Fault detection and diagnosis ingears using wavelet

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
__________________________________________________________________________________________
Volume: 02 Issue: 09 | Sep-2013, Available @ http://www.ijret.org 146
FAULT DETECTION AND DIAGNOSIS INGEARS USING WAVELET
ENVELOPED POWER SPECTRUM AND ANN
M. Lokesha1
, Manik Chandra Majumder2
, K. P. Ramachandran3
, Khalid Fathi Abdul Raheem4
1, 3, 4
Department of Mechanical Engineering, Caledonian College of Engineering, OMAN,lokjay251@yahoo.com,
2
Department of Mechanical Engineering, National Institute of Technology, Durgapur, INDIA,lokjay@gmail.com
Abstract
In this work, automatic detection and diagnosis of gear condition monitoring technique is presented. The vibration signals in time
domain wereobtained from a fault simulator apparatus from a healthy gear and an induced faulty gear. These time domain signals
were processed using Laplace and Morlet wavelet based enveloped power spectrum to detect the faults in gears. The vibration signals
obtained were filtered to enhance the signal components before the application of wavelet analysis. The time and frequency domain
features extracted from Laplace wavelet based wavelet transform are used as input to ANN for gear fault classification. Genetic
algorithm was used to optimize the wavelet and ANN classification parameters. The result shows the successful classification of ANN
test process.
Index Terms:Continuous wavelet transform, Envelope power spectrum, Wavelet, Filtering, ANN.
-----------------------------------------------------------------------***-----------------------------------------------------------------------
1. INTRODUCTION
Gears are commonly used component for the transmission of
mechanical power and variation of speed in machines. The
condition monitoring of the machine with a reliable system
can identify the fault at an early stage in order to avoid any
failure in the machines [1]. Gear failure is one of the most
common failures in the rotating machines which lead to
economic losses. Therefore it is very important to detect gear
failure [2, 3].
The defects which are usually found in gear box includes the
presence of crack in one or more of the gear tooth, chipping of
teeth, geometrical imperfection etc. Vibration based condition
monitoring techniques is commonly used for the fault
detection and diagnosis in mechanical components like gears,
bearings etc.[4,5].Vibration signals are analysed using
different techniques such as time domain, frequency domain
and time–frequency domain techniques [6-8]. The impact
produced by the faulty gear may result in non-stationary
signal, which contain abundant information about faults;
therefore, it is important to analyze the non-stationary signals.
The non-stationary nature of the signal suggests the use of
time-frequency techniques, which make it possible to look at
the time evolution of the signal’s frequency content [9, 10].
FFT based condition monitoring techniques are not suitable
for non-stationary signal, which assumes the analyzed signal
to be strictly periodic [11].The non-stationary nature in the
signal can be analyzed by the wavelet transform (WT), which
provides powerful multi resolution analysis in both time and
frequency domains. The time and frequency analysis of
signals makes the WT as a favored tool to extract the transient
features of non-stationary vibrations signals compared to fast
Fourier transform spectrum [12-14].Wavelet coefficients,
which are obtained by the wavelet analysis indicate the
correlation of the signal with the particular wavelet. In order to
extract the fault features of the signal appropriate wavelet base
function should be selected.
Laplace wavelet is a complex, single sided damped
exponential formulated as an impulse response of a single
mode system to be similar to data features commonly
encountered in health monitoring tasks. It has been applied to
the vibration analysis of an aircraft for aerodynamic and
structural testing [15] and to diagnose the wear of the intake
valve of an internal combustion engine [16]. Kurtosis is
defined as the fourth central cumulant divided by the square of
the variance of the probability distribution [17]. A high
kurtosis values indicates high impulsive content of the signal
with more sharpness in the signal intensity distribution, based
on maximum kurtosis concept, the fault detection is enhanced,
by optimizing the wavelet features [18-20].
A neural network is a massively parallel distributed processor
that has a natural tendency for storing knowledge and making
it available for use. Artificial neural network (ANN) is a type
of artificial intelligence, which has nonlinear information
processing devices, built from interconnected elementary
processing devices called neurons. Among all kinds of
intelligent diagnosis methods, pattern recognition based on an
Artificial Neural Network (ANN) has been widely used
because of its power in self- organizing, unsupervised-
learning, and nonlinear pattern classification [21].The artificial

