Research A rticle
Bearing Fault Diagnosis Based on Deep Belief Network and
Multisensor Information Fusion
Jie Tao,
1,2
Yilun Liu,
1,3
and Dalian Yang
1,4
1
School of M echanical and Electrical Engineering, Central South U niversity, Changsha 410083, China
2
Key Laboratory of Kno wledge Processing and Networked Manufacturing, Hu na n University of Science and Technology,
Xiangtan 411201, China
3
Light Alloy Research Institute, Central South University, Changsha 410083, China
4
H u na n Provincial Key Labora tory of Health Ma i ntenance for M echa n ical Equipment, H u na n University of Science and Technology ,
Xiangtan 411201, China
Correspondence should be addressed to Jie Tao; caroltaojie@.com
Received April ; Revised August ; Accepted August
Academic Editor: Ganging Song
Copyright © Jie Tao et al. is is an open access article distributed under the Creative Commons Attribution License, which
permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In the rolling bearing fault diagnosis, the vibration signal of single sensor is usually nonstationary and noisy, which contains very
little useful information, and impacts the accuracy of fault diagnosis. In order to solve the problem, this paper presents a novel
fault diagnosis method using multivibration signals and deep belief network (DBN). By utilizing the DBN’s learning ability, the
proposed method can adaptively fuse multifeature data and identify various bearing faults. Firstly, multiple vibration signals are
acquainted from various fault bearings. Secondly, some time-domain characteristics are extracted from original signals of each
individual sensor. Finally, the features data of all sensors are put into the DBN and generate an appropriate classier to complete fault
diagnosis. In order to demonstrate the eectiveness of multivibration signals, exper iments are carried out on the individual sensor
with the same conditions and procedure. At the same time, the method is compared with SVM, KNN, and BPNN methods. e
results show that the DBN-based method is able to not only adaptively fuse multisensor data, but also obtain higher identication
accuracy than other methods.
1. Introduction
Bearing is one of the critical components which has a broad
range of application in mechanical equipment. Due to the
overload, fatigue, wear, corrosion, and other reasons, bearing
is easily damaged in the process of machine operation.
Asamatteroffact,morethan%ofrotatingmachine
malfunctions are related to bearing faults [, ]. Actually, a
rolling bearing fault may lead to equipment intense shaking,
apparatus shutdown, stopping producing, and even casual-
ties. In general, the early weak fault of bearing is complicated
and hard to detec t [, ]. erefore, b earing state monitoring
and analysis is very important, in which it can discover
early weak fault of the bearing and control the fault damage
situation in time.
Recently, fault detection and diagnosis of bearing has
been attracting considerable attention. Among all the kinds
of bearing fault diagnosis methods, vibra tion signal anal-
ysis is one of the most principal and useful tools [].
In vibration-based bearing fault diagnosis, t here are t wo
kindsofapproachesthathavebeenproveneectiveto
fault diagnosis: signal processing and pattern recognition
[, ]. Conventional signal processing techniques such as
fast Fourier transform (FFT), wavelet transforms (WT), and
empirical mode decomposition (EMD) have been applied to
bearing fault diagnosis and achieved some eectiveness [,
]. For pattern recognition approaches, articial intelligence
and machine learning are extensively used and studied, for
example, fuzzy logic, support vector machine (SVM), and
articial neural network (NN) [, ]. However, most research
only focused on single vibration analysis in bearing fault
diagnosis. In fact, when using a single sensor vibration, the
fault characteristics are very weak and useful information is
limited. So, it requires intricate signal processing and feature
Hindawi Publishing Corporation
Shock and Vibration
Volume 2016, Article ID 9306205, 9 pages
http://dx.doi.org/10.1155/2016/9306205
Shock and Vibration
Visible layer
Hidden layer
BPNN
RBM
RBM
RBM
RBM
···
···
···
···
···
···
···
h
1
h
2
h
j
h
n
1
i
m
2
,
2
,
2
1
,
1
,
1
n
,
n
,
n
ij
F : Basic structure of DBN.
extraction. Sometimes the accuracy of fault diagnosis is not
stable.
