applications des réseaux de neurones pour la reconnaissance des
TRANSCRIPT
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Bearing monitoring:
from modelling to experiments:
feature selection for fault diagnosis
Marc THOMAS,
Professor in mechanical engineering
ETS, Montreal
1 Surveillance 8 International Conference - October 20-21, 2015
Roanne Institute of Technology, France
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Outline • Introduction (ETS, Dynamo)
• Bearing models
• Defect severity
• Time indicators of defects
– Statistic indicators
– Shock indicators
• Shock Filter
• Minimum Entropy Deconvolution
• Peak Hold Down Sampling (low speed operation)
• Envelop
• Empirical Mode Decomposition (EMD-EEMD)
• Teager Kaiser Energy Operator (TKEO)
• Cyclostationnarity
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Outline
• Frequency indicators
• Time (Scale)-Frequency indicators
– STFT
– Wavelet Paquet
• Application to electric current measurement
– Empirical Wavelet Transform (EWT)
• Complexity indicators
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L’École de Technologie Supérieure
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180 professors
360 staffs
6000 students
400 Ph.D. students
800 Masters
• 7 engineering programs (B.Ing.)
• 5 certificate programs
• 12 master programs (M. Sc. A.)
• 1 Ph. D. program
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Dynamo Laboratory
Structural Heath Monitoring
Fatigue
Surveillance and Diagnostic
Process dynamics
Robotized welding
Structural Dynamics
Machinery Dynamics
Robotized grinding
Multi physic modeling of manufacturing process
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Methodology for machinery
monitoring
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Introduction
• In order to better understand the dynamic behavior of
mechanical components such as bearings subjected to
defects, it may be necessary to develop dynamic models.
• These models (after experimental calibration) allows for
evaluating the sensitivity and efficiency of features for
detecting faults both in time and frequency domains, before
to apply them experimentally.
• Various experimental applications of signal processing
methods are described.
7 Thorsen, O. V., and M. Dalva. 1999. « Failure identification and analysis for high-voltage induction motors in the petrochemical
industry ». Industry Applications, IEEE Transactions vol. 35, no 4, p. 810-818
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TARGET
Develop a numerical simulator of bearing dynamics with localized defects to generate vibration responses according to all the functionning parameters .
Simulator
? ? ? ?
Bearing
parameters
Defect
parameters
working
Parameter s
Vibration
Responses
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Theoretical, Discrete and FE models Theoretical
models based on
assumptions about
expected results
Example:
Assumption that
defect produces
amplitude and
phase modulations
with harmonics
Discrete models based
on simplified physical
behavior
Example: bearing model
Finite Elements models
Example: Continuous
bearing model
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Outer
Ring
Inner
Ring
Fluid
Film
Fluid
Film
Ball
KOR KIR
KOF KIF
MOR M IR
M B
COF CIF
Discrete models of bearing in a Radial
Direction 3 D.O.F: Only
consider the
bearing
5 D.O.F.: Consider the housing,
bearing and shaft
20 D.O.F.: allows for
considering gyroscopic
effect (high speed
operations)
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Defect on
outer race
Defect on ball Defect on
inner race
Simulation of bearing defects
11 S. Sassi, B. Badri, M. Thomas, (2007), A Numerical Model to Predict Damaged Bearing Vibrations,
Journal of Vibration and Control. vol. 13 no. 11, 1603-1628.
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Loading Forces
Qi Qi
F
yi
a b
x z
y y
01
Nb
ii
QF
The equilibrium condition of the inner race
with the Nb rolling elements may be
written as follows
The bearing may be subjected to external forces with radial and axial
components yxFyFxFF rra
tan
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Load Distribution
t
ε2
ψcos11max
i
iQQ
mim When :
0Qi
Elsewhere :
2 Ym
Q i Q max
e is the load distribution factor.
which is function of the axial and radial displacement components
t is a constant that depends on the contact nature.
e tg
r
a .1.21
The load applied on any rolling element
located at angle measured from the
maximum load direction Qmax, is given by :
i
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The motion over the failed areas produces
impacts which result in shock pulses.
Impact Force During the Shock
Versus Defect Size-Ball Diameter Ratio
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
2
4
6
8
10
12
Defect Size / Ball Diameter
Static Eff
ort Magni
fication [
% ]
4
2
8
10
0
6
12
Defect Size / Ball Diameter
0.3 0.2 0.1 0.4 0.5 0.0
S
tati
c E
ffo
rt M
ag
nif
ica
tio
n
( %
)
V is the variation of speed before and after shock.
K is an impacting material coefficient
The strength of impact felt by the bearing components when the
ball is traversing a defect area depends on the relative speeds and
on the external load.
2
(1 )D SF F K V
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Exemples of constant Shock pulses
generated by a defect
( a ) on Outer Race, ( b ) on Inner Race
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22
0
100
200
300
400
500
Time ( s )
Fo
rce (
N )
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
0
500
1000
1500
2000
2500
Time ( s )
Fo
rce
( N
)
Time ( s )
F
orc
e
( N
)
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Geometric correction of the numerical
response
( a )
21
2
max
2
2
max
2 )(cos)(sin)(
RRR
Sensor
max
m :
principal
direction
O
Defective Ring ( b )
The model has been designed to generate a response according to a radial
line of maximum deformation (turning), whereas the response measured by
the sensor (fixed) is given according to a different radial line of measurement.
A correction must be added to the numerical response of the model to
correlate the numerical response with the response delivered by a fixed
sensor.
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ddef
2
max2
1
AN BdfS
QVKrandomδ
Effects of Random Perturbations
KAN is a constant,
V is the relative slip speed between the ball and the race,
Qmax is the maximum loading value (applied on the most loaded
ball),
S is the ball/race elliptic contact surface,
f (ddef / Bd ) is a weighting polynomial function.
