Research of a Fan Fault Diagnosis System Based on
Wavelet and Neural Network
Guang

zhong Cao
1
Xiao

yu Lei
2
Chang

geng L
u
o
3
Abstract
–
An online fan fault diagnosis system is proposed
based on wavelet and neural network,
and the system is
implement
ed
on the LabVIEW platform. Relying on the
noise signal from the fan, the r
ecognition
system utilizes
power spectrum
gravity center
, sound level, wavelet
frequency segment power of the
signal as feature vectors, and
the
BP network as
classifier
for fault d
iagnosis. The
experimental results show that it is effective to extract fault
information by the
combination
of wavelet and
neural
network. The entire system has
adaptability
and fault

tolerant
capability
.
Keywords

sound
pressure
level
,
power spectrum,
wavelet
,
BP network
,
fault diagnosi
s
I.
I
NTRODUCTION
The
fan
fault
s
produced by
complex mechanism
are
various
.
I
t is difficult to diagnose the
reasons of
fan fault
because of lacking the mapping relationship between
faults and symptom.
Current fault di
agnosis methods
for
rotating machinery
such as vibration detection,
temperature controlling and so on,
have to use
contact
measurement
. However, those methods cannot be
available
for many important field devices.
Either in time domain
or in frequency domai
n t
he
local
characteristics of wavelet are
good in
extract
ing
time

varying signal characteristics.
And the neural network has
a strong
capability
to
identify the
m
ulti

dimensional model
and non

linear model. Therefore
,
it is possible to improve
the accurac
y of diagnosis system
by combination of
wavelet
and
neural network.
In this paper,
the fan fault
diagnosis system based on the wavelet and neural network
is
designed
. It
us
es
the noise
produced by
fan
to
be as
the
diagnosis signal
and
adopts
non

contact
m
easurement.
This system is good in extracting features and adaptive
learning. Its diagnosis
results
are
credib
le.
II.
B
ASIC
T
HEORY
A.
Wavelet theory and Mallat algorithm
Both in time domain and
in
frequency domain,
wavelet
can
perform local analysis at the
same time. It decomposes
the signal into some independent frequency band. For fan
noise signal, the energy
variation
of different frequency
band
always
correspond
different fault. Therefore, by
calculating the signal energy of each frequency band the
chara
cteristic vector
of signal
can be extracted
. Mallat is
one of
the
fast
algorithms
of wavelet.
Contin
uous
wavelet transform of
a
function
is
Digital ref:
062
1
College of Mechatronics and Control Engineering, Shenzhen
University
,
S
henzhen.
E

mail: gzcao@szu.edu.cn
2
College of Mechatronics and Control Engineering, Shenzhen
University
,
Shenzhen.
E

mail: lxywy@139.com
3
Physics & Electronic Engineering College, Nanyang Normal
University,Nanyang
.
E

mail:
L918@163.com
defined by
[1]
(1)
w
here
,
and
s
atisfied
,which
is
as mother wavelet function
;
‘
a
’
is scaled factor and
‘
b
’
is translation factor.
i
s
the conjugate function of
.
The
w
avel
et family is described by
, here the discrete
format
of
‘
a
’
and
‘
b
’
are
and
respectively.
Thus wavelet
family
and wavelet coefficients can
be expressed by
and
respectively.
Therefore,
square integrable function
can be decomposed into linear summation of wavelet
family
and its coefficients
can be
cal
culated by wavelet transforming from binary flexing
at binary
position
[2]
.
One fast
algori
th
m
of wavelet is
Mallat. Its role in
wavelet is
the
same as FFT in Fourier transform.
Suppose
the discrete sample s
equence of the signal
is
expressed by
,
, if
is the
approximation of signal at scale
, marked by
. Th
en
, the decomposing
formula can be
described by
(2)
(3)
After reconstructing the formula, it can be described by
(4)
In formula (2) (3) (4)
[3]
,
, and N is
the length of input sequence;
is the approximate
coefficient
at
th
layer;
is the detail coefficient at
th
layer;
is the low

pass filter coefficient of the used
wavelet;
is the high

pass filter
coefficient
of the used
wavelet.
B.
Principle
of BP
network
The error back