To improve the diagnosis accuracy of bearing, some
researches put forward the multisignals. At present, fusion
of multisource signals mainly focused on three aspects: data
level, feature level, and decision level. Among them, the
data level fusion primarily mixed the diagnosis objects such
as temperature, pressure, and vibration signals [, ]. is
needs various kinds of sensors and instruments in the process
of data gathering. e monitoring cost is expensive and the
manipulation is complicated. However, in the convergence
of feature level with the same kinds of signals, it needed
complex signal analysis and weighted calculation [, ].
ese methods had some shortcomings such as poor real-
time property and weak generalization ability. In the decision
level, the intelligent approaches introduced by the literature
are, for example, expert systems, decision tree, and SVM
[, ]. However, these methods all belong to the shallow
learning method; the learning ability is lower.
Recently, deep learning became popular in articial
intelligence and machine le arning []. As a key framework
of deep learning, deep belief network (DBN) is primly
constituted by stacked restricted Boltzmann machines (RBM)
which is a generative stochastic neural network that can
learn probability distribution over abundant data []. In
, Hinton and colleagues utilized contrastive divergence
to advance the RBM training process that greatly improved
the learning eciency of the DBN. e essence of DBN
is the capability to automatically extract features through a
successive learning process; it can mine the features from
dierentaspectsofthedatainlowerlevelsasinputfor
the next layer [, ]. In addition, DBN accomplishes the
learning process with an unsupervised pretraining and super-
vised ne-tuning. So, DBN has more mapping capability and
extensive adaptability by a hierarchical structure. Due to the
greatadvantagesofDBN,ithasobtainedgoodeectinareas
such as natural language understanding, image processing,
speech recognition, and document recognition [–].
Lately, DBN gets the preliminary application in the
eld of fault diagnosis. Shao et al. [] developed particle
swarm to optimize the structure of the DBN and applied it
to analyze the simulation signals and experimental signals
of a rolling bearing, which obtained more accurate and
robust results than other intelligent methods. Tamilselvan et
al. [] originally presented a novel multisensor diagnosis
methodology which used the DBN in system health diagnosis
such as aircra engine and electric power transformer. Gan
et al. [] constructed a two-layer DBN of rolling-element
bearing fault diagnosis, and experiments showed that DBN
got highly reliable results compared to those obtained by
SVM and BPNN; Lei et al. [] proposed a method for
multistage gear fault diagnosis with deep learning, which
can adaptively extract a vailable fault characteristics from the
original data and acquire higher diagnostic accuracy t han
subsistent methods. Tran et al. [] presented an approach to
implement DBN and multi-information for fault diagnosis of
reciprocating compressors.
is paper focuses on the early weak fault of rolling
bearing and applies the DBN to integrate the time-domain
features of multivibration. e remainder of this paper is
organized as follows. In Section , the methodologies of deep
belief network are introduced. In Section , the process of
multivibration signal fusion is described. In Section , a
bearing test rig is explained and experiments are conducted
for the proposed method. In Section , implementation
of classier based on the DBN model is presented. e
obtained results and their evaluation are described. Finally,
conclusions and future work are given in Section .
2. Deep Belief Network
2.1. Deep Belief Network Architecture. DBN is a model based
on probability of energy generation, which comprises mul-
tiple layers of restricted Boltzmann machines (RBM) and a
backpropagation neural network (BPNN) []. Figure is the
fundamental structure of DBN; the multilayered architecture
makessurethatDBNcanbetrainedthroughbottom-up
learning in a sequence of RBMs and top-down ne-tuning
by BPNN [].
Restricted Boltzmann machine, the key prototype of
DBN, is structured by a layer of visible (or input) units and
a layer of hidden (or output) units. As every unit is binary,
Shock and Vibration
it is trained by the activation probabilities. e units in the
same layer are not connected to each other but have directed
symmetrical connections to the units in the next layer. In
DBN, the hidden layer of the RBM becomes the visible layer
of the next RBM, so they set up a successive hierarchy by
stacked RBMs.