As the relative motion between the rolling elements and
the races is composed of rolling and slipping, friction-
induced vibration must be added in the total computed
response.
Friction-induced vibration produces random type vibration.
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Effects of
Random Perturbations
Time ( s
)
( Total ) = ( impact ) + (random )
The relative movement between
elements = mixture of ROLLING and
SLIP
+
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Motor Radial Force
Axial Force
Damaged Bearing
Dummy
Bearing
Flexible
Coupling
Calibration with experimental testing The test rig is composed of a shaft supported by two bearings driven by a
motor. The forces comes from an inertial wheel and an axial force.
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Signals from defective rolling-element bearings available on site
http://csegroups.case.edu/bearingdatacenter/pages/apparatus-procedures
Test bench from Case western reserve
University: Bearing data center
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Comparison of time responses (simulated and measured) Damage Size = 1270 m.
[ Frequency Rotation = 11.6 Hz ; Loading Amplitude = 1242 N ; Loading Orientation = 22 degrees ]
83 ms 12 ms
Time ( s )
Measured signal
Time ( s )
Simulated Signal
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1xBPFO
2xBPFO
3xBPFO
Frequency ( Hz )
1xBPFO
2xBPFO
3xBPFO
Frequency ( Hz )
Measured
signal
Simulated
Signal
Comparison in Frequency Domain Damage Size = 1270 m on outer race
[ Frequency Rotation = 11.6 Hz ; Loading Amplitude = 1242 N ; Loading Orientation = 22
degrees ]
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Signal Analysis
Vibration Signal Analysis Diagnostic
Wavelet Transform
Wavelet Packet
Transform
Empirical Wavelet
R.M.S.
Peak level
Crest factor
Kurtosis
Envelop
Shock filter
MED
Peak Hold Down Sampling
EMD (EEMD)
TKEO
Cyclostationnarity
Time
domain Frequency
domain
Time-Frequency
domain
Spectrum analysis
Envelop
FRF
Short-Time
Fourier
Transform
Time-Scale
domain
Complexity
Apen
LPZ
etc.
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Time indicators of machinery
defects
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RMS
peak
a
aCF
RMSaSF
a
peakaIF
a
Scalar indicators Peak
Redressed Average
Root Mean Square
Crest Factor
Kurtosis Shape Factor
Impulse Factor
1
1 N
k
k
a aN
Peak to Peak
max minPP a a 2
peak
PPa
1
1 N
k
k
a aN
Average
2
1
1 N
STD k
k
a a aN
N4
k
k 1
2
2
1
1 (a a)N
Ku1 N
k
k
a aN
N3
k
k 1
32
2
1
1 (a a)N
Sk
1 N
k
k
a aN
K-Factor
*K Peak RMS
Skewness
kNk1peak asupa
or
Standard Deviation
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to analyze the sensitivity of fault
scalar indicators extracted from time
domain signals to bearing damage
manifested through an increase in
size and in the number of localized
defects.
Once calibrated, the aim of the simulator is :
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0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -10
-5
0
5
10
Time ( s )
A (
m/s
2)
0 0.0
5
0.
1
0.1
5
0.
2
0.2
5
0.
3
0.3
5
0.
4
0.4
5
0.
5
-60
-40
-20
0
20
40
60
Time
(s)
A (
m/s
2)
0 0.0
5
0.
1
0.1
5
0.
2
0.2
5
0.
3
0.3
5
0.
4
0.4
5
0.
5
-100
-50
0
50
100
Time ( s
)
A (
m/s
2)
b) small defect of 0.55 mm
c) defect of 1.52 mm
a) healthy bearing
Peak 5.1 CF 3.8 SF 1.2
RMS 1.4 KU 3 IF 4.6
Vib
ration A
mplit
ude
( m
/s2 )
Peak 26.6 CF 6.4 SF 1.4
RMS 4.3 KU 10.2 IF 9.3
Peak 75.7 CF 7.2 SF 1.6
RMS 10.4 KU 15.8 IF 11.5
Evolution of vibration responses with defect sizes
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0 0.5 1 1.5 2 2.5 3 0
50
100
150
200
250
300
350
400
450
500
Size Defect [ mm ]
Scala
r P
ara
mete
rs
RMS
Peak
Evolution of Scalar Parameters (Peak, RMS) according to the size of a defect on the Outer race
After calibration, the model allows for investigating the
sensitivity of features to damage size.
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Design of experiments: 5 speeds, 3 forces, 4
defects, 3 repetitions= 180 experiments
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Evolution of Scalar Parameters (Ku, CF, IF, SF) according to the size of a defect on the Outer race
0 0.5 1 1.5 2 2.5 3 0
2
4
6
8
10
12
14
16
18
Size Defect [ mm ]
Sc
ala
r P
ara
me
ters
Ku
C.F.
I.F.
S.F.
When the defect becomes
large, a decrease of all
features is observed
Ku and IF are indicators well
suited to detect a fault in the first
steps of degradation.
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Comparison between Kurtosis values, for defects located on Outer and Inner Races
• When the defect is affecting the inner race, numerical simulation shows that the sensitivity of Kurtosis is less pronounced than when the defect is located on the outer race.
0 0.5 1 1.5 2 2.5 32
4
6
8
10
12
14
16
18
Size Defect [ mm ]
Sca
lar
Par
amet
ers
Kurt ( Outer Race )
Kurt ( Inner Race )
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Effect of rotor speed
0
5
10
15
20
25
600 650 700 750 800 850 900 950 1000
Rpm
Scala
r am
plitu
de
Ku
IF
CF
SF
Numerical simulations show that the features are less sensitive at higher speeds
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Bearing affected by multiple defects
• The numerical simulations show that all features decrease with the number of defects.
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6
Number of Defects on OR
Scala
r In
dic
ato
rs
Kurtosis
C.F.
