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J Intell Manuf
DOI 10.1007/s10845-012-0657-2
Fault diagnosis and prognosis using wavelet packet decomposition,
Fourier transform and artificial neural network
Zhenyou Zhang ·Yi Wang ·Kesheng Wang
Received: 14 December 2011 / Accepted: 26 April 2012
© Springer Science+Business Media, LLC 2012
Abstract This paper proposes a method for classification
of fault and prediction of degradation of components and
machines in manufacturing system. The analysis is focused
on the vibration signals collected from the sensors mounted
on the machines for critical components monitoring. The
pre-processed signals were decomposed into several sig-
nals containing one approximation and some details using
Wavelet Packet Decomposition and, then these signals are
transformed to frequency domain using Fast Fourier Trans-
form. The features extracted from frequency domain could
be used to train Artificial Neural Network (ANN). Trained
ANN could predict the degradation (Remaining Useful Life)
and identify the fault of the components and machines. A case
study is used to illustrate the proposed method and the result
indicates its higher efficiency and effectiveness comparing
to traditional methods.
Keywords Diagnosis ·Prognosis ·Wavelet packet
decomposition ·Fourier transform and artificial neural
network
Z. Zhang ·K. Wang (B
)
Department of Production and Quality Engineering, Norwegian
University of Science and Technology, S. P. Andersensveien 5,
Valgrinda, 7491 Trondheim, Norway
e-mail: Kesheng.wang@ntnu.no
Z. Zhang
e-mail: Zhenyou.zhang@ntnu.no
Y. Wa n g
School of Materials, The University of Manchester, Sackville St Blg,
Manchester M13 9PL, UK
e-mail: yi.wang-2@manchester.ac.uk
Introduction
During a system failure, only a small fraction of the down-
time is spent to maintain or repair the components that cause
the fault. Up to 80 % of it is spent to locate the source of the
fault (Kegg 1984). In case of complex installation such as
automotive manufacturing plant, 1min downtime may cause
as high as $20,000 cost (Spiewak et al. 2000). Early fault
diagnosis is crucial for avoiding major malfunction and mas-
sive loss in economy and productivity. In diagnosing rotating
machinery, sound emissions or vibration signals are used to
monitor the performance of the machine and could be used to
judge whether the machine is failure or degrading. Many use-
ful techniques for signal analysis have been applied. These
techniques can be classified into three types: time domain
(Wang et al. 2010;Chen et al. 2008), frequency domain such
as Fast Fourier Transform (Corinthios 1971;Liu et al. 2010;
Rai and Mohanty 2007) and time-frequency domain such
as the Short Time Fourier Transform (Portnoff 1980),
Hilbert-Huang Transform (Yu et al. 2007), Wigner-ville dis-
tribution (Andria et al. 1994;Staszewski et al. 1997;Wang
et al. 2008) and Wavelet Transform (Chen et al. 2005;Lin and
Qu 2000;Prabhakar et al. 2002;Serhat and Emine 2003;Tse
et al. 2004;Wu and Chen 2006;Zheng et al. 2002;Wu and
Liu 2009). Autoregressive model method can also be used to
extract features of a machine or component for fault diagno-
sis and prognosis (Li et al. 2009). Wavelet transform is the
best of these tools because the short time Fourier transform
only provides a constant time-frequency resolution, and Wig-
ner-ville distribution produced interface terms on the time-
frequency domain in a critical condition (Wu and Chen 2006).
It has particular advantages for characterizing signals at dif-
ferent localization levels in time as well as signal process-
ing, image processing, pattern recognition, seismology and
machine fault diagnosis.
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J Intell Manuf
After processing vibration signals and extracting the fea-
tures, the more important thing is identifying the fault and
predicting the remaining useful life. There are many meth-
ods could be used in this area. Support vector machine
(SVM) learning is a popular machine learning application
due to its high accuracy and good generalization capabilities
(Saravanan et al. 2008). Li and Wu (2005) proposed a hid-
den Markov model (HMM)-based fault diagnosis in speed-up
and speed-down process for rotary machinery. In the imple-
mentation of the system, one PC was used for data sampling
and another PC was used for data storage and analysis. Wu
and Chow (2004) presented a self-organizing map (SOM)
based radial-basis-function (RBF) neural network method for
induction machine fault detection. The system was imple-
mented by utilizing a PC and additional data acquisition
equipment. Many methods based on ANN have been devel-
oped for online surveillance with knowledge discovery, nov-
elty detection and learning abilities (Kasabov 2001;Marzi
2004;Markou and Singh 2003). ANN, Fuzzy Logic System
(FLS), Genetic Algorithms (GA) and Hybrid Computational
Intelligence (HCI) systems were applied in fault diagnosis
and a case of centrifugal pump was utilized to show how the
methods work (Wang 2002). Decision tree method was used
to identify fault in of mean shifts in bivariate processes in
real time (He et al. 2011). Probability based Bayesian net-
work methods was used to identify vehicle fault which can
be used to diagnose single-fault and multi-fault (Huang et al.