In RBM, the visible node is denoted by V
𝑖
and the hidden
node is represented by
𝑗
.eweightsbetweenV
𝑖
and
𝑗
are
directed and denoted by w
𝑖𝑗
. e visible and hidden nodes
have their biases represented by vectors c and b,respectively.
b
𝑖
, c
𝑗
, and w
𝑖𝑗
of all RBMs make up the parameter set in
DBN. As the values of dene a probability distribution over
the joint states of the visible and hidden nodes by an energy
function,
(
k,h
)
=−
𝑚
𝑖=1
V
𝑖
c
𝑖
−
𝑛
𝑗=1
𝑗
b
𝑗
−
𝑚
𝑖=1
𝑛
𝑗=1
V
𝑖
𝑗
w
𝑖𝑗
.
()
e ultimate purpose of DBN training is to nd the best
, which can minimize the model energy error and make
the model at an equilibrium state. So, the energy function is
utilized to dene the joint probability distribution between v
and h as follows:
(
k,h |
)
=
1
(
)
−𝐸(k,h|𝜃)
,
(
)
=
k,h
−𝐸(k,h|𝜃)
.
()
Since DBN has no intralayer connections, the conditional
probability distributions of visible and hidden nodes can be
calculated by
V
𝑖
=1|h=
1
1+exp −b
𝑖
−∑
𝑗
𝑗
w
𝑖𝑗
,
()
𝑖
=1|k=
1
1+exp −c
𝑗
−
∑
𝑖
V
𝑖
w
𝑖𝑗
.
()
2.2. e DBN Training Process. Generally, the DBN training
procedure includes two parts: pretraining and ne-tuning.
e pretraining is an unsupervised learning procedure which
used the unlabeled data to train the individual RBM. e
ne-tuning is a supervised learning process which utilized the
backpropagation algorithm to further adjust the parameters.
In the pretraining, each layer is trained by the RBM rules.
Since the RBM model is with binary units, it can be learned
by stochastic gradient descent on the negative log-likelihood
probability of the training data. e functions are as follows:
ln
(
k;
)
w
𝑖𝑗
=V
𝑖
𝑗
𝑑
−V
𝑖
𝑗
𝑚
,
ln
(
k;
)
b
=
𝑗
𝑑
−
𝑗
𝑚
,
ln
(
k;
)
c
=V
𝑖
𝑑
−V
𝑖
𝑚
,
()
where :
𝑑
denotes an expectation of the data distribution
and :
𝑚
is an expectation of the distribution dened by the
model.
With the RBM property, it is easy to compute an unbiased
sample of :
𝑑
to the data distribution. However, obtaining
an unbiased sample of :
𝑚
is quite dicult []. Actually,
the RBM learning method closely approximates the gradient
objective function called contrastive divergence (CD) [], in
which :
𝑚
is substitu ted by iterations of Gibbs sampling
as expressed in (), where an iteration of alternating Gibbs
sampling includes updating all parallel visible nodes by using
(), subsequently updating all parallel hidden no des by ().
ln
(
k;
)
w
𝑖𝑗
≈V
𝑖
𝑗
0
−V
𝑖
𝑗
𝑘
,
ln
(
k;
)
b
≈
𝑗
0
−
𝑗
𝑘
,
ln
(
k;
)
c
≈V
𝑖
0
−V
𝑖
𝑘
.
()
Actually, one-step Gibbs sampling has been shown to
perform surprisingly well []. Based on (), the updated
methods for all parameters are given by the following equa-
tion, where represents learning rate whose value is between
and:
w ← V
𝑖
𝑗
0
−V
𝑖
𝑗
1
,
b ←
𝑗
0
−
𝑗
1
,
c ← V
𝑖
0
−V
𝑖
1
.
()
In the training process, dataset is usually divided into
minibatches with a small number of data vectors and the
values of are updated aer handling each minibatch. To
stabilize the RBM learning procedure, a momentum () is
oen utilized in updating the synaptic weights and biases.