__________________________________________________________________________________________
neuron receives signals analogous to the natural electro-
chemical signals. The way information is processed and
intelligence is stored depends on the architecture and
algorithms of ANN.
Expert system and artificial intelligence are playing significant
role in automated fault diagnosis and machine learning.
Machine learning using the concepts of Artificial Neural
Network (ANN) have become very popular and known for
exploiting non-linear pattern classification properties, offering
automatic detection and identification of gearbox fault
conditions. It offers an advantage that they do not require an
in-depth knowledge of the behavior of the system [22].
Artificial neural network (ANN), support vector machine
(SVM) and Fuzzy classifier are widely used as classification
tool [23].The most popular feed forward, multi-layer
perceptronneural network, is frequently exploited in fault
diagnosis systems and it has found an immense popularity in
condition monitoring applications[24].
In this paper, Wiener filter is used to enhance the fault signal
components in the vibration signal and wavelet envelope
power spectrum is used to detect localized gear tooth defects.
Vibration signals were collected from the experimental setups
with induced faults. The second part includes the application
of wavelet analysis as a feature extraction method combined
with the neural network classifier for automatic detection and
diagnosis of the gear fault.
This paper is organized as follows: section 2 covers theory on
the wiener filter and wavelet transform, section 3 explains the
experimental setups and procedure, section 4 discusses the
implementation of the enveloped wavelet power spectrum
forgear fault detection, section5 covers feature extraction
method combined with ANN as classifier and the conclusions
are presented in section 6.
2. WAVELET POWER SPECTRUM
2.1Filtering
The filtering theory works on the concept of minimizing the
difference between the filtered output and the desired output.
The Filter uses the least mean square approach to minimize,
which adjusts the filter coefficients to reduce the square of the
difference between the desired and actual waveform after
filtering.
The concept of Wiener filter approach is represented by
schematic diagram as depicted in Figure 1.
Input A(n) output B(n) error E(n)
-
+
Desired Response D(n)
Figure 1
The linear process C(z) uses the concept of finite impulse
response (FIR) filters to filter the input waveform A(n)having
both signal and noise.
The FIR filters are implemented using convolution equation
B(n) =∑ − (1)
Where, the impulse response of the linear filter is represented
by i(k). The output of the filter, B (n), can be thought of as an
estimate of the desired signal, D (n). The difference between
the estimate and desired signal’E (n)’ is determined by
subtraction
E(n) = D(n) − B(n).
To minimize error signal‘E (n)’the least mean square
algorithm is used.
E (n) can be written as:
E (n) = D (n) − B (n) = D (n) −∑ − (2)
Where M is the length of the FIR filter. In fact, it is the sum of
E (n)2
which is to be minimized. Squaring of the elements ‘E
(n)2
‘leads to a quadratic function of the FIR filter coefficients,
i(k), which contains the autocorrelation and cross correlation
elements.
In order to Minimize the error function with respect to the FIR
filtercoefficients, take derivatives with respect to i(k) and set
them to zero. This represents a series of Mequations that must
be solved simultaneouslyto solve for the FIR coefficients. The
matrix expression for these simultaneous equations is known
as the Wiener-Hopfequation and is abasic component of
Wiener filter theory [25].
2.2 Enveloped wavelet power spectrum
Wavelet analysis can use different types of probing functions,
but the family always consists of enlarged or compressed
versions of the basic function, as well as translations.
Mathematically, the wavelet transform of a finite energy
signal x (t) with the analyzing waveletψ , leads to the
definition of continuous wavelet transform as given in
equation (3).
W (a, b) = dt
a
bt
a
tx∫
∞
∞−





 −
∗ψ
1
)( (3)
Where, b (dilation parameter) acts to translate the function
across x (t) and the variable a (scaling parameter) acts to vary
the time scale of the wavelet functionψ . The ∗ indicates the
operation of complex conjugate and the normalizing parameter
Linear
Filter C (z)
∑

__________________________________________________________________________________________
1/ a ensures that the energy is the same for all values of a.
The values of a stretches and contracts the wavelet function
along the time axis. The base wavelet is generated when b=0,
and a=1, then the wavelet is in its natural form, which is
termed the mother wavelet. The wavelet coefficients W(a,b)
shows the similarity between the waveform and the wavelet at
a given combination of scale ‘a’ and position ‘b’.
The envelope detection or amplitude demodulation is the
technique of extracting the modulating signal from an
amplitude-modulated signal. The result is the time-history of
the modulating signal. Envelope analysis is the FFT
frequency spectrum of the modulating signal. The vibration
signal of a faulty gear can be viewed as a carrier signal at a
resonant frequency of the gear modulated by a decaying
envelope. The goal of the enveloping approach is to replace
the oscillation caused by each impact with a single pulse over
the entire period of the impact.
Laplace wavelet represented by equation 4 is a complex
analytical and single sided damped exponential and the view
of Laplace wavelet is shown in Figure 2
=)(tψ A e
ti c
ω
β
β