2008). Lee et al. (2006) developed an intelligent prognostics
and e-maintenance system named “Watchdog Agent” with
the method of Statistical matching, and performance signa-
ture and Support Vector Machine (SVM) based diagnostic
tool.
There exist some literatures integrating these techniques
for fault diagnosis and prognosis. Momoh and Button inte-
grated FFT and ANN to analyze and identify the fault of
aerospace DC arcing (Momoh and Button 2003). Fourier
transform and wavelet transform were integrated to detect
and identify the fault of induction motor using stator cur-
rent information (Lee 2011). Wavelet analysis techniques and
ANN were integrated for fault diagnosis in induce motors
(Lee 2011), automotive generator (Wu and Kuo 2009) and
gear box (Saravanan and Ramachandran 2010) and the results
were pretty good. However, there are no literatures integrat-
ing three techniques of WPD, ANN as well as FFT in condi-
tion monitoring or fault diagnosis and prognosis. This paper
proposes a method applying these three techniques for fault
classification and prediction. This method extracts features
using wavelet transform and Fourier transform from pre-pro-
cessed vibration signals and, then these features could be used
to train SBP neural network which could classify and predict
fault, and further to predict the remaining useful life. These
results can be used to support the maintenance decision mak-
ing and optimizing the scheduling. This paper is organized
as the following: “Data acquisition experiment” presents the
experiment setup of data acquisition; wavelet packet trans-
form and Fourier transform are introduced briefly in “Fea-
tures extraction” and “Fault diagnosis and prognosis inte-
grating WPD, FFT and ANN” respectively; a case study and
its results with discussions are presented in “Case study”; the
conclusions and future research are presented in last section.
Data acquisition experiment
To research how to diagnose the fault type and prognose the
condition of the monitored equipment, a simple experimen-
tal setup is established in Knowledge Discovery Laboratory
(KDL) in NTNU.
Experimental setup
Figure 1shows the hardware of the experimental setup which
includes a blower, three vibration sensors, power supply for
sensors, connector, DAQ card and a computer. In this setup,
the blower is selected as our monitoring object and a kind of
vibration sensor (Kistler: Type 8702B100) is chosen to col-
lect the signals from the blower. Three sensors are setup on
the blower in three directions which can collect the vibration
signals in different directions (Fig. 2). The signals are col-
lected from the sensors and processed using some processing
method like filter, de-noising and compression. Then the fea-
tures are extracted in different domain which can be used to
train and query ANN. After training, the system can judge the
real states of monitored components using real time signals.
Experimental procedure
In the present study, four different degradations of unbalance
are simulated using three different parts (Fig. 3) which are
mounted in the axis end of the blower. The unbalance degra-
dation (condition) contains 0, 0.3, 0.6 and 1 which represent
the performance states from perfect (condition 0) to abso-
lutely failure (condition 1). In the first case, power on the
blower, collect and store signals from the sensors without
amounting any simulation part. Next, power off the blower
and mount first part in the axis end and power on the blower,
then collect and store the signals from sensors. Repeat this
process until collect all the degrading signals simulated by
simulation parts. Figure 4shows the signals from perfect state
to absolutely failure.
Features extraction
Features extraction is very significant in fault diagnosis and
prognosis process. In this paper, WPD and FFT are used to
123
J Intell Manuf
Fig. 1 Hardware of experimental setup
Fig. 2 Sensors setup on blower
extract features from preprocessed signals. In this part, the
principle of WPD, FFT and how to apply these techniques in
extracting features will be described briefly.
Wavelet transform is a time-frequency decomposition of a
signal into a set of “wavelet” basic function. Wavelet analysis
has proved its great capabilities in decomposing, denoising,
and signal analysis which made the analysis of non-station-
ary signals achievable as well as detecting transient feature
components as other methods were inept to perform since
wavelet can concurrently impart time and frequency struc-
tures. Wavelet Transform (WT) gives good time and poor fre-
quency resolution at high frequencies, and good frequency
and poor time resolution at low frequencies. Analysis with
wavelets involves with breaking up a signal into shifted and
Fig. 3 Parts for simulation degradation
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J Intell Manuf
Fig. 4 Raw signals with different degradations
scaled versions of the original (or mother) wavelet, i.e., one
high frequency term from each level and one low frequency
residual from the last level of decomposition. There are three
categories of this transformation: Continuous Wavelet Trans-
form (CWT), Discrete Wavelet Transform (DWT) and WPD.