With momentum (),theupdate, at the current epoch, can
be associated with the update in the preceding epoch and
calculated as
w
𝑛
← w
𝑛−1
+V
𝑖
𝑗
0
−V
𝑖
𝑗
1
,
b
𝑛
← b
𝑛−1
+
𝑗
0
−
𝑗
1
,
c
𝑛
← c
𝑛−1
+V
𝑖
0
−V
𝑖
1
.
()
Aer the bottom-up successive learning, the following
step of t he DBN training is top-down ne-tuning. Fine-
tuning is a supervise d learning process which used the
backpropagation (BPNN) to further decrease the training
error and advance the classication accuracy of the DBN.
As the BPNN is supervised learning, ne-tuning uses labeled
data for the DBN training. Unlike the unsupervised training
in DBN that only deals one RBM at a time, the BPNN
simultaneously trains all layers in DBN. e training error of
BPNN is calculated with model outputs and the target label
data. And the backpropagation learning is continued until the
model output attains the maximum number of epochs.
Shock and Vibration
Vibrating sensor 1
Vibrating sensor 2
Vibrating sensor n
Signal acquisition
Primitive character 1
Feature extraction
Primitive character 2
Primitive character n
Deep belief
network
Information fusion
Training
Te st
Classier
Diagnosis results
Fault recognition
······
F : e ow diagram of multisensor information fusion.
3. Multisignal Fusion with DBN
Multisensor information fusion technology can obtain more
accurate, rich fault features from vibration signals [].
However, in the conventional information integration, sig-
nal processing needs to master a lot of signal processing
technologies and to be combined with rich experience in
engineering practice to extract fault features. Meanwhile,
in the pattern recognition, traditional machine learning
only contains single nonlinear transform structure; it cannot
adaptively integrate the multi-information [, ].
In this paper, we apply the deep belief network (DBN)
to adaptively fuse multivibrations. ere are four main
processes in the proposed bearing: multichannel signal
acquisition, feature extraction, information fusion, and fault
recognition.
AsshowninFigure,rstly,thevibrationsignalsare
acquainted by each sensor. Secondly, some time-domain
characteristics are extracted from original signal of every
individual sensor. irdly, without any articia l selec tion,
features data of all signal sensors are put into the DBN and
generate appropriate DBN classier. Finally , the integrated
information is used to train or test the classier, and then the
classier puts out the diagnosis results and completes fault
diagnosis.
Since t he DBN has a hierarchical structure which can
extract the features from various aspects of the data by a
layer-by-layer successive learning procedure [], the multi-
information fusion, based on deep belief network, can get
rid of complex signal processing and complicated experience
[]. It takes the unsupervised learning with RBM and
directly extracts feature from the multivibrations and then
uses the best parameters to design DBN and completes the
multi-information integration.
However,thestructureofDBNiscloselyrelatedtothe
number of hidden nodes and hidden layers; if the DBN struc-
tureistoosimple,learningabilityissopoorthatitcannot
eectively integrate the multi-information. Meanwhile, if the
DBN structure is too complicated, it not only wastes running
timebutalsoproducesproblemssuchasovertting,local
extremism, and training failure []. erefore, a method
based on data reconstruction error is used to determine the
structure of information fusion in DBN.
Figure introduces the optimization process for the DBN
structure. e reconstruct error is computed with the model
outputs and the objective label data. At the beginning of the
procedure, multichannel signal information is put into the
Multichannel signal information
Initialize the parameters M, L, and 𝜀
Train network using
RBM learning rule
Reconstruction
No
Ye s
Use the best parameter to design the DBN
Ye s
Ye s
No
No
m+1
n+1
m<M
n<L
error < 𝜀
F : e ow chart of the optimization DBN in signal fusion.
DBNandtheparametersof, ,andare initialized, where
the , ,and are the max values of the hidden nodes,
hidden layers, and reconstruction error, respectively. en,
DBN calculates the reconstruction error of training dataset by
RBM learning rules. If the reconstruction error is less than ,
it nishes the optimization and puts out the parameters ()of
DBN. Otherwise, it increases the number of hidden nodes or
hidden layers. If the numbers overow or ,theprocedure
nds the best reconstruction error from history and builds
the DBN for multi-information fusion.
