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A Machine Learning Approach toMulticomponent Fault Diagnosis of Rotating
Machines Using Sound and Vibration Signals
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Objective
Multicomponent fault diagnosis of rotatingmachines was modeled as a machine learning
problem and to develop a systematic approach to
identify the best feature-classifier combination for
automated fault diagnosis.
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ontents
Introduction
Machine learning
Literature survey
Methodology
Experimental Study
Fault Diagnosis using Statistical features
Fault Diagnosis using avelet features
!onclusion
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!ntroduction""#$%
Rotating Machines
"umps# turbines# compressors# fans# gear boxes# etc$
%otating machine components -
Shafts# rotors# bearings# gears# etc$
!ondition based maintenance -
prevent brea& down# increase productivity and reducemaintenance cost$
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!ntroduction""#&%
Fault Diagnosis
'he machine condition can be analy(ed in detail to indicate
the most li&ely cause of the problem$
'echni)ues*
ear debris +nalysis
+coustic emission
,ibration analysis
Sound signal# etc$
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!ntroduction""#'%
Vibration and Sound Signal Anal(sis
'ime domain analysis
Fre)uency domain analysis
rder analysis
'ime-Fre)uency analysis avelet analysis# etc$
.$ Alternate approach?
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Fre)uenc( domain Anal(sis
'he /FF'/ of the time waveform produces the spectrum
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3/12/16
mm/s
mm/s
8
Order Anal(sis
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Machine learning"*#$%
0oth +Learning, 1 +Labeling, Subse)uently
- Learning to Label
Learning? Labeling?
Identifying the b2ect as amember of a class to which it
belongs
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Machine Learning "*#&%
Feature extraction -
Statistical features#
3istogram features#
avelet features etc$#
Feature selection4reduction -Decision 'ree#
"rincipal !omponent +nalysis# etc$
Feature classification -
+rtificial 5eural 5etwor
Fu((y logic#
Support ,ector Machine etc$#
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Literature Surve(
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Literature Surve("*#$%
+uthor# 6ear Summary
Dyer and Stewart#
789:
'he statistical parameters such as probability density and &urtosis
can be effectively used for identification of bearing fault
%andall# 78:; For gearbox fault diagnosis# %andall proved the effectiveness of
cepstrum analysis through several case studies$
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Literature Surve("*#&%
+uthor# 6ear Summary
?uo# 788>$ +rtificial neural networ& @+55A and Fu((y logic can be used for
automatic detection of two main faults of turbine blades
Subrahmanyam and
Su2atha# 7889$
'hree different ball bearing defects are classified using neural
networ& with 8>B accuracy
0aydar and 0all #
C;;7
Sound signal is a powerful tool in detection of various types of
progressing faults in gear boxes$
"ennacchi et al$#
C;;$
'he machine learning-based methods can be effectively used to
identify the shaft crac&s in rotating machines
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Literature Surve("*#'%
+uthor# 6ear Summary
Shi et al$# 788:$ %esearch wor& reported uses the statistical features in
combinations to elicit information regarding the bearing faults
3eng and 5or#
788:$
Studied the effectiveness of sound and vibration signal in
detecting the presence of faults in rolling element bearing usingstatistical analysis method$
Statistical parameters such as crest factor# s&ewness and &urtosis
was used$
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Literature Surve("*#.%
+uthor# 6ear Summary
Saravanan et al$#C;;8$
'he decision tree algorithm is used in selecting the prominent
features and the same algorithm performs the classification
process for automated fault diagnosis of spur bevel gearbox $
Sun et al$# C;;9$ 'he redundant twelve features were effectively removed from
eighteen features using "!+ without decrease in classification
accuracy$
'he paper also reported that $B reduction of data is possible
in "!+$
idodo# C;;9 In the fault identification of induction motor# the discrimination
ability of S,M is improved when I!+ is used for feature
reduction$
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Literature Surve("*#/%
+uthor# 6ear Summary
Samanta et al$# C;; %eported the effectiveness of +55 and support vector
machine S,M in identification of bearing faults$
'he performance of S,M is better than +55$
Sugumaran et al$#
C;;9
"S,M yielded 7;;B classification efficiency in the roller
bearing fault diagnosis$
an et al$# C;;8$ 'he clone-selection programming effective in identification
of mechanical and electrical faults$
u and Liao# C;7;$ 'he various faults in the automotive air conditioner blower
can be effectively detected from the noise emission signal
using neural networ&
Singh et al$# C;7 'he various width si(es @;$>99 to 7$87= mmA of the outer
race defect in taper roller bearing have been detected with
the help of 'symlet5' wavelet coefficients
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Scope of present 0or1 * * *#$%
Most of the research work done in this area considered one or
two components with small number of fault classes.