Continuous wavelet transform
A CWT is used to divide a continuous-time function into
wavelets. Unlike Fourier transform, the continuous wavelet
transform possesses the ability to construct a time-frequency
representation of a signal that offers very good time and fre-
quency localization. The continuous wavelet transform of a
time function x(t)is given by following equation:
CT(a,b)=
∞
−∞
x(t)ψ∗
(a,b)(t)dt (1)
where ψ∗
(a,b)(t)is a continuous function in both the time
domain and the frequency domain called the mother wavelet
and * represents operation of complex conjugate. ψ∗
(a,b)(t)
can be expressed as:
ψ∗
(a,b)(t)=1
√aψt−b
awhere a,b∈R,a= 0(2)
The main purpose of the mother wavelet is to provide a source
function to generate the daughter wavelets which are simply
the translated and scaled versions of the mother wavelet. As
seen in Eq.( 2), the transform signal CT(a,b)is defined on
a−bplane, which aand bare used to adjust the frequency
and the time location of the wavelet in Eq. (2). A small a
produces a high-frequency wavelet when high frequency res-
olution is needed and the reverse is also true. The WT’s supe-
rior time-localization properties stem from the finite support
of the analysis wavelet: as bincreases, the analysis wavelet
transverses the length of the input signal, and aincreases or
decreases in response to changes in the signal’s local time
and frequency content. Finite support implies that the effect
of each term in the wavelet representation is purely localized.
This sets the WT apart from the Fourier Transform, where
the effects of adding higher frequency sine waves are spread
throughout the frequency axis.
Discrete wavelet transform
In numerical analysis and functional analysis, DWT is a
wavelet transform for which the wavelet ψ(a,b)is discretely
sampled. As with CWT, a key advantage it has over Fou-
rier transforms is temporal resolution: it captures both fre-
quency and location information (location in time). Usually,
the DWT can be derived from discretization of CWT. The
most common discretization is dyadic method:
DT(a,b)=
∞
−∞
x(t)ψ∗
(j,k)(t)dt (3)
ψ∗
(j,k)(t)=1
√2jψt−2jk
2j(4)
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Level 1
Level 2
Level 3
D1
D2
D3
A3
A1
A2
Fig. 5 3-Layer structure of wavelet packet decomposition
where aand bare replaced by 2 jand 2 jkrespectively
(Daubechies 1988;Mallat 1989). An efficient way to imple-
ment this scheme using filters was developed by Mallat (1989).
The original signal x(t)passes through two complementary
filters and emerges as low frequency called approximations
and high frequency called details. The decomposition pro-
cess can be iterated, with successive approximations being
decomposed in turn, such that a signal can be broken down
into many lower-resolution components.
Wavelet packet decomposition
The structure of wavelet packet transform (WPT) is similar
to DWT. Both have the framework of multi-resolution anal-
ysis. The main difference in the two techniques is the WPT
can simultaneously break up detail (Di)and approximation
(Ai)versions while DWT only breaks up as an approximation
version. Therefore, the WPT have the same frequency band-
widths in each resolution and DWT does not have this prop-
erty. The mode of decomposition does not increase or lose
the information within the original signals. Therefore, the sig-
nal with great quantity of middle and high frequency signals
can offer superior time-frequency analysis. The WPT suits
signal processing, especially non-stationary signals because
the same frequency bandwidths can provide good resolution
regardless of high and low frequencies.
As discussed above, WPT can decompose the signal into
two parts: low-frequency A1and high frequency D1.Inthe
process of decomposition, the lost information belonging to
the low frequency part was captured by the high frequency
part. In the next level of decomposition, this method will
also decompose A1into two parts: low-frequency A2and
high frequency D2. The lost information belonging to low
frequency A2was capture by the high-frequency D2, and
thus, a deeper level decomposition can be done. WPD is
more effective, it can decompose not only the low-frequency
part, but also high-frequency. The 3-layer structure of signal
based on WPD is shown in Fig. 5in which only approxima-
tion version is decomposed.
For the case in this paper, the sample frequency is 512Hz,
and thus D1,D
2,D
3and A3represent the frequency 256–
512, 128–256, 64–128 and 0–64 Hz respectively in Fig. 5.In
this experiment, only these four parts are analyzed to judge
the degradation of the performance. The decomposed signals
by WPD from the different degrading signals are shown in
Figs. 6,7,8and 9.