+
−
− 2
1 t ≥ 0
=)(tψ 0 t is otherwise (4)
Where β is the damping factor that controls the decay rate of
the exponential envelope in the time domain and hence
regulates the resolution of the wavelet and it simultaneously
corresponds to the frequency bandwidth of the wavelet in the
frequency domain. The frequency cω determines the number
of significant oscillations of the wavelet in the time domain
and corresponds to wavelet center frequency in the frequency
domain and A is an arbitrary scaling factor [18].
(a)
(b)
Figure 2.Laplace wavelet (a) Real part of Laplace wavelet (b)
Imaginary part of Laplace wavelet
The optimal values of β and ωc for given vibration signal can
be found by adjusting the time-frequency resolution of the
Laplace wavelet to the decay rate and the frequency of the
impulses to be extracted. A high kurtosis values indicates high
impulsive content of the signal with more sharpness in the
signal intensity distribution
Let x (n) be a real discrete time random process, and WTaits N
point Laplace wavelet transform at scale a. The Laplace
Wavelet Kurtosis (LWK) for x(n) is defined as the kurtosis of
the magnitude of WTa at each wavelet scale a as in the
equation (5)[19].
LWK (a)= 2
1
2
1
4
))],),((([
)),),(((
c
N
n
a
c
N
n
a
nxWTabs
nxWTabs
ωψ
ωψ
β
β
∑
∑
=
=
(5)
The objective of the Laplace wavelet shape optimization
process is to find wavelet shape parameters which maximize
the Laplace wavelet kurtosis.
Genetic algorithm is used to optimize the wavelet parameters.
A genetic algorithm (GA) is computerized search and
optimization algorithms based on the mechanics of natural
genetics and natural selection. The principal idea of the GA is
to search for the optimal solution in a large population.The
basic steps involved in the genetic algorithm are shown below.
1. [Start] Generate random populationof chromosomes
2. [Fitness] Evaluate the fitness function of each
chromosomein the population
3. [New Population] Create a new population using selection,
crossover and mutation until the new population is complete
4. [Replace] Use new generated population for a further run of
the algorithm
5. [Test] If the end condition is satisfied, stop, and return the
best solution in current population
6. [Loop] Go to step 2
In this research roulette wheel, Arith-crossover and uniform
mutation is used to find optimum solution.
0 5 10 15
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0 5 10 15
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4

__________________________________________________________________________________________
The scale-kurtosis distribution of the wavelet transform using
Laplace wavelet is depicted in the Figure 3.
Figure 3: Scale-Kurtosis distribution
The Morlet wavelet is defined as given in equation (6)[25].
The view of Morlet wavelet is shown in Figure 4
=)(tψ
2
t
e−
cos (
2ln
2
π t) (6)
Figure4. Morlet wavelet
The wavelet transform (WT) of a finite energy signal x(t),
with the mother wavelet ψ (t), is the inner product of x(t) with
a scaled and conjugate wavelet ψ ∗ a,b. Since the analytical
and complex wavelet is employed to calculate the wavelet
transform, the result of the wavelet transform is also an
analytical signal as shown in equation (7) and (8).
WT{x(t),ab} = <x(t), ψ a,b(t)> =
∫
∞
∞−
∗
dtttx
a
)()(
1
ba,ψ (7)
= Re [WT (a, b)] + iIm [WT (a, b)] =A(a, b) e
).( baiθ
(8)
Whereψ a,bis a family of daughter wavelet, defined by the
dilation parameter a and the translation parameter b, the factor
1/ a is used to ensure energy preservation. The time-varying
function A(a, b) is the instantaneous envelope of the resulting
wavelet transform (EWT) which extracts the slow time
variation of the signal, and is given by equation (9)
A (a, b) = EWT (a, b) = 22
}b)][WT(a,Im{}b)][WT(a,Re{ + (9)
For each wavelet, the inner product results in a series of
coefficients which indicate how close the signal is to that
particular wavelet. To extract the frequency content of the
enveloped correlation coefficients, the wavelet-scale power
spectrum (SWPS) (energy/unit scale) is given by equation (10)
SWPS (a, ω ) =
∫
∞
∞−
ωω daSEWT
2
),( (10)
Where SEWT (a,ω ) is the Fourier transform of EWT (a,b).
The total energy of the signal x (t) is given in equation (11)
TWPS = ∫
2
)(tx dt =
∫
∞
∞−
daaSWPS ),(
2
1
ω
π
(11)
3. EXPERIMENTAL SETUPS AND PROCEDURE
OF DATA COLLECTION
3.1Experimental Setup1
The fault simulator setup 1consists of variable speed motor,
single stage gear box, couplings, belt & pulleys, loading
system, and bearings as depicted in Figure 5. The electric
motor of capacity 0.5 HP and variable speed maximum up to
10,000RPM is connected to one gear of the gear box through
coupling and belt & pulleys system and the other gear is
connected to a loading system. The gear and pinion has 30 and
20 teeth respectively. The steel shafts of 5/8” diameter connect
gears with motor and loading system. The shafts are supported
through bearings. The vibration data is collected from the
drive end bearing of gear box using the accelerometer with a
NI Data Acquisition Device. The views of healthy and faulty
gears are shown in Figure 6. The collected vibration data are
exported as data file to MATLAB software for further
processing of the signal to identify the fault.
In the experimental investigation, the vibration signal was
collected from a healthy gear at shaft speed of 900RPM under
constant load condition. The Gear mesh frequency (GMF) is
calculated to be 20*900/60 =300Hz. Further faults were
induced in two different stages as shown in Table 1 and the
corresponding vibration readings were taken. The sampling
frequency of 16,000 Hz was used to collect the data for 2
seconds. The data was collected from the setup after reaching
the required speed.
0 10 20 30 40 50 60 70 80 90
0
5
10
15
20
25
30
laplace Wavelet kurtosis
wavelet scale
Laplacewaveletkurtosis
healthy
Stage 1
Stage 2
Stage 3
0 200 400 600 800 1000 1200
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5