propagation
neural
network
is
called BP
n
etwork. This algorithm makes the problem
between
training sample
input
s and target outputs
become
a
nonlinear optimization problem
. T
hen using gradient
descent method
obtains the weight
value
between nodes.
Actually,
it
reflects the mapping relationship be
tween the
input and output in the form of weight
value
.
The structural model of BP network
is shown in F
ig.1,
which is
consist
ed
of input layer, hide layer and output
layer.
Here, the input layer receives characteristic
parameter information; the hide lay
er
learned
and
processes input information and connects the input layer
and output layer by weight
[4]
; the output layer compares
with target value continually and propagates the error back.
Fig. 1:
The structure model of BP network
The weight from inpu
t layer to hide layer and
the
one
from hide layer to output are corrected continually by
continual forward propagation and back propagation
of the
training sample
.
Finally, the hidden inherent law of
input
samples is found. In the F
ig.1,
is input characteristic
parameter
;
is the number of input nodes;
is the
weight from input layer to hide layer;
is the output of
hide layer;
is the number of h
ide layer nodes;
is the
weight from hide layer to output layer;
is the output
signals
;
is the number of output layer nodes;
is the
target value of the network.
F
or
ward
propagation
process
can be described as
follows.
Input layer: Adopting the linear input function makes
any
output
equal to its input
;
Hide layer: Any input
signal
is the weighted
sum
mation
of forward outputs
,
, here
is the threshold of hide layer nodes. The output
is
;
can
use the
function,
that
is,
.
Output layer: the
weighted sum
mation
of hide layer
output
s
is
the
input of output layer
. Adopting linear output
function makes the
k
th
output
be
,
where
is an integ
ral
number
.
During back propagation
process
, the error function
is defined
by
;
if the output
error is not satisfied with the
requirement
, the network
propagates errors back to modify the weight.
For
correction
of the
w
eight
, the learning algorithm of
BP network adopts gradient descent method to
adjust the
weight value. Adjusted quantity is,
.
F
rom this formula we can obtain the weight correction
between hide layer and output layer
is
, here
is learning rate,
; the
weight correction between input layer and hide layer is
, here
.
C. The evaluating indictor of sound pressure leve
l
The pressure fluctuations in the media
are due to sound
disturbance
and its value of pressure over the original
static pressure is called sound pressure level.
For a period
of time
, the root mean square value of i
nstantaneous sound
pressure
is descr
ibed by
[5]
,
(5)
w
here
is instantaneous sound pressure,
is the time
interval,
is the equivalent sound pressure.
The sound pressure level is calculated by
(6)
w
here
the sound pressure level
is signed by
,
is the reference acoustic pressure,
is
the equivalent sound pressure. Weighting sound pressure
level can be obtained by A, B, C and D weighting network
respectively
.
It is well known that the A
weighting
scale
corresponds most closely to the response of the ear.
III.
D
ESIGN OF
D
I
AGNOSIS
S
YSTEM
A.
Structure of hardware system
It has been shown in F
ig.2 that the fan
under test
is
diagnostic target.
Microphone
converts the noise signal
produced by
fan into voltage signal.
The
amplifying circuit
enlarges the voltage signal to a sc
ope r
equired
and
the A/D
data
acquisition card is PXI

4472 made by NI
Company
for converting analogous signal to digital signal.
Then
the
digital signal is
read
by control in Lab VIEW and a
wavelet neural network (WNN) fault
diagnosis
platform
is
constructed in
Lab VIEW.
Fig.2. Structure of hardware system
B.
Design of software system
As shown in Fig.3, the software system is consisted of
training sample, network training and on

line diagnostics.
The function of
each
part is described as follows.
Training
sample
: r
elying on the target
under test
sets
frequency of sampling, number of samples, sample size,
state
of sampling
signal
such as normal
state
,
paper
choking
,
eccentric blade
,
blade breaks
, and so on, and then
acquires
a certain number samples of signal in d
ifferent
state. Finally, it calculates the characteristic vector of each
state and saves the vector to specified location.
The function of
n
etwork training: setting the node
number of input layer, hide layer and output layer;
initializing
the weights and
threshold values of each layer;
training network and saving the correlation parameter for
calling.
On