Fast Fourier transform
Fourier transform is a mathematical operation that decom-
poses a signal into its constituent frequencies. The origi-
nal signal depends on time, and therefore is called the time
domain representation of the signal, whereas the Fourier
transform depends on frequency and is called the frequency
domain representation of the signal. The term Fourier trans-
0 0.2 0.4 0.6 0.8 1
-0.4
-0.2
0
0.2
0.4
D1
Time (s)
Amplitude
00.2 0.4 0.6 0.8 1
-0.4
-0.2
0
0.2
0.4
D2
Time (s)
Amplitude
0 0.2 0.4 0.6 0.8 1
-0.2
-0.1
0
0.1
0.2
0.3 D3
Time (s)
Amplitude
00.2 0.4 0.6 0.8 1
-0.2
-0.1
0
0.1
0.2 A3
Time (s)
Amplitude
Fig. 6 Decomposed signal of condition 0
123
J Intell Manuf
0 0.2 0.4 0.6 0.8 1
-0.1
-0.05
0
0.05
0.1 D1
Time (s)
Amplitude
00.2 0.4 0.6 0.8 1
-0.2
-0.1
0
0.1
0.2 D2
Time (s)
Amplitude
0 0.2 0.4 0.6 0.8 1
-0.2
-0.1
0
0.1
0.2 D3
Time (s)
Amplitude
00.2 0.4 0.6 0.8 1
-0.2
-0.1
0
0.1
0.2 A3
Time (s)
Amplitude
Fig. 7 Decomposed signal of condition 0.3
0 0.2 0.4 0.6 0.8 1
-0.1
-0.05
0
0.05
0.1 D1
Time (s)
Amplitude
0 0.2 0.4 0.6 0.8 1
-0.2
-0.1
0
0.1
0.2 D2
Time (s)
Amplitude
0 0.2 0.4 0.6 0.8 1
-0.2
-0.1
0
0.1
0.2 D3
Time (s)
Amplitude
0 0.2 0.4 0.6 0.8 1
-0.2
-0.1
0
0.1
0.2 A3
Time (s)
Amplitude
Fig. 8 Decomposed signal of condition 0.6
0 0.2 0.4 0.6 0.8 1
-0.2
-0.1
0
0.1
0.2 D1
Time (s)
Amplitude
0 0.2 0.4 0.6 0.8 1
-0.4
-0.2
0
0.2
0.4 D2
Time (s)
Amplitude
0 0.2 0.4 0.6 0.8 1
-0.4
-0.2
0
0.2
0.4 D3
Time (s)
Amplitude
0 0.2 0.4 0.6 0.8 1
-0.4
-0.2
0
0.2
0.4 A3
Time (s)
Amplitude
Fig. 9 Decomposed signal of condition 1
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J Intell Manuf
0 200 400 600 800 1000
0
5
10
15 FD1
Frequency (Hz)
|Y(fft)|
0 200 400 600 800 1000
0
2
4
6
8
10 FD2
Frequency (Hz)
|Y(fft)|
0 200 400 600 800 1000
0
5
10
15 FD3
Frequency (Hz)
|Y(fft)|
0 200 400 600 800 1000
0
5
10
15
20 FA3
Frequency (Hz)
|Y(fft)|
Fig. 10 FFT for each version signal of condition 0
0 200 400 600 800 1000
0
2
4
6
FD1
Frequency (Hz)
|Y(fft)|
0 200 400 600 800 1000
0
2
4
6
8
FD2
Frequency (Hz)
|Y(fft)|
0 200 400 600 800 1000
0
2
4
6
8FD3
Frequency (Hz)
|Y(fft)|
0 200 400 600 800 1000
0
10
20
30
40 FA3
Frequency (Hz)
|Y(fft)|
Fig. 11 FFT for each version signal of condition 0.3
form refers both to the frequency domain representation of
the signal and the process that transforms the signal to its
frequency domain representation. A FFT is an efficient algo-
rithm to compute the discrete Fourier transform (DFT) and
it’s inverse. Commonly, the FFT of a signal can be calculated
by the following equation (Sohn et al. 2010):
FFT(k)=
N
n=1
x(j)ω(n−1)(k−1)
N(5)
ωN=e(−2πi)/N(6)
where Nis the number of samples for one signal and ωN
is an Nth root of unity. In “Wavelet packet decomposition”,
the original signal was decomposed as on approximation and
details. Then, the decomposed signals are transformed with
FFTwhichareshowninFigs.10,11,12 and 13 which present
different conditions from condition 0 to condition 1. From
the result of FFT, some kinds of features can be chosen. In
this paper, the peaks for each part are selected as features to
judge the condition of monitored equipment.
Fault diagnosis and prognosis integrating WPD, FFT
and ANN
The pattern classification theory has become a key factor in
fault diagnosis and prognosis. Some classification methods
for equipment performance monitoring use the relationship
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J Intell Manuf
0200 400 600 800 1000
0
2
4
6FD1
Frequency (Hz)
|Y(fft)|
0 200 400 600 800 1000
0
5
10
15 FD2
Frequency (Hz)
|Y(fft)|
0200 400 600 800 1000
0
2
4
6
8
10 FD3
Frequency (Hz)
|Y(fft)|
0 200 400 600 800 1000
0
10
20
30
40
50 FA3
Frequency (Hz)
|Y(fft)|
Fig. 12 FFT for each version signal of condition 0.6
0 200 400 600 800 1000
0
2
4
6
8FD1
Frequency (Hz)
|Y(fft)|
0 200 400 600 800 1000
0
5
10
15
20 FD2
Frequency (Hz)
|Y(fft)|
0 200 400 600 800 1000
0
5
10
15 FD3
Frequency (Hz)
|Y(fft)|
0 200 400 600 800 1000
0
2
4
6
8
10 FA3
Frequency (Hz)
|Y(fft)|
Fig. 13 FFT for each version signal of condition 1
between the type of fault and a set of patterns which is extract
from the collected signals without establishing explicit mod-
els. Currently, ANN is one of the most popular methods in this
domain. ANN is a model that emulates a biological neural
network (Wang 2005). The origin of ANN can be traced back
to a seminar paper by McCulloch and Pitts (1943) that dem-
onstrated a collection of connected processors, loosely mod-
eled on the organization of brain, could theoretically perform
any logical or arithmetic operation. Then, the development of
ANN techniques is very fast which is extensive to many cate-
gories containing Back-propagation (BP), Self-organization
Mapping (SOM) and Radial Basis Function (RBF), etc. The
application of artificial neural network models lies in the fact
that they can be used to infer a function from observations.
