4 1.5587e�004
c5 0.0095
c6 0.0452

6794 L. Batista et al. / Expert Systems with Applications 40 (2013) 6788–6797
distribution lies on the ROC convex hull, which is defined as being
the smallest convex set containing the points of the ROC curve. Fi-
nally, by taking into account several operating points, the ROC
curve allows for analyzing these systems under different classifica-
tion costs (Fawcett, 2006). A similar way to evaluate systems is
through a DET (Detection Error Trade-off) curve, in which the false
negative rates (FNR) are plotted as function of the false positive
rates, generally, on a logarithmic scale.

In this work, ROC and DET curves are computed from the output
probabilities provided by the classifiers. The validation set, vld, is
used for this task. In order to test a given classifier, its correspond-
ing ROC operating points (thresholds) are applied to the set, tst. Re-
sults on test are shown as well in terms of equal error rate (EER),
which is obtained when the threshold is set to have the false neg-
ative rate approximately equal to the false positive rate.

3.3. Iterative Boolean Combination (IBC)

Ensembles of classifiers (EoCs) have been used to reduce error
rates of many challenging pattern recognition problems. The moti-
vation of using EoCs stems from the fact that different classifiers
usually make different errors on different samples. When the re-
sponse of a set of C classifiers is averaged, the variance contribution
in the bias-variance decomposition decreases by 1C, resulting in a
smaller classification error (Tumer and Ghosh, 1996).

It has been recently shown that the Iterative Boolean Combina-
tion (IBC) (Khreich et al., 2010) is an efficient technique for com-
bining systems in the ROC space. IBC iteratively combines the
ROC curves produced by different classifiers using all Boolean func-
tions (i.e., a _ b, :a _ b, a _:b, :(a _ b), a ^ b, : a ^ b, a ^:b,
:(a ^ b), a � b, and a � b), and does not require prior assumption
that the classifiers are statistically independent. At each iteration,
IBC selects the combinations that improve the Maximum Realiz-
able ROC (MRROC) curve – i.e., the convex hull obtained from all
individual ROC curves – and recombines them with the original
ROC curves until the MRROC ceases to improve. For more details
on the IBC technique, please refer to Algorithms 1 to 3 in Khreich
et al. (2010).

4. Simulation results and discussions

Two main experiments are performed. In the first experiment,
each database DB(nc)(1 6 nc 6 6) is employed in the generation of
a baseline system S(nc). For each DB(nc):

� trn is used to train n different classifiers ci, 1 6 i 6 n, by employ-
ing different SVM parameters;
� vld is used to validate each individual classifier ci, by means of

ROC curves, and select that one with the highest AUC. The select
classifier is called S(nc);
� tst is used to test the performance of S(nc).

In the second experiment, the IBC technique (Khreich et al.,
2010) is used to combine the best classifier of each noise
configuration.

4.1. Experiment 1

The goal of the first experiment was to obtain the best baseline
system for each one of the noise configurations defined in Table 5.
For each database DB(nc)(1 6 nc 6 6), several SVMs were trained
using the grid search technique (Chang and Lin, 2001), so that



10
−1

10
0

10
1

10
2

10
−1

10
0

10
1

10
2

FPR (%)

FN
R

 (%
)

DET curves (tst = 40db)

IBC
Individual systems

10
−1

10
0

10
1

10
2

10
−1

10
0

10
1

10
2

FPR (%)

FN
R

 (%
)

DET curves (tst = 30db)

IBC
Individual systems

10
−1

10
0

10
1

10
2

10
−1

10
0

10
1

10
2

FPR (%)

FN
R

 (%
)

DET curves (tst = 20db)

IBC
Individual systems

10
−1

10
0

10
1

10
2

10
−1

10
0

10
1

10
2

FPR (%)

FN
R

 (%
)

DET curves (tst = 15db)

IBC
Individual systems

10
−1

10
0

10
1

10
2

10
−1

10
0

10
1

10
2

FPR (%)

FN
R

 (%
)

DET curves (tst = 10db)

IBC
Individual systems

10
−1

10
0

10
1

10
2

10
−1

10
0

10
1

10
2

FPR (%)

FN
R

 (%
)

DET curves (tst = 5db)

IBC
Individual systems

Fig. 6. DET curve obtained with IBC using the test sets (tst). The DET curves of the 6 individual systems are shown as well.