Line d
iagnostics: acquiring the noise signal of fan;
calculating the characteristic vector; inputting the
trained
network
; outputting and saving the fau
lt probability and
alarm message.
Fig.3.
Structure of software system
C.
Extracting the characteristic
vector
How to extract the characteristic vector and which
parameter should be selected
a
ffect the
performance
of
diagnosis s
ystem directly. In the proposed system, the
characteristic vector is consisted of A

weighted
sound
level, power
spectrum
gravity centre and
signal energy of
each frequency band after wavelet decomposition.
The power spectrum gravity center (FC) is ca
lculated
by
(7)
w
here
,
is
the frequency and
is magnitude.
If fault
occurs
, the magnitude
s
of some frequency
would chan
ge
and
a
ffect the position of power spectrum
gravity center, the energy distribution of
different
frequency band after wavelet decomposition and the
measuring
results
of A

weighted sound level.
IV.
E
XPERIMENTS
Four fans
RDM8025S
made by RUILIAN SC
IENC were
used
to do the fault diagnosis experiment
.
One fan is
normal
, the other three are paper
choking
,
eccentric blade
,
and
blade
break
s
respectively.
A.
The
network
structure
design
The characteristic vector
was
input of the netw
ork. The fault modes such as normal
,
paper choking
,
eccentric blade
and
blade
break
s
composed into the output
vector
. For example,
shows that the fan fault is
paper choking
.
The n
ode
number of input
layer equals
four which is
the
dimension
of
.
Similarly
, the node number of output
layer equals the dimension of
. And the node numb
er of
hide layer was two which is
empirical
.
Linear act
ion
function is
chosen
at input and output layer. The
action
function of hide layer is
the
function.
B.
Signal
acquisition
Setting the sampling frequency
was 5000
and
the
number of samples was 2048.
of Daubechies
was
used by wavelet and the decomposition level was four.
Under each one of four states, we acquired ten sets data
in
which two sets were s
elected to calculate the
char
acteristic
vector
. The results are shown in the table1.
For the
second
, fourth, sixth and eighth
sets of signal
samples,
their
power spectrum and the
position of centre
of gravity
are shown in
Fig.4. It has been shown that there
is obvious difference
in different
set.
From the
second
row
of table1, we can find that the difference of
power
spectrum
gravity center
is obvious too.
Wavelet
function
was used in the
second
, fourth,
sixth and eighth sets of signal samples to perfor
m
four
layer wavelet decomposition. The time domain waveform
of h
igh

frequency coefficient
s at the fourth and
third layer
are listed
in
Fig.5.
In the fourth and fifth row of table1, it
is obvious that the third and fourth layers
’
energy
of each
group signa
l
and each
energy ratio of high

frequency
coefficients
are all different with others.
C
.
Network training
To
keep
the
stable
learning rate and avoid network
oscillating
, the learning rate, weight and the error of target
should be selected suitably wh
ile executing the network
training.
If the learning rate is too speedy, there would be a
constant oscillation in the network making it difficult to
achieve the
target value; if the error of target is too small,
to satisfy requirement in specified iteration
number could
not be achieved.
The initial weight and threshold value were s
et
as
the
random number
between 0 and 1.
To set the error of target
as 0.05 and the maximal iteration number as 5000.
After the network was trained, the relationship between
act
ual output error and iteration number is shown in Fig.6.
In figure
(a)
, the learning rate is 0.7.
There
was a biggish
oscillation during the training and when the output error
achieved the
requirement
the iteration number
was
3822.
In figure (b), the learn
ing rate is 0.2. However, the
oscilla

Table
1:
C
haracteristic value
of training sample acquired and the corresponding fault modes
Number
of
Samples
x1
（
FC
）
x2
(
dBA
)
x3(d4)
x4(d3)
Mode
1
200.170
78.350
46.306
27.273
N
ormal
2
190.829
77.913
44.669
23.890
N
ormal
3
300.180
83.114
61.277
32.537
P
aper
choking
4
295.919
82.746
59.160
33.841
P
aper
choking
5
132.724
80.684
65.717
28.857
E
ccentric
blade
6
134.868
81.450
83.176
38.774
E
ccentric
blade
7
113.926
74.022
31.793
18.459
B
lade
breaks
8
122.163
75.550
36.515
19.621
B
lade
breaks
a The
second
group
b the fourth group
c The
sixth group d The eighth
group
Fig.4:
Power spectrum and the gravity centre position of sam
ples
a. The
fourth layer
high