This is particularly useful in applications where the complex-
ity of the data or task makes the design of such a function by
hand impractical. This attribution is very nontrivial in diag-
nostic problems. BP neural network is a main type of ANN
used to solve fault diagnosis and prognosis problems.
ANN can deal with complex non-linear problem without
sophisticated and specialized knowledge of the real systems.
It is an effective classification techniques and low opera-
tional response times needed after training. The relationship
between the condition of component and the features is not
linear but non-linear. BP neural network does not need to
know the exact form of analytical function on which the
model should be built. This means neither the functional
type nor the number and position of the parameters in the
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Backward Phase
Forward Phase
InputLayer HiddenLayer Outputlayer
Features from WPD and FFT
x1
x2
xm
vji wkj
yi
E1
E2
t1
t2
Target
value
z1
z2
zn
Entn
Degradation
Fig. 14 A BP neural network with single hidden layer
model-function need to know. It can deal with multi-input,
multi-output, quantitative or qualitative, complex system
with very good abilities of data fusion, self-adaptation and
parallel processing. Therefore, it is very suitable to select as
a method of fault diagnosis and prognosis. There are many
papers dealing with the use of ANN and most of their contri-
butions are ANN training efficiency and strategies for ANN
itself. ANN proposed in this paper is work with other two
methods together as a completed process of diagnosis and
prognosis. Wavelet analysis is a better method than FFT and
STFT for signal process and feature extraction. There are
many papers selecting entropy of coefficients or energy of
sub-signals of WT as features to train ANN. In more compli-
cated system, these features do not contain enough informa-
tion of the machine. The frequency properties for every sub-
signal could be very useful to judge the component condition,
and thus the FFT is selected to get these kinds of information.
By integrating the WT, FFT and ANN, the condition can be
diagnosed and predicted using trained ANN. Therefore, this
paper proposes a method applying these three techniques for
fault classification and prediction. In this section, BP neu-
ral network is introduced briefly followed by the procedure
of fault diagnosis and prognosis integrating WPD, FFT and
ANN.
BP neural network
BP neural network which is the most widely used neural net-
work model currently was proposed by Rumelhart et al. in
1986. It is a multilayer feed-forward network usually contain-
ing the input layer, hidden layer, and output layer (Fig. 14),
which trained by an error back propagation algorithm. The
biggest advantage of ANNs trained by back propagation is
that there isn’t need to know the exact form of analytical func-
tion on which model should be built. So it’s not necessary
have neither the function type not even the number and posi-
tion of the parameters in the model function. Moreover, BP
network can learn and store a lot of input-output model map-
ping without mathematical equations which describing this
mapping. The learning method of BP is the steepest descent
method which is adjusting the weights and thresholds of the
network to minimize the sum of squared errors. The gen-
eral procedure of BP network training can be summarized as
follows (Wang 2005):
(1) Initialize the weights to small random vales (−1, 1);
(2) Select a training vector pair (input and the correspond-
ing desired output) from the training set and present the
input vector to the inputs layer of the ANN;
(3) Calculate the actual outputs (forward phase);
(4) Adjust the weights wji to reduce the difference between
actual output and target (backward phase);
(5) Return to step 2 and repeat for each pattern p until the
total error has reached an acceptable level;
(6) Stop.
Figure 14 shows a BP network structure with a single hidden
layer.
xand
tare input and target of training data respec-
tively. vji and wkj are weights between input and hidden layer,
and between output and hidden layer respectively. yiand zk
are outputs of hidden and actual output of output layer. The
objective of ANN training is to obtain all the suitable weights
to meet the input and the target of training data. After the
training of BP network, for each set of test data or query data,
there is a set of output calculated by the final updated weights.
For a specific application in fault diagnosis and prognosis,
after training by features extracted from processed historic
data, the BP network can classify the fault and predict the
states of the monitored components or machine units. In this
case, the input features are peak values of FFT series from
decomposed signals using WPD while the output means the
degradation for each monitored equipment or component.
The procedure of fault diagnosis and prognosis
The peak values of FFT for decomposed signals with WPD
of vibration signals are used to estimate the condition of com-
ponents and machines. BP neural network made up of one
input layer, one output layer and one hidden layer. And it has
been proved that such three layers’ BP neural network model
can approach any continuous functions at any precision. The
structure of the BP network is shown in Fig. 14. The values of
output are from 0 to 1 which represent from perfect condition
to complete failure of specific kinds of fault as mentioned in
“Data acquisition experiment”.