__________________________________________________________________________________________
Figure5.Fault Simulator set up 1
(a)
(b)
(c)
Figure 6.Gears with induced fault in 2 stages. (a) Stage 0. (b)
Stage 1. (c) Stage 2.
Table 1.Stages of induced fault for Fault Simulator set up 1
Stage Condition of the gear Fault description
Stage 0 Healthy gear Without any induced fault
Stage 1 Faulty gear The chipped tooth
Stage 2 Faulty gear Tooth was completely
removed
3.2 Experimental Setup2
The fault simulator2 used for the experimentation to collect
the data is shown in Figure 7. It consists of a motor, single
stage gear box and loading system. The gearbox input side
was connected to 0.5 HP, 2900 RPM electric motor through
coupling and the output side was connected to a loading
system. The gear and pinion has 46 and 23 teeth respectively.
The shafts of 25mm diameter connect gears with motor and
loading system. All drive shafts are supported at its ends with
antifriction bearings. The vibration data was collected from
the drive end bearing of gear box using the accelerometer
(model 621B40, IMI sensors, sensitivity is 1.02 mV/m/s2 and
frequency range up to 18 kHz) with a NI Data Acquisition
Device. The view of the healthy gears is depicted in Figure 8.
The vibration data collected are exported as data file to
MATLAB software for further processing of the signal to
identify the fault.
Figure 7.Fault Simulator set up 2.
Figure 8.View of healthy gears
In the experimental investigation, the vibration signal was
collected from a healthy gear at shaft speed of 2850 RPM
under constant load condition. The Gear mesh frequency
(GMF) is 23*2850/60 =1092.5Hz. Further faults are induced
in three different stages as shown in Table 2 and the
corresponding vibration readings were taken. The views of
faulty gear are shown in Figure 9. The sampling frequency of
Motor
Gear box
Load
Healthy gear

__________________________________________________________________________________________
16,000 Hz was used to collect the data for 2.4 seconds. The
data was collected from the setup after reaching the required
speed.
Stage Condition of
the gear
Fault description
Stage 0 Healthy gear Without any induced fault
Stage 1 Faulty gear A crack of 3mm is induced at
the root of the tooth
Stage 2 Faulty gear Tooth was partially broken
Stage 3 Faulty gear Tooth was completely removed
Table 2: Stages of induced fault for Fault Simulator set up 2.
(a)
(b)
(c)
Figure9 Gears with induced fault in 3 stages. (a) Stage 1. (b)
Stage 2. (c) Stage 3
4. IMPLEMENTING OF WAVELET POWER
SPECTRUM
This section presents several application examples to visualize
the performance of the proposed approach. The proposed
approach is applied for the detection of localized gear fault. It
is well known that the most important components in gear
vibration spectra are the tooth meshing frequency and its
harmonics, together with sidebands due to modulation
phenomena. The increment in the number and amplitude of
sidebands indicate a fault condition.
A typical time domain signal obtained from the experimental
setup with gear fault, using accelerometer is given in Figure
10.The time data obtained from the setups are processed with
the Wiener filter technique to enhance the signal components.
This is further processed using various signal processing
techniques like wavelet enveloped power spectrum based on
Morlet wavelet and Laplace wavelet. The GMF and its side
bands are represented in various power spectrums with
indication of data cursor value.The rotational frequency of
pinion, gear, GMF and some of theside bands of GMF are
depicted in Table 3 for both the experimental setups.
Figure 10.Time domain signal of gear with fault
Table 3.Frequency of rotation
Description Experimental set
up 1(Frequency)
Experimental set
up 2(Frequency)
Pinion rotational
frequency
48 15
Gear rotational
frequency
24 10
GMF 1093 300
Side band
frequency at GMF
1045 285
Side band
frequency at GMF
1140 290
0 0.5 1 1.5 2 2.4
-600
-400
-200
0
200
400
600
Time (Sec)
Acceleration(m.sec-2)

__________________________________________________________________________________________
4.1 Laplace Wavelet Enveloped Power Spectrum for
the Experimental Set Up 1
(a)
(b)
(c)
Figure 11.Laplace wavelet enveloped Power Spectrums for
experimental set up 1. (a) Without any defect. (b) 1st
stage of
defect. (c) 2nd
stage of defect
Figure 11 (a) to 11(d) depicts that vibration amplitude at
GMFis increasing in line with the severity of fault from 170 to
599 mm/s2
with dominant sidebands. Side bands in the
spectrum indicate the severity of the fault. The side bands
level remains low for healthy condition of gears and the side
bands are risingwith the severity of the fault.
4.2 Laplace Wavelet Enveloped Power Spectrum for
the Experimental Set Up 2
(a)
(b)
(c)
200 250 300 350 400 450 500 550 600 650
0
200
400
600
800
1000
1200
X: 303.2
Y: 170.4
Frequency (Hz)
PowerSpectrum
lp Wavelet Enveloped Power Spectrum healthy condition
X: 606
Y: 37.53
X: 293
Y: 26.09
X: 313
Y: 18.31
X: 323.2
Y: 34.28
200 250 300 350 400 450 500 550 600 650
0
200
400
600
800
1000
1200
X: 300.8
Y: 277.7
Frequency (Hz)
PowerSpectrum
lp Wavelet Enveloped Power Spectrum 1st stage fault
X: 286.1
Y: 359
X: 291.5
Y: 127.2
X: 312
Y: 218.2
200 250 300 350 400 450 500 550 600 650
0
200
400
600
800
1000
1200
X: 300.8
Y: 599.5
Frequency (Hz)
PowerSpectrum
lp Wavelet Enveloped Power Spectrum 2nd stage fault
X: 286.1
Y: 774.9
X: 277.3
Y: 408.2
X: 312
Y: 471.1
600 800 1000 1200 1400 1600 1800 2000 2200 2400
0
500
1000
1500
2000
2500
X: 1098
Y: 367.5
Frequency (Hz)
PowerSpectrum
lp Wavelet Enveloped Power Spectrum healthy condition
X: 1050
Y: 255.4
X: 1146
Y: 221.8
600 800 1000 1200 1400 1600 1800 2000 2200 2400
0
500
1000
1500
2000
2500
Frequency (Hz)
PowerSpectrum
lp Wavelet Enveloped Power Spectrum 1st stage fault
X: 1094
Y: 499
X: 998.5
Y: 441
X: 1236
Y: 431.8
X: 1046
Y: 147.1
600 800 1000 1200 1400 1600 1800 2000 2200 2400
0
500
1000
1500
2000
2500
X: 1099
Y: 554.2
Frequency (Hz)
PowerSpectrum
lp Wavelet Enveloped Power Spectrum 2nd stage fault
X: 1008
Y: 1046
X: 1053
Y: 156.4
X: 2207
Y: 112.9