I.F.
S.F.
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Development of a new indicator based on Ku and RMS,
which always increases with the defect size .
It needs a RMS0 reference when healthy ( zone 1).
1.0
2.0
3.0
4.0
5.0
0 0.5 1 1.5 2 2.5 3
Defect Diameter [ mm ]
TA
LA
F
Null
slope
Zone
I
Zone
II
Zone
III
Zone
IV
TALAF
0
logRMS
RMSKuTALAF
Sassi S., Badri B. and Thomas M., 2008. Tracking surface degradation of ball bearings by means of new time domain scalar
descriptors, Internat. journal of COMADEM, ISSN1363-7681, 11 (3), 36-45
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Detection of defect severity
There is a double impact: one at entry and one at the exit of the defect.
The time between both allows for detecting the defect size.
Ref: Singh S., Explicit dynamic finite element modelling of defective rolling
element bearing, 2014, U. Adelaide ( Au)
Experimental measurement
Defect size
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The shock filters
• The Shock filter
• Minimum Entropy Deconvolution (MED)
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TARGET of Shock Filter
Shock Filter
? ? ?
Random
vibration
(slip, friction)
Shocks
(defects) Harmonic
vibration
(unbalance,
misalignment)
Filtered
Vibration
Response
Time
Extract the shock response from the other sources of perturbation
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The Shock filter At each sample (i) of the time signal, the Kurtosis of a window C centered on i
(i-n; i+n) is computed and compared to the ones calculated on windows located
to the left L (i-3n; i-n) and right R (i+n; i+3n) of the current sample (i).
Once the Kurtosis has
been evaluated for each of
the three windows, a
selection is conducted:
•If the energy of the central
window is greater than the
two others into the left and
right window, we declare
the presence of a shock
and the peak amplitude of
the signal at position (i) is
assigned to the shock
extractor.
•Otherwise, there is no
shock and the shock
extractor takes a null value.
Badri B., Thomas M. and Sassi S., July 2012. The envelop Shock detector: a new method to detect impulsive signals, International
journal of COMADEM.13 p.
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Shock Detector (SD)
Introduction de la problématique
L’usinage et ses contraintes
L’usinage à haute vitesse, Particularités
État de l’art
Présentation du Broutement
Modélisation des broches
Monitoring des CNC
Capteurs
Suivi de l’usinage
Traitement de signal
Diagnostic intelligent
Objectifs
Modélisation
Simulation
Stabilité de l’usinage
Originalités
Condition de fonctionnement
Rotor et Palier
Effet gyroscopique
Transmissibilité
Effort de coupe
SIPVICORP
Quantification des VFD
Détection du broutement
Analyse Expérimentale
Régime permanent
Régime transitoire
Mesure en coupe
SipviCorp
Présentation des Articles
ESD
Étude du comportement des roulements dans les
Rotors à Haute vitesse
Spindle Bearings Simulator
Synthése et conclusion
Modélisation
Surveillance
Comportement à vide
Comportement en coupe
Perspective de développement.
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40 0 0.1 0.2 0.3 0.4 0.5
-60
-40
-20
0
20
40
60
Réponse temporelle
Temps (s)
Am
plitu
de
SNR (Signal noise Ratio) = 92.398 %Nb. Choc/s = 78.5062
The Shock Filter
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Evaluation of defect severity with SD signals Defect =0,18mm Defect =0,56mm SNR 82% SNR 63%
Comparing the RMS level of the filtered signal with the original signal gives an indication on the severity of damage.
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Detection of multiple defects
2 shocks at 180o
Bearing SKF 1210 ETK9 operating at 720 RPM
with 2 defects on outer race:1mm @ 0deg and 0,8 mm @ 180deg
Original response
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Original signal
SD Filtered
signal
1st shock signal
2nd shock signal
Identification of shock sources
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Detection of defects by neural network
44
Three layers
5 Neurons into the hidden layer
Activation with log-Sigmoïde
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Identification of damage severity by neural network
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• A minimum entropy is aimed to reduce the disorder.
• Minimum Entropy Deconvolution: The method allows for highlighting
the shocks present into the original signal
Maximizing the Kurtosis with the Minimum
Entropy Deconvolution ( MED)
June-Yule Lee et A.K. Nandi, Extraction of impacting signals using blind deconvolution. Journal of Sound and
Vibration 1999. 232(5): p. 945-962.
Endo H., Randall R.B. (2007), Application of a minimum entropy deconvolution filter to enhance Autoregressive
model based gear tooth fault detection technique, Mechanical Systems and Signal processing, 21, 906,919.
Tomasz B. Nader S. (2012), Fault Detection Enhancement in Rolling Element Bearings Using the Minimum
Entropy Deconvolution, Archives of Acoustics, Vol 37, No. 2, pp. 131-141.
We must optimize the filter in order to maximize
the Kurtosis:
Maximise The
Kurtosis of x(n)
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When using MED, the filter size and number of
iterations must be selected
In this example, N=128
with 20 itérations was
selected
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Tian Ran Lin, Eric Kim, Andy C.C. Tan. (2013) A practical signal processing approach for condition
monitoring of low speed machinery using Peak Hold Down Sample algorithm, MSSP 36, 256-270.
0 0.5 1 1.5 2
x 105
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
Samples
Accele
rati
on
(m
m/s
²)
Application to low speed operations
• Peak Hold Down Sampling
help to reduce the length of signal by segmentation
In low speed operations, the periods are very long and the length of signals very big.
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Bearing faults diagnosis using PHDS and MED when operating at low
speeds
• The method first uses MED to maximize the Kurtosis, and then uses the
PHDS to reduce the signal length. The enveloppe is then applied.