In this study# the rotational elements shaft# bearing# gear and
rotor are considered together with C= fault classes$
'he influence of number of components or fault classes on thecapability of machine learning methods for rotating machine
fault diagnosis is found$
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Scope of present 0or1 * * *#&%
Machine learning based sound signal analysis was not well
explored in rotating machine fault diagnosis.
'he behavior of statistical features and wavelet features of the
sound signal is studied in detail and compare with vibration
signal$
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Scope of present 0or1 * * *#'%
There is a need for identification of the best suited feature
selection technique for fault diagnosis of multi component
rotating machine.
'he use of three dimensionality reduction techni)ues such as
decision tree# principal component analysis and independent
component analysis in rotating machine fault diagnosis is
discussed and compared in this research wor&$
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Scope of present 0or1 * * *#.%
lonal selection classification algorithm !"A# is a newly
de$eloped technique. %ut $ery few works were carried out in
machine fault diagnosis
!S!+ has been extensively studied using sound and vibration
signal$
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Scope of present 0or1 * * *#/%
&eaturelassifier combination is essential for automated
fault diagnosis.
'he best feature-classifier pair of both the vibration signal and
sound signal was identified for multicomponent fault
diagnosis$
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Machine Learning 2echni)ues Feature extraction -
Statistical features and avelet features
Feature selection4reduction -Decision 'ree @D'A#
"rincipal !omponent +nalysis@"!+A and
Independent !omponent +nalysis@I!+A$
Feature classification -
Decision 'ree@D'A#
Support ,ector Machine@S,MA#
!lonal selection classification algorithm@!S!+A and "roximal support vector machine@"S,MA$
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Methodolog(
Data Ac)uisition and
Signal onditioning
Feature 34traction -
Statistical and 5avelet features
Feature lassification -
D26 SVM6 SA and 7SVM
Machine Fault Diagnosis
Feature Selection -
D26 7A and !A
Rotating machines 0ith Sensors
#accelerometer and microphone%
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34perimental Studies
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34perimental Setup
Rotating machine fault simulator
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Location of accelerometer and microphone
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Spur bevel gearbo4
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Specification of accelerometer
Ma&e * Dytran Instruments Inc$ GS+
Model 5umber * ;>07
eight * C$> grams
Description * >;; g range
Fre)uency * ;$> H C; &3(
%esonance Fre)uency* => &3(
Sensitivity * 7; m,4g
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Specification of microphone
Ma&e * ebronics# India
Model 5umber * E0-7;; SM
Sensitivity * C d0
Directivity * mni-directional
Fre)uency %esponse * >;-7>;;;3(
Impedance * C ohms
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Dactron FF2 Anal(8er
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9ood and fault conditions of rotating elements "#$%
9ood bearing and good gear
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9ood and fault conditions of rotating elements "#&%
Outer race fault bearing!nner race fault bearing
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9ood and fault conditions of rotating elements "#'%