__________________________________________________________________________________________
(d)
Figure 12.Laplace wavelet enveloped Power Spectrums for
stage of
defect. (c) 2nd
stage of defect(d) 3rd
stage of defect
Figures 12(a)-12(d) depicts the Laplace wavelet enveloped
power spectrums for the healthy and faulty gear in three
different stages of fault for the experimental setup2. The
vibration amplitude at GMFis increasing in line with the
severity of fault from 367.5 to 648 mm/s2
with dominant
sidebands, indicating severity of fault. Side band level remains
low as seen in Figure 12(a), for a gear box in good condition.
4.3 Morlet Wavelet Enveloped Power Spectrum for
Experimental Set Up 1:
(a)
(b)
(c)
Figure 13.Morlet wavelet enveloped Power Spectrums for
stage of
defect. (c) 2nd
stage of defect
The vibration data of the experimental set up 1used to develop
the Morlet wavelet enveloped power spectrums are shown in
Figure 13(a) – 13(d). Amplitude of GMF is increasing from
328to 1431 mm/s2
for healthy gear and faulty gear in 2
different stages. The significant increase in amplitude of side
bands above the GMF amplitude indicates the severity of
fault.
4.4Morlet wavelet enveloped Power Spectrum for the
experimental set up 2
(a)
(b)
600 800 1000 1200 1400 1600 1800 2000 2200 2400
0
500
1000
1500
2000
2500
Frequency (Hz)
PowerSpectrum
lp Wavelet Enveloped Power Spectrum 3rd stage fault
X: 1094
Y: 648.9
X: 1141
Y: 1103
X: 1046
Y: 2276
X: 1189
Y: 486.5
X: 974.9
Y: 508.4
200 250 300 350 400 450 500 550 600 650
0
200
400
600
800
1000
1200
1400
1600
X: 303.2
Y: 328.2
Frequency (Hz)
PowerSpectrum
mor Wavelet Enveloped Power Spectrum healthy condition
X: 282.7
Y: 27.59
X: 293
Y: 49.72
X: 313
Y: 40
X: 323.2
Y: 49.8
200 250 300 350 400 450 500 550 600 650
0
200
400
600
800
1000
1200
1400
1600
X: 300.8
Y: 662.9
Frequency (Hz)
PowerSpectrum
mor Wavelet Enveloped Power Spectrum 1st stage fault
X: 286.1
Y: 521.6
X: 330.1
Y: 645
X: 315.9
Y: 183.3
200 250 300 350 400 450 500 550 600 650
0
200
400
600
800
1000
1200
1400
1600
Frequency (Hz)
PowerSpectrum
mor Wavelet Enveloped Power Spectrum 2nd stage fault
X: 300.8
Y: 1431
X: 286.1
Y: 1126
X: 330.1
Y: 1392
X: 315.9
Y: 395.7
600 800 1000 1200 1400 1600 1800 2000 2200 2400
0
500
1000
1500
2000
2500
X: 1098
Y: 109.8
Frequency (Hz)
PowerSpectrum
mor Wavelet Enveloped Power Spectrum healthy condition
X: 1050
Y: 72.15
X: 1123
Y: 77.34
X: 2197
Y: 463.3
X: 2149
Y: 328.6
600 800 1000 1200 1400 1600 1800 2000 2200 2400
0
500
1000
1500
2000
2500
X: 1094
Y: 389.3
Frequency (Hz)
PowerSpectrum
mor Wavelet Enveloped Power Spectrum 1st stage fault
X: 1126
Y: 314.6
X: 1058
Y: 267.2
X: 2184
Y: 468.4
X: 2235
Y: 567.3
X: 2139
Y: 749.2