After MED
After PHDS Melki O., Kedadouche M., Badri B. and Thomas M. October 2014. Monitoring bearing operating at very low speeds. Proceedings of the
32e CMVA, Montreal, 14 p
Using directly PHDS is too much noisy. The signal needs to be previously unnoised.
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20 40 60 80 100 120 1400
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5x 10
-3
Frequency (Hz)
Acce
lera
tio
n (
g)
BPFO = 7.7 Hz
20 40 60 80 100 120 1400
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5x 10
-3
Frequency (Hz)
Acc
eler
atio
n (
g) BPFO = 7.5 Hz
20 40 60 80 100 120 1400
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5x 10
-3
X: 12.3
Y: 0.0009106
Frequency (Hz)
Acce
lera
tio
n (
g)
BPFO=12.3Hz
20 40 60 80 100 120 1400
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5x 10
-3
Frequency (Hz)
Acc
eler
atio
n (g
)BPFO = 12.3 Hz
Experimental applications on test bench
Defect size 50 microns
A - PHDS B - MED +PHDS
B - MED +PHDS A - PHDS
60 RPM
100 RPM
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Huang, N. E., Shen, Z., and Long, S. R., The Empirical Mode Decomposition and Hilbert Spectrum for Nonlinear and Non-Stationary Time
Series , Proc. R. Soc. London, Ser. (1998)
51
EMD (Empirical Mode Decomposition)
SIGNAL
UPPER Envelop:
U(t)
Lower
Envelop:(L(t)
Mean:
m(t)
EMD
The empirical mode decomposition
assumes that any real signal s(t) can
be divided into “a local average” m(t)
and “a strongly oscillating component”
h1(t) as follows:
1 i
i
s t h t m t h t r t
The mean of the upper and lower envelopes
is defined as:
( ) ( )
2
U t L tm t
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EMD Method • The mean is subtracted from the signal, leading to the first
component, until it is the first Intrinsic Mode Function(IMF1):
IMF1 contains the highest frequency band.
• An IMF is a function respecting the following conditions:
The number of extrema and the number of zero crossings are either equal or
differ at most by 1;
The value of the moving average between the superior envelope (defined by
local maxima) and the inferior envelope (defined by local minima) is zero.
• Iterative steps: the same procedure is applied by removing IMF1 to
the signal, etc..
52
1 1
11 1 11
1 1 1 1k k k
d t s t m t
d t d t m t
IMF d t d t m t
1 1
2 1 2
1n n n
r t s t IMF t
r t r t IMF t
r t r t IMF t
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IMFs Spectre of IMFs: from highest to lowest
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54
Example: Simulated Signal of bearing defect
Resonance with modulation
frequencies at IMF2
Misalignment detected at IMF 7
The simulated signal (assumptions about expected results) contains:
• excitation at the resonance (2000 Hz) modulated by BPFO +
• unbalance (70 Hz)+
• misalignment (140 Hz)+
• noise (50%)
Unbalance detected at IMF8
Noise at IMF1
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55
Mode mixing problem with EMD
0.5cos(40 ) 1
cos 8 2
6 3
x t t
x t t
x t t
1 2 3x t x t x t x t
Ensemble EMD
Example:
The EMD decomposition may give erroneous results
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56
Usual EEMD
• The noise level to add
is unknown
• Usually 20% of the
RMS signal is arbitrary
selected
A noise must be added to the signal
0 200 400 600 800 1000 1200 1400 1600 1800 2000-0.2
0
0.2
0 200 400 600 800 1000 1200 1400 1600 1800 2000-0.2
0
0.2
0 200 400 600 800 1000 1200 1400 1600 1800 2000-0.1
0
0.1
0 200 400 600 800 1000 1200 1400 1600 1800 2000-0.1
0
0.1
0 200 400 600 800 1000 1200 1400 1600 1800 2000-0.5
0
0.5
0 200 400 600 800 1000 1200 1400 1600 1800 2000-0.5
0
0.5
0 200 400 600 800 1000 1200 1400 1600 1800 2000-1
0
1
0 200 400 600 800 1000 1200 1400 1600 1800 20000
5
0 200 400 600 800 1000 1200 1400 1600 1800 20000
0.5
1
Sample
IMF 1
IMF 2
IMF 3
IMF 4
IMF 5
IMF 6
IMF 7
IMF 8
IMF 9
Wu Z H and Huang N E. Ensemble empirical mode decomposition: a noise assisted data analysis method Adv. Adapt. Data Anal
(2009). 1 1–41
This method takes time
(>100 averages)
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57
Optimum EEMD
1 11
2 2
1 11 1
( ( ) ( )( ( ) ( )( )
( ( ) ( ) ( ( ) ( )
k k k k
N
N
i
k
N
k k ki i
IMF i IMF IMF i IMFr k
IMF i IMF IMF i IMF
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Co
effi
cien
t o
f C
orr
elat
ion
(A)
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
2
3
4
5
7
9
1011
Level [L]
Nu
mb
er o
f IM
F (B)
Correlation ( IMF1 & IMF2 )
Correlation ( IMF2 & IMF3 )
Correlation ( IMF3 & IMF4 )
Correlation ( IMF4 & IMF5 )
L=6E-5 0 200 400 600 800 1000 1200 1400 1600 1800 2000-1
-0.5
0
0.5
1IMF 1
0 200 400 600 800 1000 1200 1400 1600 1800 20000
2
4
6
Sample
IMF 3
0 200 400 600 800 1000 1200 1400 1600 1800 2000-2
-1
0
1
2IMF 2
The correlation between each subsequent IMF is computed with
the noise level in order to find the optimal noise level.
M. Kedadouche, M. Thomas and A. Tahan. 2015. A comparative study between Empirical wavelet transforms (EWT) and Empirical
Mode Decomposition methods: Application to bearing defects , submitted to MSSP
The IMF (3) is identified in this case
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Complementary Ensemble Empirical Mode
decomposition (CEEMD)
58
Yeh J. R., Shieh J. S. et Huang N. E., Complementary Ensemble Empirical Mode
Decomposition: A novel noise enhanced data analysis method, Advances in Adaptive
Data Analysis, 2 (2) (2010) 135-156.