7inion 0heel 0ith tooth bro1en Disc 0ith unbalancing mass
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34perimental Stud(
(hase)
7C fault classes of shaft# rotor and bearing
-,ibration signal
-Sound signal
(hase))
C= fault classes of shaft# rotor# bearing and gear$
-,ibration signal
-Sound signal
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Details of $& fault conditions of shaft6 rotor and bearing
5otation used Fault description
a7 good shaft 1 good bearing
aC good shaft with rotor unbalance 1 good bearing
a good shaft 1 inner race fault @I%FA bearing
a= good shaft with rotor unbalance 1 I%F bearing
a> good shaft 1 outer race fault@%FA bearing
a good shaft with rotor unbalance 1 %F bearing
a9 bent shaft 1 good bearing
a: bent shaft with rotor unbalance 1 good bearing
a8 bent shaft 1 I%F bearing
a7; bent shaft with rotor unbalance 1 I%F bearing
a77 bent shaft 1 %F bearing
a7C bent shaft with rotor unbalance 1 %F bearing
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Details of &. fault conditions of shaft6 rotor6 bearing and gear
5otations used Fault description A* good shaft + good bearing + good gear
A, good shaft with rotor unbalance + good bearing + good gear
A- good shaft + )& bearing + good gear
A/ good shaft with rotor unbalance + )& bearing + good gear
A5 good shaft + 0& bearing + good gear
A1 good shaft with rotor unbalance + 0& bearing + good gear
A2 bent shaft + good bearing + good gear
A3 bent shaft with rotor unbalance + good bearing + good gear
A4 bent shaft + )& bearing + good gear
A* bent shaft with rotor unbalance + )& bearing + good gear A** bent shaft + 0& bearing + good gear
A*, bent shaft with rotor unbalance + 0& bearing + good gear
A*- good shaft + good bearing + fault gear
A*/ good shaft with rotor unbalance + good bearing + fault gear
A*5 good shaft + )& bearing + fault gear
A*1 good shaft with rotor unbalance + )& bearing + fault gear
A*2 good shaft + 0& bearing + fault gear
A*3 good shaft with rotor unbalance + 0& bearing + fault gear A*4 bent shaft + good bearing + fault gear
A, bent shaft with rotor unbalance + good bearing + fault gear
A,* bent shaft + )& bearing + fault gear
A,, bent shaft with rotor unbalance + )& bearing + fault gear
A,- bent shaft + 0& bearing + fault gear
A,/ bent shaft with rotor unbalance + 0& bearing + fault gear
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2ime domain plots of vibration signals"#$%
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2ime domain plots of vibration signals"#&%
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2ime domain plots of sound signals"#$%
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Fault Diagnosis using
Statistical Features
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Fault diagnosis using statistical features Feature extraction -
Statistical features Feature selection4reduction -
Decision 'ree#
"rincipal !omponent +nalysis and
Independent !omponent +nalysis$
Feature classification -
Decision 'ree#
Support ,ector Machine#
!lonal selection classification algorithm and
"roximal support vector machine$
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Feature 34traction - Statistical features
7$ Mean
C$ Standard Error$ Median
=$ Standard Deviation
>$ Sample ,ariance
$ ?urtosis
9$ S&ewness
:$ %ange
8$ Minimum
7;$ Maximum
77$ Sum
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Feature Selection - Decision 2ree"#$%
Feature selection using decision tree involves two steps$
'hey are
7$ +rrange the eleven statistical features in the order of their