frequency coefficients
of the second
group
sample
b. The
third layer
high

frequency coefficients
of the second
group
sample
c. The
fourth layer
high

frequency coefficients
of the fourth
group sample d. The
third layer
high

frequency coefficients
of the fourth group sample
e. The
fourth
layer
high

frequency coefficients
of the
sixth
group sample f. The
third
layer
high

frequency coefficients
of the
sixth
grou
p sample
g. The
fourth layer
high

frequency coefficients
of the
eighth
group sample h. The
third
layer
high

frequency coefficients
of the
eighth
group sample
Fig.5:
The third and fourth high

frequency coefficients of samples after wavele
t
decomposing
(a) Learning rate is 0.7
(b)
Learning rate is 0.2
Fig.
6
:
Relationship between
output error and iteration number
Table
2:
F
ault modes
of training
samples and outputs of network
Number
of
samples
Fault modes
Outputs of network
t1
t2
t3
t4
y1
y2
y3
y4
1
1
0
0
0
0.9695
0.0104
0.0002
0.0005
2
1
0
0
0
0.9769
0.0087
0.0001
0.0009
3
0
1
0
0
0.0567
0.9804
0.0007
0.0000
4
0
1
0
0
0.0441
0.9754
0.0021
0
.0000
5
0
0
1
0
0.0003
0.0000
0.9921
0.0054
6
0
0
1
0
0.0005
0.0000
0.9434
0.0236
7
0
0
0
1
0.0268
0.0000
0.0325
0.9194
8
0
0
0
1
0.0299
0.0000
0.0146
0.9858
Table
3
:
C
haracteristic
parameter
of training sample acquired and
outputs of network
T
raining
sample
Characteristic parameter
Outputs of network
X
1
（
FC
）
x2
(
dBA
)
x3(d4)
x4(d3)
y1
y2
y3
y4
1
(
Normal
)
221.104
79.039
46.127
24.898
0.976
0.047
0.001
0.000
2
（
Paper
choking
）
273.696
81.797
54.367
31.075
0.016
0.980
0.005
0.000
3
（
eccentric
blade
）
135
.684
78.717
60.857
26.812
0.003
0.060
0.994
0.010
4
（
blade
breaks
）
110.927
74.364
31.303
17.032
0.002
0.000
0.044
0.997
tion during the training was small. When the output
error
was down from 31.2 to 0.049997 and achieved the
requirement
, the iteration n
umber was 3677. The fault
mode of training sample (t1
, t2,
t3,
t4
) and the
actual
output of network (y1, y2, y3, y4) are listed in Table2. It
can be seen from Table2 that the fault mode of
acquired
samples has already been
recognized
accurately by the
net
work. The error is less than 0.1. At last, the related
parameters of this network were stored in the specified
location.
D
.
On

line diagnostics
The well trained network was used to diagnose the fan
under test
to
acquire
the noise signal
produced by fan
working at each mode. Then
using the sampling value
calculate
d
the corresponding characteristic vector
which
was
input
to
the well trained network in order to
perfor
m
on

line diagnostics.
Table3 lists the characteristic
pa
rameters and the corresponding ne
twork output. From
Table3, we can find that although the characteristic
vectors of fan under test are different with the training
samples,
the proposed system diagnoses accurately.
V.
C
ONCLUSION
In the proposed intelligent fault diagnosis system,
the
n
oise produced by fan was diagnosis signal
;
non

con
tact
measurement
was adopted
and
using the wavelet neural
network performed the non

linear mapping from feature
space to
fault
space.
Modular programming is adopted
in
this system
, so it is easier to extend
and to change the
characteristic parameters of fault and structure parameters
of the network. Utilizing the learning, memory and
reckoning
abilit
ies diagnoses the fault adaptively.
V
I
.
A
CKNOWLEDGEMENTS
The
authors
would
like
to
thank
the research
funds:
2006AA040105
,
2007BAF15B01
,
2007BAF15B03
,
2008A011400006
,
2007B090400056
, and Shenzhen
government
fund,
for
their
support
.
V
II
.
R
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Mallat
.
A theory for multiresolution signal
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.
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achine Intell.,
1989,
11
(
7
):
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: '
Intelligent
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' (
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, 2000
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78,108

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Olivier Rioul
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Fast Algorithms for Discrete and Continuous
Wavelet Transforms
.
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Fault Diagnosis of Plane Electric Starting
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(
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