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59
Teager Kaiser Energy Operator (TKEO)
TKEO extracts the amplitude modulation and the frequency
modulation from the signal.
TKEO has a great time resolution since the operator only
needs three samples into the signal to be computed.
TKEO is very easy to implement efficiently.
Maragos, P., J. F. Kaiser et T. F. Quatieri. 1993. « On amplitude and frequency demodulation using energy operators ». Signal
Processing, IEEE Transactions on, vol. 41, no 4, p. 1532-1550.
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Numerical application of TKEO
60
Fm=BPFO f1 f2 A B
100 Hz 1800 Hz 4000 Hz 0,1 0,8 Bad detection of BPFO
• The signal needs to be mono
component and must be previously
filtered.
• TKEO is very sensitive to noise
and the signal needs to be
previously unnoised
Sheen, Yuh-Tay. 2004. « A complex filter for vibration signal demodulation in bearing defect diagnosis ». Journal of Sound and
Vibration, vol. 276, no 1–2, p. 105-119.
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61
Monitoring Machines by Using a Hybrid Method
Combining MED, EMD, and TKEO
MED EMD
IMF
1
IMF
2
IMF
3
IMF 4 IMF
5
IMF
6
IMF 7 IMF
8
IMF 9 IMF
10
IMF
11
0.86 0.53 0.16 0.22 0.17 0.12 0.07 0.06 0.04 0.03 0.01
M. Kedadouche, M. Thomas and A. Tahan, 21 april 2014. Monitoring bearing defects by using a method combining EMD, MED and
TKEO. Advances in Acoustics and Vibration., Vol 2014, ID 502080,10 p.
Multi-components and
noisy signal Denoising the signal
Selection of the most correlated IMF to the signal
TKEO of
IMF1
Correlation
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62
D0 D1 D2
Experiments on test bench of bearing fault detection by mixing
MED, EMD, and TKEO from acoustic emission
Bearing W
Healthy 0
Defect 1 50 µm
Defect 2 100 µm
30
0 rp
m
60
0 rp
m
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Envelope-Derivative Operator (EDO)
• The EDO is given by:
• For a discrete signal x(n), the EDO is defined in
discrete format by
where h(n) is the discrete Hilbert transform and
defined as h(n) = H[x(n)].
63
222)()()()()( nxHtxnxjHtxtx
)1()1()1()1(4
1)( 2222 nhnhnxnxtx
)1()1()1()1(2
1 nhnhnxnx
(6)
J.M.O. Toole, A. Temko and N. Stevenson, Assessing instantaneous energy in the EEG: a non-negative, frequency-weighted energy
operator, IEEE conference proceedings, (2014) 3288–3291.
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4 experiments of EDO: No fault, 56, 104 and 152 microns
64
Amplitude at BPFO: 156 Hz
No fault 56 microns
104 microns 152 microns
Y. IMAOUCHEN, M. KEDADOUCHE, R. ALKAMA and M. THOMAS, The Envelope-Derivative Operator for Bearing Fault Detection,
Surveillance 8
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65
Cyclostationnarity:
Computation of angular statistics
1. Data acquisition ( pre-recorded vibration signals)
2. Re sampling in the angular domain
3. Computation of the angular statistics
+
+
Périod 1 réalization
Angular statistics= angular mean, variance, power, Kurtosis 4) Angular analysis (FFT, Angle-frequency, etc.)
Lamraoui M., Thomas M., El Badaoui M. et Zaghbani I., Juin 2010. Le kurtosis angulaire comme outil de diagnostic, Vibration, Choc
et bruit (VCB2010), Lyon, France, article AC 29, 21 p.
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66
Applying cyclostationnarity to machining
4 cycles of 1 block
Angular average
Angular Variance
4 peaks corresponding to teeth
Signal (blue) with its mean (red) and angular variance (green)
Time signal
Blocks of cycles after synchronization,
(10 cycles by block)
10 Cycles
Lamraoui M., Thomas M., El Badaoui M. et Zaghbani I., Juin 2010. Le kurtosis angulaire comme outil de diagnostic, Vibration, Choc
et bruit (VCB2010), Lyon, France, article AC 29, 21 p.
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67
The Angular Kurtosis decreases when chatter
or tool wear
Healthy tool Chatter In resonance After tool wear
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68
Effect of tool wear on the angular power
Angle between two teeth
Angle-frequency representation
Measurement of rake angle
Test 1: before wear Test 4: after wear
For an important wear, a strong increase of
the angular power amplitude is detected
Angle [°] Angle [°]
The 4 peaks are
corresponding
to the passage
of every tooth.
Lamraoui M., Thomas M., El Badaoui M. et Zaghbani I., Juin 2010. Le kurtosis angulaire comme outil de diagnostic, Vibration, Choc
et bruit (VCB2010), Lyon, France, article AC 29, 21 p.
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• Fourier analysis breaks down a signal into constituent sinusoids of
different frequencies.