importance from the decision tree representation$
C$ 'he optimum number of features are chosen based on the
classification accuracy
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Feature Selection - Decision 2ree"#&%Set of If-Then rules
It is a tree based knowledge representation methodology
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Feature Selection - Decision 2ree"#'%
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Vibration signals for $& fault classes at Speed /:: rpm
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Application of Decision 2ree"#$%
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Vibration signals for $& fault classes at Speed ;:: rpm
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Application of Decision 2ree"#&%
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Vibration signals for $& fault classes at Speed
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3/12/16
Vibration signals for $& fault classes at Speed $$:: rpm
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Application of Decision 2ree"#.%
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3/12/16
Vibration signals for $& fault classes
'he order of importance of ten features is standard error# sample
variance# median# standard deviation# s&ewness# maximum#
minimum# &urtosis# range and mean$
'he feature sum was not used in all the four decision tree
representation$
'he same decision tree algorithm was used to select the best
number of features by input these ordered eleven features with
the removal of least important feature every time$
51
Application of Decision 2ree"#/%
A li ti f D i i 2 #?%
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3/12/16
Vibration signals for $& fault classes
Sl* =o=umber
of features
Decision tree - lassification 3fficienc( >
Meanclassification
efficienc( >Speed /::
rpm
Speed
;:: rpm
Speed 89$8C 8:$ 88$;; 8:$;;
C 7; 8$9> 89$8C 8:$ 88$;; 8:$;;
8 8$: 8:$;; 8:$C> 8:$: 89$8:= : 8$8C 8:$;; 8:$;: 8:$: 89$8
> 9 89$;: 8:$79 8:$C> 8:$: 8:$;:
89$C> 89$: 8:$>: 8:$: 8:$7C
9 > 89$ 89$>: 8:$>: 8:$>: 8:$;C
: = 87$>: 8$: 8=$;: 8:$79 8=$=C8 87$: 8$9 87$;: 89$8C 8$
7; C =$>: $;: $;; 9C$;: 9$78
77 7 =7$>: $ $ >;$;; 8$>
7erformance of decision tree in dimensionalit( reduction
52
Application of Decision 2ree"#?%
A li i f D i i 2 #;%
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3/12/16
Vibration signals for $& fault classes
!onditions to select the number of dominant features for
classification study are
!hoose the number of features which maximi(es classification
efficiency
!hoose the number which satisfies the conse)uence of
dimensionality reduction$
53
Application of Decision 2ree"#;%
A li i f D i i 2 #@%
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3/12/16
Vibration signals for $& fault classes
1 2 3 4 5 ! " # 1$ 1135.$$
45.$$
55.$$
5.$$
!5.$$
"5.$$
#5.$$
Mean Classification Efficiency %
lassification efficienc( of decision tree in dimensionalit( reduction
54
Application of Decision 2ree"#@%
A li ti f D i i 2 #
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3/12/16
Vibration signals for &. fault classes
C= fault classes of shaft# rotor# bearing and gear$
'he eleven statistical features were arranged in the descending order
of importance with the help of decision tree representation of the
four speeds$
'hey are s&ewness# standard error# minimum# median# sample
deviation# range# minimum# &urtosis# maximum# mean and sum$
5umber of dominant features re)uired for classification can be chosen
with the help of same decision tree algorithm$
55
Application of Decision 2ree"#