__________________________________________________________________________________________
(c)
(d)
Figure 14.Morlet wavelet enveloped Power Spectrums for
stage of
defect. (c) 2nd
stage of defect (d) 3rd
stage defect
Morlet wavelet enveloped power spectrums developed for the
experimental set up2 data are shown in Figure 14(a)–14(d).
Amplitude at GMF is increasing from 109 to 1206 mm/s2
for
healthy gear and faulty gear in 3 different stages.Vibration
amplitude of side bands are significant. Changes in the
number and strength of the side bands are noticed.
5. LAPLACE WAVELET TRANSFORM AND ANN
FOR FAULT CLASSIFICATION
Although analysis of wavelet enveloped power spectrum by an
experienced technical person is possible, computerized
inspection is easier and recommended for the increasing
demand for on-line automated condition monitoring
applications. Artificial neural network (ANN) is used for an
automated detection and diagnosis of gear conditions. To
speed up the classification process and to make it suitable for
the online condition monitoring, the data processed using
Laplace-wavelet transform is used as input to ANN. The
extracted features in time and frequency domain are used as
the ANN input vectors for the gear condition identification.
The ANN classifier parameters are optimized using GA by
minimizing the mean square error (MSE).
As shown in Figure 3, the scale-kurtosis distribution for
different gear conditions, it could be seen that the scales range
of 20-30 are the mostly dominant scales, which can reveal the
gear condition sufficiently. The predominant Laplace wavelet
transform scale based on the scale-kurtosis value has been
selected for features extraction.
The four extracted features in time and frequency domain for
the dominant scale are:
1) Time domain features: This includes Standard Deviation
(SD), and Kurtosis factor(KF).
2)Frequency domain features: This includes the ratio of
SWPSpeak frequency (fmax) to the shaft rotational frequency
(frpm), and the ratio of SWPS maximum amplitude (Amax) to the
overall amplitude (Sum (Ai)).
The scheme of feature extraction and overall architecture of
ANN is depicted in Figure 15.
Figure 15: features extraction and ANN architecture
A feed-forward multi-layer perceptron (MLP) neural network
with three layers has been developed namely Input layer,
Hidden layer and output layer. The features extracted from the
predominant scale of Laplace wavelet transform in time and
frequency domain are used as input to ANN with four source
nodes. The hidden layer with seven computation nodes has
been used. The number of the hidden nodes is optimized using
a genetic algorithm by minimization of Mean Square Error
(MSE) between the actual network outputs and the
corresponding target values. The output layer has three nodes
to represent working conditions of gear.
The three digit output target nodes need to be mapped by the
ANN are represented as [1,0,0] for the healthy
condition,[0,1,0] for the stage 1, and [0,0,1] for stage 2 of
gear.
600 800 1000 1200 1400 1600 1800 2000 2200 2400
0
500
1000
1500
2000
2500
X: 1053
Y: 533.5
Frequency (Hz)
PowerSpectrum
mor Wavelet Enveloped Power Spectrum 2nd stage fault
X: 1099
Y: 653.5
X: 2207
Y: 1562
X: 2152
Y: 1558
600 800 1000 1200 1400 1600 1800 2000 2200 2400
0
500
1000
1500
2000
2500
X: 1094
Y: 1206
Frequency (Hz)
PowerSpectrum
mor Wavelet Enveloped Power Spectrum 3rd stage fault
X: 1046
Y: 2460
X: 1141
Y: 2468
X: 2187
Y: 985
X: 2140
Y: 994.2

__________________________________________________________________________________________
The activation function f1, bias b and weight w are used to
transform the input vector to intermediate vector h and the
output vector Oof the network is obtained from the vector of
the intermediate variable h through a similar transformation
using activation function f2 at the output layer. The connection
weights and biases are modified iteratively to optimize the
performance criterion, while training the network. Commonly
used minimization of mean square error(MSE) is used as the
performance criterion. The process is repeated until the overall
MSE value drops below some pre-determined threshold
(stopping criterion). After the training process, the ANN
weights are fixed and the system is deployed for the unseen
vibration data.
In this work MATLAB software is used for ANN process with
Levenberg-Marquarat Back-propagation (LMBP) training
algorithm, a MSE of 10E-10, a minimum gradient of 10E-20
and maximum iteration (epochs) of 1000 were used. The
training process would stop if any of these conditions were
met. The initial weights and biases of the network were
generated automatically by the program
5.1 Implementing WT and ANN
The data collected from the experimental setup with different
working conditions are used to train and test the ANN. The
neural network input feature vectors consisting of four groups
representing the different gear conditions are used to train the
network. The data sets of size 1920 samples each is used to
train the network.The parameters used for the network are
shown in Table 4
Table 4: Parameters used for the network
Transfer Function of Hidden Layer Sigmoid
Transfer Function of output Layer Linear
Training Algorithms Levenberg-
Marquarat
Maximum number of epochs 1000
MSE stopping criteria 1e-10
Minimum performance gradient 1e-20
Number of input nodes 4
Number of hidden nodes 7
The training can ceaseaccording to any one of the criteria of
mean square error (MSE), the number of epochs of training or
minimum performance gradient reaches certain value set as
shown in Table 4. The result of ANN learning processhas R
value of above 0.99 for training, testing and validation, which
is the indication of the relationship between the outputs and
targets of ANN The ANN learning process and the
performance plot is depicted in Figure 16, which shows that
the training with 82 epochs met the MSE stopping criteria
(MSE less than 10E-10).
Figure 16: ANN Learning process and performance plot
The ideal output target nodes needs to be mapped by the ANN
are represented as [1,0,0] for the healthy condition,[0,1,0] for
the stage 1, and [0,0,1] for stage 2 of gear condition is
depicted in Figure 17(a)and the testing process is depicted in
Figure (b).The successful classification of ANN test process
for unseen vibration data of the trained ANN for the healthy,
stage1 and stage 2 of gear condition are shown in Figure17(c)-
17(e) respectively.
(a)
(b)
0 healthy stage 1 stage 2
-2
-1
0
1
2
0 480 960 1440
-2
-1
0
1
2