Frequency Analysis: FFT
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Bearing frequencies if both
races are rotating
70
cos cos11 1
2
cos
d di o
d d
B o
B i
d d
i
B BFTF
P P
BPFO N FTF
BPFI N FTF
P BBSF FTF
Bd
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0 10 20 30 40 50 60 70 80 90 100 110 120
Fréquence
0.05
0.1
0.15
0.2
0.25
0.3 Velocity in/sec
0
Residual life greater than 10%
No significant sign of degradation
Bandwidth where must appear the first signs de degradation
Bandwidth
for bearing
frequencies
1 x RPM
2 x RPM
3 x RPM
First step of bearing
degradation
71
Berry. 1991. « How to track rolling bearing health with vibration signature analysis ». Sound and Vibration, p. 24-35
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0 10 20 30 40 50 60 70 80 90 100 110 120
Fréquence Kcpm
0
0.05
0.1
0.15
0.2
0.25
0.3
1 x RPM
2 x RPM
3 x RPM Modulation à 1 x RPM
Natural frequency
Second step of bearing
degradation Vélocité en po/sec
72
Bandwidth where must appear the first signs de
degradation
Residual life greater than 5%
Small noise
Increase in acceleration amplitude
Needs analysis in log scale
Berry. 1991. « How to track rolling bearing health with vibration signature analysis ». Sound and Vibration, p. 24-35
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0 10 20 30 40 50 60 70 80 90 100 110 120
Fréquence Kcpm
0
0.05
0.1
0.15
0.2
0.25
0.3
Vélocité en po/sec
1 x RPM
Natural frequency with bearing
frequency modulationst
BPFO BPFI
2 x BPFO 2 x BPFI
Third step of bearing degradation
73
Bearing frequencies
with harmonics and
modulations
Residual life greater than 1%
Noise increases
Temperature increases
Acceleration amplitude increases
Berry. 1991. « How to track rolling bearing health with vibration signature analysis ». Sound and Vibration, p. 24-35
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Severity based on amplitude at the
bearing frequency
BPFO or BPFI or
2BSF
f0
f ( Hz )
V ( mm/s )
74
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Frequency analysis (FFT) from numerical bearing model
75
1xBPFO
2xBPFO
3xBPFO
Frequency ( Hz )
Bearing defect of 1.2 mm on outer race
Harmonics of BPFO: detection at the third stage of
degradation Modulation
frequencies
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Features in frequency domain
0
0,5
1
1,5
2
2,5
3
0,00 200,00 400,00 600,00 800,00 1000,00 1200,00 1400,00 1600,00
Am
plitu
de
Defect size ( microns)
Amplitude around BPFO and modulations
BPFO
BPFOBEAT
The features in the frequency domain
consider the amplitude at the bearing
frequencies and the harmonics
(n*BPFO) including the modulations (f0)
BPFO+/- 1.1 f0
f0
Numerical simulation
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Design of experiments: 5 speeds, 3 charges, 4
defects, 3 repetitions= 180 experiments
77
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0 10 20 30 40 50 60 70 80 90 100 110 120
Fréquence Kcpm
0
0.05
0.1
0.15
0.2
0.25
0.3
Vélocité po/sec
Bearing
frequencies with
harmonicss
Random like vibrations in high
frequency domain
1 x RPM
BPFO
BPFI
Last stage of bearing degradation
78
Residual life lower than 0.2%
High Noise
High Temperature
Velocity amplitude increases
Acceleration amplitude decreases
Berry. 1991. « How to track rolling bearing health with vibration signature analysis ». Sound and Vibration, p. 24-35
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Time-frequency analysis
79
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STFT from numerical bearing model
80
Time
Fre
quency
0 0.1 0.2 0.3 0.4 0.5
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
50
100
150
200
250
300
350
400
-2.5 -2 -1.5 -1 -0.5 0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0 0.1 0.2 0.3 0.4 0.5
-50
0
50
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81
STFT Measurement (after denoising):
high vibration observed at 23 000 rpm
during transients (up, stable and down
speed) due to coincidence between:
harmonics of spindle bearing and
natural frequencies
Computation of variation of
natural frequencies with speed
due to gyroscopic effect.
Badri B., M. Thomas; S. Sassi; I. Zaghbani; V. Songméné, Juin 2010, Étude du comportement des roulements dans les rotors tournant
à haute vitesse, Revue Int. sur l’Ingénierie des Risques Industriels, 3(1), 1-16
Increase and decrease of speed up to 30 000 rpm on machining center
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82
Application in machining: Cyclostationnarity and Angle-
Frequency of the residual signal
The peaks corresponding to the four teeth are very well defined when there is no
wear.
When the wear becomes important, the spikes of the angular Kurtosis disappeared
and it is less easy to distinguish the frequencies of the residual signal.
The wear involves a decrease of impulses, and thus a flattening of angular Kurtosis.
Low wear Advanced wear
Lamraoui M., Thomas M., El Badaoui M. et Zaghbani I., Juin 2010. Le kurtosis angulaire comme outil de diagnostic, Vibration, Choc
et bruit (VCB2010), Lyon, France, article AC 29, 21 p.
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Wavelet decomposition
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Wavelet Packet Decomposition
Example: Three-level Wavelet Packet
Decomposition tree
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WPD
S(0,0)
0-24kHz
S(1,0)
0 - 12kHz
S(1,1)
12 - 24kHz
S(2,0)
0 - 6kHz
S(2,1)
6 - 12kHz
S(2,2)
12- 18kHz
S(2,3)
18 - 24kHz
S(3,0)
0-3kHz
S(3,1)
3-6kHz
S(3,2)
6-9kHz
S(3,3)
9-12kHz
S(3,4)
12-
15kHz
S(3,5)
15-18kHz
S(3,6)
18-21kHz
S(3,7)
21-24kHz
Wavelet Packet Decomposition
Niv
J=0
Niv
J=1
Niv
J=2
Niv
J=3
Fe/2=(48/2)kHz
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Comparison between WPD and HT+WPD
Y. Imaouchen, R. Alkama and M. Thomas. October 2014. Bearing Fault Detection Using Motor Current Signal Analysis
Based on Wavelet Packet Decomposition and Hilbert Envelope. 2e AVE, Blois (Fr)
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Acoustic
Emission
Sampling Frequency
48kHz Vibration Current probe
Sensor (Hall effect)
Materiel and Test Bench: application to electric current measurement
Bearing SKF : 1210 EKTN9
Experimental Test Bench
Data acquisition system
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Bearing defect
• The bearing is SKF1210.