Because of convenience of handling the signal collec-
tion, a signal processing and interface thing, Labview is
selected as program software in this project. However, the
capability of mathematical calculation of Labview is not as
good as Matlab. Therefore, both kinds of software are com-
bined to apply in this study. The procedure of diagnosis and
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J Intell Manuf
Data acquisition
Signal processing
Classfication
Predict the condition of the
condition and evaluate
remaininguseful life
Collectinghistorical signals
from sensors
Filter, amplification, denoising
conditioning,and
extractingweak signals
Data acquisition in real
time
Signal process
End
ANN training
(SBP)
Feature extraction WPDandFFT
Feature extraction
Maintenance Decision
Making
Fig. 15 The procedure of diagnosis and prognosis
prognosis is shown in Fig. 15. The historic data is collected
and processed which are first two steps. Then, the processed
signals can be decomposed by WPD. Each part of decom-
posed signals can be transformed using FFT and the peak
value for each of them is selected as feature to train BP net-
work. After training, the signals in real time are collected and
used to query the BP network, and then the condition of the
monitored components can be obtained. Finally, the remain-
ing useful life is evaluated for decision making of mainte-
nance according to the condition.
Case study
A framework called Intelligent Blower Fault Diagnosis and
Prognosis is developed in KDL to show how apply proposed
method in real system and to validate the correctness of
proposed techniques. This framework is a part of SFI-Nor-
man project called Condition based Maintenance in order to
achieve near zero-breakdown manufacturing and further to
reach zero-defect manufacturing. In this section, some exper-
iments are done to certify the correctness, robustness and pre-
cision of proposed methods and comparison of the different
result among using different inputs.
The hardware of the framework was shown in Fig. 1while
the monitored component was shown in Fig. 2. Figure 16
shows the interface of software in which the condition of the
blower can be seen in real time. The raw signals collected
from sensors in real time are displayed on the top right of
the interface. One can set the number of training data. After
training, the conditions of the monitored components which
are presented in the condition textbox can be calculated by
ANN. The results are displayed graphically as seen on the left
side of this figure. The area inside the blue circle represent
safe condition; the area between blue circle and yellow circle
represent warning condition while the area between yellow
circle and red circle represent failure condition. The points
located in radial line represent the conditions of the specific
components. From this figure, the conditions of monitored
components can be presented clearly.
Experiment and results
In this case study, four conditions for the monitored com-
ponent are defined which include 0, 0.3, 0.6 and 1 which
represent from perfect performance to completely fail-
ure discretely. For each condition, 200 training signals
were collected and processed. The training signals are pre-
processed firstly and then decomposed by WPD. For each
part of decomposed signal, calculating the peak value in
its frequency domain transformed using FFT which called
PFD1, PFD2, PFD3, and PFA3. In this case, there are three
Raw signals
Graphical
results of
components’
conditions
Results of
components’
conditions
The number
of training
data
Fig. 16 The interface of the system
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Table 1 Part of training data
Sensor 1 Sensor 2 Sensor 3 C
PFD1 PFD2 PFD3 PFA3 PFD1 PFD2 PFD3 PFA3 PFD1 PFD2 PFD3 PFA3
4.20 3.18 3.768 49.05 4.07 3.756 3.26 95.17 4.325 4.323 2.816 101.08 0
4.46 2.965 2.788 20.38 4.54 3.404 3.346 102.0 3.891 4.108 3.248 107.36 0
4.58 4.039 3.874 317.6 6.15 3.603 3.704 4,170 4.663 3.55 5.447 1,094.9 0.3
3.42 3.802 3.227 314.3 3.46 3.765 3.659 4,220 4.261 3.42 4.659 1,132.5 0.3
4.87 4.238 5.951 482.2 5.19 4.184 4.617 6,975 3.523 3.845 2.723 1,889.8 0.6
4.49 3.745 4.178 395.6 4.03 4.412 4.289 6,828 4.781 3.705 3.022 1,861.4 0.6
6.41 3.007 18.46 1,933 4.94 3.053 5.048 2,035 5.095 2.919 5.601 6,189.9 1
4.54 4.304 18.43 1,936 4.72 4.23 4.73 2,103 4 4.506 6.062 6,391.8 1
……………………………… …
Table 2 Test data and the results
Sensor 1 Sensor 2 Sensor 3 Results Deviation
PFD1 PFD2 PFD3 PFA3 PFD1 PFD2 PFD3 PFA3 PFD1 PFD2 PFD3 PFA3 NC TC
3.71 3.382 2.941 37.608 4.636 4.582 3.018 99.027 4.095 3.719 4.749 107.685 0 0.04 0.038
4.755 3.079 3.049 30.693 6.705 4.092 3.187 81.135 3.951 3.525 3.583 105.698 0 0.05 0.046
4.29 4.083 2.418 20.416 4.258 4.069 3.583 85.343 6.563 3.09 4.254 100.095 0 0.04 0.041
4.803 3.506 3.056 39.464 4.561 3.792 2.952 76.756 4.398 4.545 4.052 111.304 0 0.03 0.033