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3/12/16
Vibration signals for &. fault classes
1 2 3 4 5 ! " # 1$ 1135.$$
4$.$$
45.$$
5$.$$
55.$$
$.$$
5.$$
!$.$$
!5.$$
"$.$$
"5.$$
Mean Classification Efficiency %
lassification efficienc( of decision tree in dimensionalit( reduction
56
Application of Decision 2ree"#$:%
A li ti f D i i 2 #$$%
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3/12/16
Sound signals for $& fault classes
'he eleven statistical features were arranged in the descending order of
importance with the help of decision tree representation of the four speeds$
'hey are standard deviation# sample variance# range# &urtosis# s&ewness#
minimum# median# maximum# standard error# mean and sum$
5umber of dominant features re)uired for classification can be chosen with
the help of same decision tree algorithm$
57
Application of Decision 2ree"#$$%
A li ti f D i i 2 #$&%
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Application of Decision 2ree"#$&%
3/12/16
Sound signals for $& fault classes
1 2 3 4 5 ! " # 1$ 115$.$$
55.$$
$.$$
5.$$
!$.$$
!5.$$
"$.$$
Mean Classification Efficiency %
lassification efficienc( of decision tree in dimensionalit( reduction
58
Application of Decision 2ree #$'%
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3/12/16
Sound signals for &. fault classes
Sl* =o
=umber
of
features
Decision tree - lassification 3fficienc(
> Mean
classification
efficienc( >Speed
/:: rpm
Speed
;:: rpm
Speed
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3/12/16
Dimensionality reduction techni)ue$
'he "!+ reduces the higher dimensional inter-related redundant
data to lower dimensional uncorrelated principal components$
Feature reduction involves two steps$ 'hey are
7$ +rrange the principal components in the order of their
importance using eigen values$
C$ 'he optimum number of components are chosen based on the
classification accuracy using decision tree algorithm$
60
7rincipal omponent Anal(sis
A li ti f 7A #$%
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Application of 7A"#$%
3/12/16
Vibration signals for $& fault classes
S733D
rpm
3!93= VALU3
7 $ 7 & 7 ' 7 . 7 / 7 ? 7 ; 7 @ 7 < 7 $: 7 $$
>;; 9$999 C$;;; ;$:;; ;$9 ;$;>9 ;$;C ;$;;8 ; ; ; ;
9;; 9$8=7 C$;;; ;$9C8 ;$C8 ;$;= ;$; ;$;77 ; ; ; ;
8;; 9$87> C$;;C ;$9; ;$799 ;$7= ;$;= ;$;7 ; ; ; ;
77;; :$C7 7$8 ;$>: ;$7>8 ;$; ;$;=: ;$;7= ; ; ; ;
3igen values of the principal components
61
A li i f 7A #&%
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Application of 7A"#&%
3/12/16
Vibration signals for $& fault classes
1 2 3 4 5 !3$.$$
4$.$$
5$.$$
$.$$
!$.$$
"$.$$
#$.$$
1$$.$$
Mean Classification Efficiency %
lassification efficienc( of D2 0ith 7A in dimensionalit( reduction
62
Application of 7A #'%
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Application of 7A"#'%
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Vibration signals for &. fault classes
3igen values of the principal components
Speed
rpm
3igen value
7 $ 7 & 7 ' 7 . 7 / 7 ? 7 ; 7 @ 7 < 7 $: 7 $$
>;; $8= C$;;9 7$> ;$= ;$;9 ;$;7 ;$;77 ;$;;C ; ; ;
9;; 9$=:> C$;;> ;$8=> ;$=C ;$7;C ;$;C> ;$;;8 ; ; ; ;
8;; 9$C C$;; ;$:= ;$ ;$7C7 ;$;C ;$;77 ;$;;7 ; ; ;
77;; 9$>:: C$;;8 ;$8> ;$C88 ;$7C7 ;$;79 ;$;7 ; ; ; ;
63
Application of 7A #.%
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Application of 7A"#.%
3/12/16
Vibration signals for &. fault classes
lassification efficienc( of D2 0ith 7A in dimensionalit( reduction
1 2 3 4 5 !3$.$$
35.$$
4$.$$
45.$$
5$.$$
55.$$
$.$$
5.$$
!$.$$
!5.$$
"$.$$
Mean Classification Efficiency %
64
Application of 7A #/%
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Application of 7A"#/%