• Two experiments:
– healthy
– 1.06 mm on the outer race
• The electric signal (Canada) is 30 Hz (120 Hz/4 pôles).
• At 900 RPM (15 Hz), BPFO is 116.6 Hz.
• The supply voltage frequency is modulated by the
bearing defect .
• The envelope of the current signal contains thus
the fault-related frequencies.
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Conventional spectral analysis
• The healthy bearing is in blue
• The defective bearing is in red
• We only notice an amplitude increase at each frequency: difficulty for diagnosing a defect.
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fa fr Modulation effect on stator current Related nodes
|fa-BPFO| = 86.6 Hz (11 – 04) : [82.03-93.75Hz]
30Hz 15Hz |fa+BPFO| = 146.6 Hz (11 – 10) : [140.6-152.3Hz]
|fa-2*BPFO| = 203.26 Hz (11 – 25) : [199.2-210.9Hz]
|fa+2*BPFO| = 263.26 Hz (11 – 29) : [257.8-269.5Hz]
The bearing frequencies into the current signal
may be identified by :
Bearing frequencies into the current signal
.fault BPFOmff a
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Energy Comparison
Condition
Frequency range
Node (11 – 5)
(70.31-82.03Hz)
Node (11 – 4)
(82.03-93.75Hz)
Node(11 – 12)
(93.75-105.46Hz)
Healthy 0.47 0.22 2.17
outer race
defect 0.9 5.16 2.38
ENERGY COMPARISON AROUND 86.6HZ
Condition
Frequency range Node (11 – 14)
(128.9-140.6Hz)
Node (11 – 10)
(140.6-152.3Hz)
Node(11 –11 )
(152.3-164.1Hz)
Healthy 0.023 0.016 0.17 outer race
defect 0.23 0.84 0.28
ENERGY COMPARISON AROUND 146.6HZ
The energy is compared around the defect frequencies for the
healthy and the defective bearing.
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Spectrum Comparison between WPD and HT+WPD
WPD applied on the node containing 86,6 Hz
HT+ WPD applied on the node containing 86,6 Hz
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Spectrum Comparison between WPD and HT+WPD
WPD applied on the node containing 146,6 Hz
HT+ WPD applied on the node containing 146,6 Hz
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94
The Empirical Wavelet Transform
1 1
1cos 1
2 2
1 1
0
n
n
n n
n n
if w w
w ww w
if w w w
otherwise
Scaling function: low pass Filter
1
1
1
1 1
1 1 1
11
2 2
1 1
1 1
2 2
1 1
0
ˆ
n n
n
n
n n
n
n
n
n n
if w w w
cos w ww
if w w ww
sin w ww
if w w w
otherwise
Wavelete function: band pass filter
The filter supports are defined
accordingle the frequential content
Spectral segmentation
Jérôme Gilles, Empirical Wavelet Transform, IEEE transactions on signal processing, vol. 61, no. 16, august 15, 2013
Adaptative Filter
The main idea of EWT is to extract different modes by designing appropriate
wavelet filter banks adapted to the signal.
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95
Numerical simulation of EWT
0 200 400 600 800 1000 1200 1400 1600 1800 2000-1
-0.5
0
0.5
1IMF 1
0 200 400 600 800 1000 1200 1400 1600 1800 2000-2
-1
0
1
2IMF 2
0 200 400 600 800 1000 1200 1400 1600 1800 20000
2
4
6
Sample
IMF 3
0 200 400 600 800 1000 1200 1400 1600 1800 2000-1
0
1
2
3
4
5
6
7
8
0 10 20 30 40 50 60 70 80 90 1000
1000
2000
3000
4000
5000
6000
7000
X: 20
Y: 509.3
Frequency (Hz)
X: 4
Y: 1109
1 2 3x t x t x t x t
Spectral segmentation
for selecting the support
filters
Construction of filter banks
, , . ˆ )ˆ (x n nW n t x t x w w
1 10, , . )ˆˆ (xW t x t x w w
The detail coefficients are
The approximation coefficients are
1
1
0, ˆˆ ˆ ˆ( , )N
x x n
n
x t W w w W n w w
The signal is given by:
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96
Empirical Wavelet Transforms : application to bearing defect
0 500 1000 1500 2000 2500 3000 3500 4000-3
-2
-1
0
1
2
3
Sample
0 50 100 150 200-2
-1
0
1
2
3
Sample0 1000 2000 3000 4000 5000 6000
0
10
20
30
40
50
Frequency (Hz)
FFTResonance frequency
0 1000 2000 3000 4000-1
0
1
0 1000 2000 3000 4000 5000 60000
0.1
0.2
0 1000 2000 3000 4000-1
0
1
0 1000 2000 3000 4000 5000 60000
0.1
0.2
0 1000 2000 3000 4000-1
0
1
0 1000 2000 3000 4000 5000 60000
0.1
0.2
0 1000 2000 3000 4000-1
0
1
Sample 0 50 100 150 200
0
0.1
0.2
Frequency (Hz)
2*FrFr
Third frequency resonance
Second frequency resonance
First frequency resonance
IMF 4
IMF 3
IMF 2
IMF 1
(A) (B)
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97
Experimental application of EWT
0 0.5 1 1.5 2-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time (sec)
Am
plit
ud
e (V
)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 104
-0.2
0
0.2
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 104
-0.2
0
0.2
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 104
-0.1
0
0.1
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 104
-0.2
0
0.2
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 104
-0.2
0
0.2
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 104
-0.02
0
0.02
Sample
IMF 1
IMF 2
IMF 3
IMF 4
IMF 5
IMF 6
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 104
-0.2
0
0.2
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 104
-0.2
0
0.2
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 104
-0.2
0
0.2
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 104