__________________________________________________________________________________________
(c)
(d)
(e)
Figure 17: ANN train and testing process (a) Training process
(b) Testing process (c) Test process for unseen healthy data
(d) Test process for unseen stage1 data(e) Test process for
unseen stage 2 data
CONCLUSIONS
Wavelet enveloped power spectrum and ANN used for gear
fault detection and diagnosis is presented in this paper.Various
stages of induced fault and healthy conditions of gear are
studied using Laplace and Morlet wavelet based envelop
power spectrum. Wiener filter is used toenhance the fault
signal components, which support for the early detection of
the fault.
Further, the studies conducted indicates that both Morlet and
Laplace wavelet based enveloped power spectrum depicts
significant increase in magnitude of vibration amplitude at
GMF along with increase inthe size of fault.Laplace wavelet
analysis is more powerful inisolating peaks at multiple RPM
sidebands of GMF which canprovide more precise information
about defect condition. Wavelet and ANN parameters are
optimized using Genetic algorithm. Features extracted from
optimized wavelet scale are used as input vectors to ANN.The
application of proposed technique shows its effective detection
and classification of ANN test.
REFERENCES:
[1] WandelJ.. 2006. Multistage gearboxes: Vibration based
quality control, KTH Engineering Sciences, Stockholm,
Licentiate Thesis,TRITA-AVE 2006:27 ISSN1651-7660.
[2] M.E.M. El Badaoui, F. Guillet, J. Daniere, New
applications of the real cepstrum to gear signals: including
definition of a robust fault indicator, Mechanical Systems and
Signal Processing 18 (5) (2004) 1031–1046.
[3] W. Staszewski, K. Worden, G.R. Tomlinson, Time-
frequency analysis in gearbox fault detection using the
Wigner–Ville distribution and pattern recognition, Mechanical
Systems and Signal Processing 11 (5) (1997) 673–692.
[4] Abu-Mahfouz I.A., 2007. Gearbox health monitoring
experiment using vibration signals. Journal of Engineering
Technology, Vol.24, No. 1, pp. 26-31.
[5] Omar F.K. and Gaouda A.M.,2009. Gearbox diagnostics
using wavelet based windowing technique. Journal of Physics:
Conference Series, Vol. 181, No.No. 1, Conf. Ser. 181 012089
[6] Lin J, Zuo M.J., 2003. Gear box fault diagnosis using
adaptive wavelet filter,Mechanical Systems And Signal
Processing, Vol. 17,No. 6, pp. 1259-1269.
[7] Saravanan N. Ramachandran K.I.,.2010. Incipient gear box
fault diagnosis using discrete wavelet transform for feature
extraction and classification using artificial neural network An
international journal of Expert Systems with Applications,
Vol. 37, pp.4168-4181
[8] Choy F.K., Huang, J.J., Zakrajsek R.F, Handschuh T.P,
Townsend.1994.Vibration signature of a faulted gear
transmission system NASA, Technical Memorandum 106623,
Technical Report ARL-TR-475 AIAA-94-2937
[9] Dalpiaz G., Rivola A. And Rubini R.,1998 Gear fault
monitoring: comparison of vibration analysis techniques
Proceedings of the 3rd International Conference on Acoustical
and Vibratory Surveillance Methods and Diagnostic
Techniques, Vol. 13, pp, 623-637
[10] Randall R.B. 1982. A new method of modeling gear
faults. Journal ofMechanical Design, Vol. 104, pp. 259-267
[11] Pan M.C., Sas P., 1996. Tansient analysis on machinery
condition monitoring International Conference on Signal
Processing, Proceedings, ICSP 2,pp. 1723-1726.
[12]Peng Z.K., Chu F.L., 2004 Application of the wavelet
transform in machine condition monitoring and fault
0 500 1000 1500
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 480 960 1440
-2
-1
0
1
2
0 480 960 1440
-2
-1
0
1
2