3/12/16
Sound signals for $& fault classes
3igen values of the principal components
Speed
rpm
3igen value
7$ 7& 7' 7. 7/ 7? 7; 7@ 7< 7$: 7$$
>;; >$>= C$C 7$=> 7$C>7 ;$: ;$7:: ;$7>7 ;$;;C ; ; ;
9;; >$C;8 C$=9: 7$= 7$;:> ;$8 ;$C=> ;$7C ;$;;= ; ; ;
8;; >$8 C$79 7$>7= ;$:89 ;$:= ;$7CC ;$;: ;$;77 ; ; ;
77;; >$=: C$>=7 7$=> ;$:9> ;$C= ;$;99 ;$;= ;$;; ; ; ;
65
Application of 7A #;%
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Application of 7A"#;%
3/12/16
Sound signals for $& fault classes
lassification efficienc( of D2 0ith 7A in dimensionalit( reduction
1 2 3 4 5 ! "
4$.$$
45.$$
5$.$$
55.$$
$.$$
5.$$
!$.$$
Mean Classification Efficiency %
66
Application of 7A #@%
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Application of 7A"#@%
3/12/16
Sound signals for &. fault classes
3igen values of the principal components
Speed
rpm
3igen value
7$ 7& 7' 7. 7/ 7? 7; 7@ 7< 7$: 7$$
>;; >$87 C$C:= 7$>> ;$8:> ;$>;9 ;$7> ;$77= ;$;;= ; ; ;
9;; =$:9 C$ 7$9; 7$C8 ;$=88 ;$CC7 ;$78= ;$;;= ; ; ;
8;; >$79 C$C8 7$C7 7$7>C ;$=; ;$C7 ;$7> ;$;;= ; ; ;
77;; =$888 C$7 7$9>: 7$7C9 ;$:8 ;$C ;$7= ;$;; ; ; ;
67
Application of 7A #
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Application of 7A"# Mean
classification
efficienc( >
Speed
/::rpm
Speed
;::rpm
Speed
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!ndependent omponent Anal(sis
Dimensionality reduction techni)ue$
'ransforms multivariate random signals into statistically
independent components without much information loss$
Feature reduction involves two steps$ 'hey are
7$ +rrange the independent components in the order of their
importance using eigen values$
C$ 'he optimum number of components are chosen based on the
classification accuracy using decision tree algorithm$
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Application of !A #$%
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Application of !A"#$%
3igen values of the independent components
S733D
rpm
3!93= VALU3
! $ ! & ! ' ! . ! / ! ? ! ; ! @ ! < ! $: ! $$
>;; $9= 7$97 ;$;=;$;;>
9
;$;;;
7
7$;E
-;
7$8;E-
;
; ; ; ;
9;; C$88 ;$8: ;$;9=;$;;
;$;;;
7C
8$>E
-;
:$:E-
;9; ; ; ;
8;; C$88C ;$> ;$;=:=;$;;7
8
;$;;;
79
8$=E
-;
$>8E-
;9; ; ; ;
77;; $> 7$=9 ;$;>:> ;$;;C9
;$;;;7C
:$89E-;
>$=8E-;9
; ; ; ;
Vibration signal for $& fault classes
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Application of !A #&%
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Application of !A"#&%
1 2 3 4 5 !3$.$$
4$.$$
5$.$$
$.$$
!$.$$
"$.$$
#$.$$
1$$.$$
Mean Classification Efficiency %
lassification efficienc( of D2 0ith !A in dimensionalit( reduction
Vibration signal for $& fault classes
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Application of !A #'%
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Application of !A"#'%
3igen values of the independent components
Speed
rpm
3igen value
!$ !& !' !. !/ !? !; !@ !<!
$:!$$
>;; =9:$C88=$=C
>
7$=7;$;7>
=
;$;;=7;$;;;7
=
=$99E-
;>
$;:E-;> ; ; ;
9;; =::$77 =>$9 7$C:;$;78
7;$;77
;$;;;C
9
>$C7E-
;>$>;E-;> ; ; ;
8;; =:;$=87=$7:
7$>7=
;$;C
7;$;7:
;$;;;
:$E-
;>=$:E-;> ; ; ;
77;; =9>$=8==$9=
7$C
;$;C=
9;$;7C8
;$;;;C
8
9$C7E-
;>=$E-;> ; ; ;
Vibration signal for &. fault classes
3/12/16 72
Application of !A #.%
8/19/2019 Automated Fault Diagnosis
73/174
Application of !A"#.%
1 2 3 4 5 ! "1$.$$
2$.$$
3$.$$
4$.$$
5$.$$
$.$$
!$.$$
"$.$$
Mean Classification Efficiency %
lassification efficienc( of D2 0ith !A in dimensionalit( reduction
Vibration signal for &. fault classes
3/12/16 73
Application of !A #/%
8/19/2019 Automated Fault Diagnosis
74/174
Application of !A"#/%
Speed
rpm
3igen value
!$ !& !' !. !/ !? !;
!