-0.2
0
0.2
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 104
-0.2
0
0.2
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 104
-0.2
0
0.2
Sample
IMF 1
IMF 2
IMF 3
IMF 4
IMF 5
IMF 6
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 104
-0.2
0
0.2
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 104
-0.2
0
0.2
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 104
-0.2
0
0.2
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 104
-0.2
0
0.2
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 104
-0.2
0
0.2
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 104
-0.2
0
0.2
Sample
IMF 2
IMF 3
IMF 4
IMF 5
IMF 6
IMF 1
0 0.5 1 1.5 2-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time (sec)
Am
plitu
de (
V)
0 0.5 1 1.5 2-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time (sec)
Am
plitu
de (
V)
Healthy bearing
Defect 50µm
Defect 100µm
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98
Empirical Wavelet Transforms: Index selection,
( ) ( )_
( ) ( )
i damaged i Healthy
damaged Healthy
kurtosis IMF kurtosis IMFindex selection
kurtosis x kurtosis x
Decision
<1 The is not selected
=1 The difference between the distribution of amplitude of the both
IMF (healthy & damaged) is the same as the raw signal (healthy
& damaged)
>1 The IMF is more impulsive than the raw signal. It is selected
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99
Empirical Wavelet Transforms, IMF > 1
0 500 1000 15000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
Frequency (Hz)
Am
plitu
de (
V)
BPFO
0 500 1000 15000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
Frequency (Hz)
Am
plitu
de (
V)
BPFO
Index selection greater
than 1
D1=50 µm -0,68 3,77 1,47 1,27 1,17 0,36
D2=100 µm -1,23 4,13 1,35 0,85 0,33 0,31
1IMF2IMF3IMF4IMF5IMF6IMF0 500 1000 1500
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
Frequency (Hz)
Ampl
itude
(V)
0 20 40 60 80 1000
0.002
0.004
0.006
0.008
0.01
Frequency Rotaion of the shaft and its harmonics
ZOOM
D1 D2
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100
Improvement: The selection will be easier if the signal is
monocomponent
Kedadouche, M., Thomas, M., Tahan, A. (2014) « An effective method based on empirical mode decomposition and empirical
wavelet for extracting bearing defect». 4th International Conference on Condition Monitoring of Machinery in Non-Stationary
Operations (CMMNO), December 15-16, Lyon, France.
1i i i iCMF C IMF IMF
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Lempel-Ziz Complexity
S=0 Q_Buff=0 SQ_Buff=00 SQπ_Buff=0 SQπ _Buff contain Q_buff
c(n)=c(n)+1
S=0
i=1
i=2 Q_Buff=01 SQ_Buff=001 SQπ _Buff=00 SQπ _Buff doesn’t contain
Q_buff
i=3 S=001 Q_Buff=1 SQ_Buff=0011 SQπ _Buff=001 SQπ _Buff contain Q_buff
S=001 Q_Buff=11 SQ_Buf=00111 SQπ _Buff=0011 SQπ _Buff contain Q_buff i=4
.
.
N
New subsequence : 0◊01◊1
0◊01
0◊01◊11
0◊01◊111 Ruqiang Yan and Robert X. Gao,Complexity as a Measure for Machine Health Evaluation, IEEE transactions on instrumentation
and measurement, vol. 53, no. 4, august 2004
if x(t) < mean,
x(t)=0
otherwise= 1
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Complexity :Approximate entropy (ApEn)
Complexity ApEn represents a
quantification of regularity in
sequences and time series data.
Complexity increases with the noise
1, 0
0, 0
xx
x
r=k*standard deviation of the x(t)
Yan, R. and R. X. Gao. 2007. « Approximate Entropy as a diagnostic
tool for machine health monitoring ». Mechanical Systems and
Signal Processing, vol. 21, no 2, p. 824-839.
It is an effective tool to distinguish between
the random and the cyclic shocks since
ApEn of noise is high.
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103
Index for defect severity
4
21
4
1
* ( ) *
N
i
i
x xN
INDEX Kurtosis Energy x f ApEnRMS
M. Kedadouche, M. Thomas and A. Tahan. 2015. A comparative study between Empirical wavelet transforms (EWT) and Empirical
Mode Decomposition methods: Application to bearing defects , submitted to MSSP
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104
Early detection with EMD+EWT+Index:
experiments of acoustic emission on bearing test bench
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-1
-0.5
0
0.5
1
Time (Sec)
Am
plitu
de (
V)
Frequency (HZ)
Com
bine
d IM
F
0 0.5 1 1.5 2
x 104
1
2
3
4
5
100 200 300 400 500 600 700 800 900 1000
0.5
1
1.5
2
2.5
3
3.5
4
Frequency (Hz)
Am
plitu
de (
mV
)
BPFO=36,62 Hz
Velocity: 300 rpm
BPFO: 36.6 Hz
0 1 2 3 4 5 6 7 8 9
x 104
-0.2
0
0.2
C 1
0 1 2 3 4 5 6 7 8 9
x 104
-0.2
0
0.2
C 2
0 1 2 3 4 5 6 7 8 9
x 104
-0.2
0
0.2
C 3
0 1 2 3 4 5 6 7 8 9
x 104
-0.2
0
0.2
C 4
0 1 2 3 4 5 6 7 8 9
x 104
-0.2
0
0.2
Sample
C 5
0 0.5 1 1.5 2
x 104
0
0.51
0 0.5 1 1.5 2
x 104
00.5
1
0 0.5 1 1.5 2
x 104
0
0.51
0 0.5 1 1.5 2
x 104
0
0.51
0 0.5 1 1.5 2
x 104
00.5
1
Frequency (Hz)
C 1
C 2
C 3
C 4
C 5
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Thank you for your attention
You do things right because you have experience
You have experience because you did things wrong
105