4.114 3.856 2.557 32.64.77 4.005 3.258 112.054 4.752 3.517 3.48 116.38 0 0.04 0.038
4.133 3.684 3.162 275.02 4.114 3.736 3.227 4,135.45 4.701 3.452 4.835 1,199.69 0.30.28 0.017
4.433 3.475 3.589 280.23.944 3.532 3.121 4,174.94 4.215 3.701 3.25 1,223.66 0.30.28 0.025
5.301 3.352 3.539 280.78 4.89 4.044 4.023 4,280.03 5.667 4.422 4.008 1,259.53 0.30.29 0.014
5.346 6.322 4.353 257.69 4.934 3.491 3.361 4,175.62 5.982 5.922 3.044 1,212.37 0.30.28 0.02
3.852 3.516 3.548 303.43 4.874 3.825 3.852 4,193.24 3.817 3.952 3.428 1,233.34 0.30.29 0.011
4.699 3.421 3.31 311.82 4.327 4.911 5.273 7,101.38 4.158 3.558 3.183 2,098.35 0.60.61 0.005
4.087 4.644 3.008 278.09 3.865 3.482 5.644 7,211.46 5.392 4.981 3.51 2,147.95 0.60.54 0.059
3.978 3.719 3.463 286.09 4.321 3.635 5.177 7,122.77 4.196 3.682 3.883 2,094.52 0.60.60.002
4.347 2.976 3.434 279.05 5.284 5.405 4.546 7,157.75 3.978 4.449 3.333 2,126.02 0.60.57 0.033
4.44 3.505 3.345 262.11 5.521 3.628 4.63 7,080.43.991 3.587 4.037 2,082.84 0.60.57 0.031
3.603 4.235 8.397 910.92 5.633 5.258 9.274 21,669.13.839 3.875 5.985 6,824.31 1 1 0.002
5.451 3.87 6.187 885.07 4.922 6.128 12.67 21,416.95.687 3.643 8.407 6,661.59 1 1 0
5.957 3.575 8.829 918.75.764 5.873 8.867 21,244.54.995 4.161 4.444 6,594.82 1 1 0.002
4.818 3.049 8.352 882.03 6.918 5.931 10.12 20,684.65.035 3.511 8.835 6,461 1 1 0.002
3.745 3.083 8.32 885.89 6.902 5.976 10.920,605 5.183 3.216 8.642 6,455.84 1 1 0.002
sensors and thus there are 12 parameters are input to input
nodes of ANN and one output value which represents con-
dition of the monitored component (Called C). A part of
training data is shown in Table 1. After training, test data or
query data obtaining from real system can be used to test or
query ANN. In this case, 20 sets of test data (Table 2)are
used to test ANN.
There is no mathematical method to select the best struc-
ture of the SBP network, but the three layers SBP structure
was validated its powerful function to build a complex model.
The SBP structure in this experiment is set to three layer
12×20×1 networks. 12 means the number of input param-
eters (features in this experiment), 20 means the number of
the hidden layer nodes and 1 means only one output in this
ANN structure (condition). Its maximum training epoch is
set to 5,000. For each condition, 80 training sets are used to
train ANN and 20 sets of features are chosen to test it. Table 2
shows the results of the test data. As mentioned before, there
are 20 sets of test data in which there are 5 sets of them for
each condition. The nominal condition is called NC while the
output condition of test is called TC in this table. From this
table, the results are 100 % correct in the above parameter
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Fig. 17 Remaining useful life
distribution for each condition
for simulated component
0 50 100 150 200 250 300 350 400 450 500
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Remainin
g
useful life (Hours)
RUL Distribution of Condition 1.0
RUL Distribution of Condition 0.6
RUL Distribution of Condition 0.3
RUL Distribution of Condition 0
sets. However, the output is not exactly the same as the nom-
inal condition and there are deviations between them. The
precision of the output is discussed next part.
After the condition of the component is predicted, the
remaining useful life can be evaluated according to the condi-
tion. Most current RUL estimation methods are based on the
event data or condition monitoring data which want to find
the relationship between RUL and time the component used
or RUL and feature values (Si et al. 2011;Lee et al. 2006;
Tian 2006). This paper tries to find the relationship between
the RUL and the condition of a component that is evalu-
ating RUL by the condition and RUL distribution for each
condition (Fig. 17). The distributions of RUL are obtained
by the statistical methods. For example, if the condition of
a component is 0, the remaining useful is 350 h with a cer-
tain standard deviation. When the condition is 1.0, the RUL
is much closed to 0 which means the component has to be
maintained or repaired.
It is easy to understand that the later method (proposed this
paper) need far less history datasets to train neural network
than the former because the life cycle could be a very long
time and need huge data to express its process while there
only some of conditions and only a few data can express its
process. The later method’s result is clearer and sometimes
the customers can obtain satisfactory result even if only know
the condition because it has a direct relation with RUL. From
Fig. 17, the RUL distribution become narrow that means the
RUL evaluation is more accuracy when the condition closed
to failure. Therefore the confidence value of RUL increase
with the condition deterioration.