@ !<
!$
:
!$
$
>;;
:$C9=
C
;$;9:
C
;$;7;C
7 ;$;;7;
>$7E-
;>
C$9:E-
;
C$9E-
;9 ; ; ; ;
9;;:$7:CC9
= ;$C;;$;;7
C ;$;; ;$;;;C=$8CE-
;7$=E-
;9 ; ; ; ;
8;;
>$>=8C>
9
;$C;7
:
;$;;>=
9 ;$;;C ;$;;;CC
=$=9E-
;
7$;E-
;9 ; ; ; ;
77;; >$78=9
;$8>
:
;$;;8C
;$;;C98 ;$;;;7=
$CE-
;
7$;=E-
;9 ; ; ; ;
3igen values of the independent components
Sound signal for $& fault classes
743/12/16
Application of !A #?%
8/19/2019 Automated Fault Diagnosis
75/174
Application of !A"#?%
lassification efficienc( of D2 0ith !A in dimensionalit( reduction
1 2 3 4 5 !1$.$$
2$.$$
3$.$$
4$.$$
5$.$$
$.$$
!$.$$
Mean Classification Efficiency %
Sound signal for $& fault classes
3/12/16 75
Application of !A #;%
8/19/2019 Automated Fault Diagnosis
76/174
Application of !A"#;%
Speed
rpm
3igen value
!$ !& !' !. !/ !? !; !@ !<
!
$:
!
$$
>;; ;$;> ;>;$7=;8
=
;$;:;
:
;$;79
8 ;$;;;: $97E-;> 7$:8E-;>
$;;E-
; ; ; ;
9;; =7$;::C;$7>7;
8
;$;:C>
C
;$;;==
8 ;$;;;8 >$>E-;> 8$:;E-;
>$CE-
; ; ; ;
8;; =>$7>8 ;$7877;$7C>C
;$;;99
;$;;7C: ;$;;;7 7$;E-;>
:$8E-
; ; ; ;
77;; =:$98779;$C>
9
;$;:79
;$;7;;
= ;$;;7= :$C:E-;> 7$;8E-;>
9$>E-
; ; ; ;
3igen values of the independent components
Sound signal for &. fault classes
3/12/16 76
Application of !A #@%
8/19/2019 Automated Fault Diagnosis
77/174
Application of !A"#@%
Sl*
=o
=umber
of
features
!A Decision tree - lassification
3fficienc( > Mean
classification
efficienc( >Speed
/:: rpm
Speed
;:: rpm
Speed
: ;$C9
7erformance of D2 0ith !A
Sound signal for &. fault classes
3/12/16 77
Selection of dimensionalit( reduction techni)ue"#$%
8/19/2019 Automated Fault Diagnosis
78/174
( ) # %
omparison of dimensionalit( reduction techni)ues
Vibration signal for $& fault classes
3/12/16 78
Selection of dimensionalit( reduction techni)ue"#&%
8/19/2019 Automated Fault Diagnosis
79/174
( ) # %
'he five most discriminating ability features are
7$ Standard error#
C$ Sample variance#
$ Median#
=$ Standard deviation and
>$ S&ewness$
Vibration signal for $& fault classes
Selection of dimensionalit( reduction techni)ue"#'%
8/19/2019 Automated Fault Diagnosis
80/174
( ) # %
omparison of dimensionalit( reduction techni)ues
Vibration signal for &. fault classes
3/12/16 80
Selection of dimensionalit( reduction techni)ue"#.%
8/19/2019 Automated Fault Diagnosis
81/174
( ) # %
'he four most discriminating ability features are
7$ S&ewness#
C$ Standard error#
$ Minimum and
=$ Median$
Vibration signal for &. fault classes
Selection of dimensionalit( reduction techni)ue"#/%
8/19/2019 Automated Fault Diagnosis
82/174
( ) # %
omparison of dimensionalit( reduction techni)ues
Sound signal for $& fault classes
3/12/16 82
Selection of dimensionalit( reduction techni)ue"#?%
8/19/2019 Automated Fault Diagnosis
83/174
( ) # %
'he five features can be chosen for the classification
analysis using sound signal for twelve fault classes$ 'hey are
7$ Standard Deviation#
C$ Sample variance#