Table summarizes the procedure of bearing fault diag-
nosis using multi-information fusion with DBN. As shown
in the table, the rst step is gating the vibration signals
from multichannels and collecting vibration data from each
sensor. As the raw samples are nonlinear and unstable, it is
necessary to extract some features from each sample. en,
thepreprocessedvibrationdataaredividedintotraining
and testing datasets. e DBN structure is optimized by
reconstruc tion error of training dataset and obtains the
suitable DBN to accomplish the multi-information fusion.
Shock and Vibration
Motor
Timing
belt pulley
Coupling
Support
abutment
Load device
Bearing
pedestal
Rotation axis
(a)
S
1
S
2
S
3
(b)
F : Rotating machinery fault simulation platform of QPZ-II: (a) experiment platform; (b) sensors locations.
T : Procedure for bearing fault diagnosis using multi-informa-
tion with DBN.
Step
Description
Step 1
Gather multichannel vibration signals
Step 2
Extract features of each channel sample
Step 3
Input all features of training samples and initial
parameters of the DBN
Step 4
Optimize the DBN structure using reconstruction
error of multi-information fusion
(1) Each layer of the DBN is trained using RBM
learning rule
(2) Fine-tune the DBN using backpropagation
learning
(3) Calculate the reconstruction error using model
outputs and the target label data
(4) If the reconstruction error is smaller than
output the DBN structure; otherwise, ←+1
andreturntostep(1)
(5)Ifthereconstructionerrorisnotsmallerthan
and =, ←+1andreturntostep(1)untilis
more than
Step 5
Develop the DBN using the structure with the best
reconstruction error
Step 6
Perform diagnosis using the training DBN classier
model
4. Experimental Setup
Inordertomeasurethevalidityofthesuggestedmethod,a
bearing experimental platform is set up as shown in Figure .
e bearing fault simulation platform was produced by Qian
Peng Company with QPZ-II in China.
As shown in Figure , the experimental table is mainly
constituted with motor, belt coupling, bearing pedestal, and
soon.ebearingisinstalledinthepedestal,andthree
magnet acceleration sensors are installed in the pedestal,
labeled by
1
,
2
,and
3
, respectively. e position of
1
is located on the vert ical side of the bearing pedestal;
2
and
3
are, respectively, located on the lateral and front
of the bearing pedestal. In the experiments, the variety of
typical fault bearings can be installed and dismounted for
multivibration collection.
e test bearings are produced by Harbin Bearing Man-
ufacturing Company, China, with the bearing designation
being NU, which have cylindr i cal rollers. e inner
diameter is mm, the outer diameter is mm, and the
thickness of the bearing is mm. As shown in Figure ,
four experiments are carried out under each of the following
bearing health conditions: the inner race fault, outer race
fault, ball fault, and normal. All the faults are linear cutting
with electrical discharge machining, and the cutting diameter
is . mm; the cutting depth is . mm.
In the process of testing, a variable velocity motor directly
drives a sha. e belt on the right of the sha brings along
the coupling which runs with the same speed of motor. In the
experiment, the sampling frequency is hz, the bearing
speed is rpm, and the sampling time is seconds.
According to the steps shown in Table , each experiment
continuously acquainted signal points. Meanwhile, the
bearing rotated cycles. We select the signal points of a
rotation cycle to construct a sample. So, signal points
constitute a data sample. ere are four conditions dened for
classication and ( ×) training samples in dataset.
en, we randomly selected samples constituting the test
dataset. e dataset description is shown in Table . When the
rolling bearing has local damage, it will cause the vibration
signal mutation. e local damage position is dierent and
the change of the vibratio n signal usually is not the same.
Figure is the amplitudes waveform of rolling bearing in
dierent conditions.
It is seen from Figure that the vibration signals wave-
forms are similar, and it is dicu lt to distinguish the various
fault types of rolling bearings. So, some time-domain features
are extracted from the original signals; the method is as
follows:
()
𝑖
(=1,2,...,)is the discrete-time series of the th
sensor, and the vibration signals of bearing rotating a
cycle are
𝑖
=[
1
,
2
,...,
𝑚
], = (× 60) ÷ ,