Discussions
In this section, three issues will be discussed. The first one
is how many training sets should be used in order to achieve
enough accurate condition of the machine from SBP net-
work. The second one is attempting to discuss the relationship
between the accuracy and the number of hidden layer nodes.
The last issue is convergent time of the BP network training.
To discuss the first issue, the numbers of training sets for
each condition are changed from 1 to 200. The number of hid-
den layer nodes is set to 20 and the number of training epoch
is set to 5,000. For each testing data, compare the output
of ANN and the nominal value which is called “error from
nominal value” which is average value of testing data for each
condition. The values of these errors are shown in Fig. 18.
We can see from this, the result is believable whatever the
condition of the component is when the number of training
data is larger than 20. For condition 0 and condition 1, the
result is still believable even if the number of training data
is smaller than 20. It is clear that the result will be believ-
able if there are only two conditions (0 and 1 or good and
fault) even if the number of training data is very small. But if
there are more conditions, the number of training data should
be increased. Therefore, the number of conditions should be
considered in designing of how many training sets are used
to trained SBP neural networks.
To discuss the second issue, the number of hidden layer
nodes is changed from 5 to 135. The number of training data
is set to 80 and the number of maximum training epoch is
set to 5,000. For each training process, several test sets for
every condition are used to test the trained SBP networks. The
results are shown in Fig. 19. From the figure, with the increas-
ing of the number of hidden layer nodes, the fluctuations of
the output for each condition are small. So the changing of
the number of hidden layer nodes does not affect the accuracy
of the output. What’s more, there is no mathematical method
to prove what the number of it is best. Therefore, the number
of hidden layer nodes does not need to be considered much.
To discuss the last issue, the number of hidden layer nodes
is set as 20 and the training epoch is set as 2,000. Figure 20
shows the BP network training time with the number of train-
ing data increasing from 10 to 200. From the figure, train-
ing time is not apparently increasing with the increasing of
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Fig. 18 Errors for each
condition
020 40 60 80 100 120 140 160 180 200
0
0.05
0.1
0.15
0.2
0.25
No. of training data
Errors from nominal value
Condition 0
Condition 0.3
Condition 0.7
Condition 1
Fig. 19 Output with different
number of hidden layer nodes
0 20 40 60 80 100 120
0
0.2
0.4
0.6
0.8
1
No. of hidden layer nodes
Output condition
Condition 0
Condition 0.3
Condition 0.6
Condition 1
Fig. 20 ANN training time
with the increasing of training
data
0 20 40 60 80 100 120 140 160 180 200
15
20
25
30
35
No. of training datasets
Training time (s)
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Fig. 21 ANN training time
with the increasing of hidden
layer nodes
0 20 40 60 80 100 120 140
15
20
25
30
35
40
45
No. of hidden layer nodes
Training time (s)
training data sets. Therefore, when the BP network is need,
we should use as many as possible data sets to complete the
training. Figure 21 shows the training time changes with the
increasing of hidden layer nodes. The number of training data
sets is set as 200 and the training epoch is set as 2,000. From
Fig. 21, the training time increase gradually with the increas-
ing of hidden layer nodes. Therefore, when a BP network
need to trained, the number of hidden layer nodes should be
considered. However, from the experience of previous work,
the numbers of the hidden layer neurons depends both on the
input layer number and the output layer neuron number but
the numbers could not be too many (Meng and Meng 2010).
Conclusions and future research
In this paper, a new method applying WPD, FFT and BP neu-
ral network for fault diagnosis and prognosis was proposed.
To verify the correctness and effectiveness of this method,
a framework called Intelligent Blower Fault Diagnosis and
Prognosis System was established as a case study. From the
case, the proposed method for diagnosis is very effective and
efficient. This method can also predict the degradation and
further to predict remaining useful life of monitored com-
ponent as well. Finally, this method has many advantages
because of using artificial neural network such as the ability
to easily deal with complex problems without sophisticated
and specialized knowledge, the ability to carry out classifi-
cations, the ability to deal with non-linear systems and low
operational response times after the learning phase.
In this paper, the minimum bandwidth 0–64 Hz is chosen
in WPD because of the fundamental frequency of the vibra-
tion signal is the 47.5 Hz. In a real system, the minimum
bandwidth of WPD (which means how many levels should
be decomposed) should be selected according to the real fun-
damental frequency. The peak values of FFT for decomposed
signals are selected as features to judge the degradation of the
monitored machine. In a real application, some other param-
eters may be chosen as features to judge the condition accord-
ing to what kinds of faults need to prognose and/or prognose.
In the case study of this paper, there is only one kind of fault
was simulated. In the future, multi-fault diagnosis and prog-
nosis should be a research topic. The degradation information
could be very useful for maintenance decision making and
thus, how to apply this degradation information in mainte-
nance decision making should be a research issue as well in
the future.
Acknowledgments This paper is a result of Norwegian Manufactur-
ing Future project in Center of Research and Innovation of Norwegian
Manufacturing Future (SFI Norman), which is financially supported by
Norwegian Research Council.
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