L. Batista et al. / Expert Systems with Applications 40 (2013) 6788–6797 6795
the SVM providing the highest AUC is selected. To train the SVMs
with RBF kernel, the following values were employed: c =
({2�4,2�3,2�2,2�1,20} and C = {2�5,2�4,2�3,2�2,2�1,20,21,22,23, 24,25}.
Since the obtained ROC curves reached AUC close to 1, as indi-
cated in Table 8, DET curves on a log–log scale are presented in-
stead (see Fig. 3 (a)). Note that the curve representing system



Table 12
Average EER ±r (%) on test data over 10 trials.

tst IBC technique Majority vote Single best (S(nc=6))

40 db 0.04 ± 0.04 0.06 ± 0.06 0.57 ± 0.27
30 db 0.00 0.01 ± 0.02 0.32 ± 0.16
20 db 0.11 ± 0.06 0.06 ± 0.06 0.10 ± 0.06
15 db 0.11 ± 0.04 0.10 ± 0.04 0.15 ± 0.06
10 db 0.29 ± 0.09 � 0.68 ± 0.26
5 db 0.33 ± 0.07 � 0.36 ± 0.08

Table 13
Additional error rates ±r (%) obtained with IBC over 10 trials.

tst FNR (%) FPR (%) Average (%)

Expected FPR = 1%
40 db 0.02 ± 0.02 10.70 ± 7.66 5.36
30 db 0.01 ± 0.01 8.61 ± 5.09 4.31
20 db 0.13 ± 0.15 5.34 ± 3.92 2.73
15 db 0.16 ± 0.09 6.48 ± 3.50 3.32
10 db 0.18 ± 0.11 8.94 ± 2.78 4.56
5 db 0.09 ± 0.10 21.87 ± 8.68 10.98

Expected FPR = 0.1%
40 db 0.03 ± 0.03 0.37 ± 0.65 0.40
30 db 0.01 ± 0.02 0.15 ± 0.33 0.08
20 db 0.18 ± 0.13 0.01 ± 0.01 0.09
15 db 0.23 ± 0.10 0.09 ± 0.12 0.16
10 db 0.36 ± 0.13 1.35 ± 0.62 0.85
5 db 0.15 ± 0.08 5.74 ± 1.21 2.94

Expected FPR = 0.01%
40 db 0.05 ± 0.04 0.10 ± 0.27 0.07
30 db 0.03 ± 0.04 0.03 ± 0.07 0.03
20 db 0.50 ± 0.31 0.00 0.02
15 db 0.56 ± 0.36 0.02 ± 0.03 0.29
10 db 1.60 ± 1.14 0.14 ± 0.10 0.87
5 db 0.28 ± 0.13 0.95 ± 0.44 0.61

Expected FPR = 0.001%
40 db 0.09 ± 0.09 0.11 ± 0.26 0.10
30 db 0.07 ± 0.14 0.03 ± 0.07 0.05
20 db 0.63 ± 0.38 0.00 0.31
15 db 0.94 ± 0.66 0.01 ± 0.02 0.47
10 db 3.38 ± 3.20 0.06 ± 0.07 1.72
5 db 0.48 ± 0.29 0.51 ± 0.53 0.49

Expected FPR = 0.0001%
40 db 0.09 ± 0.10 0.11 ± 0.26 0.10
30 db 0.10 ± 0.18 0.03 ± 0.07 0.06
20 db 0.66 ± 0.37 0.00 0.33
15 db 0.96 ± 0.68 0.01 ± 0.02 0.48
10 db 3.68 ± 3.56 0.06 ± 0.07 1.87
5 db 0.52 ± 0.34 0.46 ± 0.55 0.49

6796 L. Batista et al. / Expert Systems with Applications 40 (2013) 6788–6797
S(nc=1) does not appear in the graphic because a complete separa-
tion of both classes was obtained.

Fig. 4 shows the DET curves obtained on test data (tst) using the
validation operating points. Observe that DET curves plotted in a
same graphic are the results of a same system on different test
data. Therefore, these curves are useful in order to analyse the
robustness of each system regarding individual noise levels. It is
worth noting that system S(nc=1) provided a complete class separa-
tion for 40 db (that’s why the corresponding DET curve does not
appear in the graphic), and, in a similar way, S(nc=2) and S(nc=3) pro-
vided a complete class separation for 40 db and 30 db.