__________________________________________________________________________________________
diagnostics: a review with bibliography. Mechanical Systems
and Signal Processing, Vol. 18, No. 2, pp. 199–221
[13] Purushotham V., Narayanan S, and Suryanarayana,
Prasad A.N., 2005Multi-fault diagnosis of rolling bearing
elements using wavelet analysis andhidden Markov model
based fault recognition. NDT & E International Vol. 38,No. 8,
pp. 654-664.
[14] Shi D.F., Wang W.J. and Qu L.S., 2004. Defect detection
for bearing using envelope spectra of wavelet transform.
ASME J of Vibration and Acoustics, Vol.120, pp. 567-574.
[15] Freudinger L.C., Lind R., and Brenner M.J., 1998.
Correlation filtering of modal dynamics using the Laplace
wavelet Proceeding of the 16th International Modal Analysis
Conferences, Vol. 2, pp. 868-877.
[16] Yanyang Z., Xuefeng C. Zhengila H. And Peng C., 2005.
Vibration basedmodal parameters identification and wear fault
diagnostics using Laplacewavelet. Key Engineering Materials,
Vol. 293-294, pp. 183-190.
[17] Juan Jos´eGonz´alez de la Rosa, Member, IEEE, A.
Moreno, A. Gallego, R. Piotrkowski and E. Castro “Termites
detection via spectral kurtosis and waveletde-noising of
acoustic emission signals”journal of acoustic emission, 26,
2008.
[18]Al-Raheem K.F, Roy. A, Ramachandran.K.P. 2006.
Detection of rollingelement bearing faults using optimized –
wavelet denoising technique.
International Conference on Signal Processing, Beijing, China
[19]Al-Raheem K.F., Roy A., Ramachandran K.P, Harrison
D.K., Grainger S.,2009, International Journal of Advanced
Manufacturing Technology, Vol. 40, pp.393-402.
[20] Al-Raheem K.F., Roy A., Ramachandran K.P, Harrison
D.H., Grainger, S.2007. Rolling element gearing fault
diagnosis using Laplace-wavelet envelop power spectrum
EURASIP Journal on Advances in Signal Processing, Vol.
2007,articleid 73629, 14pages
[21]S.N.Sivanandan, S.Sumati, S.N.Deepa, Introduction to
neural network using Matlab 6.0, Mcgraw hill education
(India) private limited, 2006, ISSN:978-0-07-059112-7
[22] J. Rafieea,_, F. Arvania, A. Harifib, M.H. Sadeghic
(2007)Intelligent condition monitoring of a gearbox using
artificial neural network; Mechanical systems and signal
processing;21:1746-1754
[23]B. Samanta, K.R. Al-Balushi, Artificial neural network
based fault diagnostics of rolling element bearings using time-
domain features, Mechanical Systems and Signal Processing
17 (2) (2003) 317–328.
24] W. Bartelmus, R. Zimroz, H. Batra, Gearbox vibration
signal pre-processing and input values choice for neural
network training,Artificial Intelligence Methods, Gliwice,
Poland, 5–7 November, 2003.
[25] Semmlow J.L. 2004.Bio signal and biomedical image
processing Marcel Dekker, Inc.New York, USA, ISBN0-
8247-4803-4.
BIOGRAPHIES:
Mr. M. Lokesha received his B.E.
degree in Mechanical Engineering from
Mysore University, Mysore, India
in1989 and M.TECH. Degree in
Maintenance engineering from Mysore
University, Mysore, India in
1994.Presently, he is working as a
Senior Lecturer in the Department of Mechanical and
Industrial Engineering at Caledonian College of Engineering,
Muscat. He has been working for 22 years in engineering
institutions. His research focuses on vibration instrumentation
&measurement, condition monitoring of rotating machinery.
He is currently PhD research student at National Institute of
Technology, Durgapur, India.
Dr. Manik Chandra Majumdar is a
Professor in the Department of
Mechanical Engineering and Member,
Board of Governors of NIT Durgapur
India. He has a PhD from the Indian
Institute of Technology, Kharagpur,
India. He has guided many Ph.D.
scholars. His prime area of research is Tribology /Design
&Production
Dr. K. P. Ramachandran B.E,
M.Tech, PhD is currently working as
Associate Dean (Post Graduate Studies
& Research), Caledonian College of
Engineering, Muscat, Sultanate of
Oman. He has been working for more
than 25 years in engineering
institutions and as a consultant for many industries. He has
research interest in the vibration instrumentation
&measurement, analysis and control, condition monitoring of
rotating machinery. He has many publications to his credit and
has been conferred Sir C.V. Raman award for the best
technical paper published in the Journal of Vibration &
Acoustics (1997). He is on the editorial board and technical
reviewer for many international journals and conferences. He
has guided many PhD students in the area of condition
monitoring and maintenance management.
Dr. Khalid Fatihi Abdul-Raheem,
B.E., M.Tech from University of
Technology, Iraq and PhD from
Glasgow Caledonian University, UK
Presently he is working as a Associate
professor in the Department of
Mechanical Engineering at Sohar
University, Sohar, Oman. He has been
working for more than 22 years in engineering institutions and
many industries He has many publication sto his credit. He has
research interest in condition monitoring and signal analysis,

__________________________________________________________________________________________
artificial intelligence, automatic control system, mechanical
vibration analysis and control.

Fault detection and diagnosis ingears using wavelet

More Related Content

What's hot (17)

Viewers also liked (20)

Similar to Fault detection and diagnosis ingears using wavelet (20)

More from eSAT Publishing House (20)

Recently uploaded (20)

Fault detection and diagnosis ingears using wavelet