Table 9 presents the average EER – as well as the standard devi-
ation, r – obtained for each noise level during test, over 10 trials.
The symbol ‘�’ indicates that the system has a random (or worse
than random) behaviour for a given test set. A similar situation
was observed in the work ofLazzerini and Volpi (2011), where clas-
sification accuracies of 50% or less were obtained for high levels of
noise. As expected, the systems become more robust to higher
noise levels as they are gradually incorporated to the training
phase.
4.2. Experiment 2

In the second experiment, IBC was used to combine the best
classifier of each noise configuration, found in the first experiment.
For all classifiers, a same validation set containing all noise levels
(i.e., 40, 30, 20, 15, 10 and 5 db) was employed. Since a high num-
ber of combinations is performed, the number thresholds per curve
was limited to 500 (in the previous experiment, all validation
scores were employed as thresholds).

Fig. 5 shows the DET curve obtained with IBC, along with the
DET curves of the six systems employed during the combination
process. Note that IBC improved the Maximum Realizable DET
(MRDET) curve of the individual systems.

The operating points falling on the IBC curve are presented on
Table 10. Each point is the result of a Boolean combination of dif-
ferent individual classifiers. For instance, the operating point 5,
which gives the EER, corresponds to a boolean combination (BC)
of all 6 classifiers (cj,1 6 j 6 6), that is, BC{EER} = (c1 ^ c2 ^ c3 ^ c4 ^ -
c5 ^ c6), using the decision thresholds indicated in Table 11.

It is worth noting that the AND rule emerges most of the time in
the IBC curve of Fig. 5. In the ideal case, when the classifiers are
conditionally independent, and their ROC/DET curves are proper
and convex, the AND and OR combinations are proven to be opti-
mal, providing a higher performance than the original ROC curves
(Khreich et al., 2010). Indeed, the datasets employed to design the
proposed system are independent, randomly generated by using
the simulator BEAT.

Fig. 6 shows the DET curves obtained on test data using the IBC
points indicated in Fig. 5, and Table 12 presents the average EER
(over 10 trials) obtained with IBC, Majority vote and with the best
single classifier. The Majority vote rule reached very low EER with
respect to 40, 30, 20 and 15 db noise levels. On the other hand, a
random behaviour was observed for 10 and 5 db noisy data. The
reason is due to the fact that the majority of the individual classi-
fers presents a random behaviour for high levels of noise.

Observe that IBC provided an improvement for almost all test
datasets with respect to the single best classifier obtained in the
previous experiment.

Finally, Table 13 presents additional results of IBC on test data,
when the threshold is set in order to reach FPR (%) =
{1,0.1,0.010.001,0.0001}. These intermediate points are obtained
by using interpolation (Scott et al., 1998). Note that the FPR de-
creases at the expense of an FNR increasing. In practice, the
trade-off between FPR and FNR can be adjusted by the operators
according to the current error costs.
5. Conclusion

In this paper, a new system based on the fusion of classifiers in
the ROC space was proposed in order to detect the presence of
absence of bearing defects in noisy environments. Noise robust-
ness was achieved through the incorporation of noisy vibration
signals (ranging from 40 to 5 db) during the training phase, along
with the Iterative Boolean Combination (IBC) of different SVMs,
each one designed to deal with a specific noise configuration. In
order to generate enough vibration signals, considering as well
different defect dimensions, the BEAring Toolbox (BEAT) was
employed.

Experiments performed using time- and frequency- domain
indicators (i.e., RMS, peak, Kurtosis, crest factor, impulse fac-
tor, shape factor, BPFO, BPFI, 2BSF, and hamonics) indicated
that the proposed system can significantly reduce the error
rates, even in the presence of high levels of noise. Future work
consist of validating the proposed strategy with real vibration
signals.



L. Batista et al. / Expert Systems with Applications 40 (2013) 6788–6797 6797
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	A classifier fusion system for bearing fault diagnosis
	1 Introduction
	2 The state-of-the-art in automatic bearing fault diagnosis
	3 Methodology
	3.1 Datasets
	3.2 Performance evaluation methods
	3.3 Iterative Boolean Combination (IBC)

	4 Simulation results and discussions
	4.1 Experiment 1
	4.2 Experiment 2

	5 Conclusion
	References