$ ?urtosis#
=$ S&ewness and
>$ %ange$
Sound signal for $& fault classes
Fault classification
8/19/2019 Automated Fault Diagnosis
84/174
Fault classification
'he chosen features of the four cases were used for classification study$
'here are two main ways of classification of data$
'he one way is to train the algorithm by passing all the data set with their
class and test the trained algorithm by sending only the particular class
dataset for identification of the class to which the dataset belongs$
In the next one# input all the data set with their class to the algorithm$ 'he
algorithm gets trained with the dataset and does the cross fold validation
with the help of same dataset$
Fault lassification - Decision tree"#$%
8/19/2019 Automated Fault Diagnosis
85/174
Fault lassification Decision tree"#$%
2esting 7arameterSpeed in rpm
Mean/:: ;:: ;$;> ;$;C ;$; ;$;9>
2otal number of
instances
7C;; 7C;; 7C;; 7C;; 7C;;
orrectl( classified
instances77: 7797 77: 77: 779
Misclassified instances C C8 79 79 C=
lassificationefficienc( >
89$ 89$>: 8:$>: 8:$>: 8:$;79>
Fault classification results of decision tree
Vibration signal for $& fault classes
3/12/16 85
Fault lassification - Decision tree"#&%
8/19/2019 Automated Fault Diagnosis
86/174
Fault lassification Decision tree"#&%
a$ a& a' a. a/ a? a; a@ a< a$: a$$ a$&
a$
8/19/2019 Automated Fault Diagnosis
87/174
Fault lassification Decision tree"#'%
2esting 7arameterSpeed in rpm
Mean/:: ;::
2otal number of instances C=;; C=;; C=;; C=;; C=;;
orrectl( classified instances C;C> 78>C 7888 7:C: 78>7
Misclassified instances 9> ==: =;7 >9C ==8
lassification efficienc( > :=$: :7$ :$C8 9$79 :7$C:
Fault classification results of decision tree
Vibration signal for &. fault classes
3/12/16 87
Fault lassification - Decision tree"#.%
8/19/2019 Automated Fault Diagnosis
88/174
# %
onfusion matri4 of decision tree at $$:: rpm -
Vibration signal for &. fault classes
A
1 A2
A
3
A
4
A
5 A6
A
7
A
8
A
9
A1
0
A1
1
A1
2
A1
3
A1
4
A1
5
A1
6
A1
7
A1
8
A1
9
A2
0
A2
1
A2
2
A2
3
A2
4
A1
9
4 4 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
A2 2 74 0 23 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
A3 0 1
9
1 6 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0
A4 1 27 7
6
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
A5 0 0 0 0
9
8 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0
A6 3 0 0 0 0 87 0 0 0 0 0 0 1 2 0 0 0 0 2 0 5 0 0 0
A7 0 0 0 0 0 0
9
3 0 4 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0
A8 2 0 0 2 0 0 0
9
5 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
A9 0 0 0 0 0 0 3 1
7
9 17 0 0 0 0 0 0 0 0 0 0 0 0 0 0
A1
0 0 0 0 0 0 0 4 0 42 54 0 0 0 0 0 0 0 0 0 0 0 0 0 0
A1
1 0 0 2 1 0 0 0 0 0 0 97 0 0 0 0 0 0 0 0 0 0 0 0 0
A1
2 0 0 0 0 0 0 0 0 0 0 1 99 0 0 0 0 0 0 0 0 0 0 0 0
A1
3 0 0 0 0 0 3 0 0 0 0 0 0 79 1 0 1 0 3 0 1 3 0 0 9
A1
4 0 0 0 0 0 2 0 0 0 0 0 0 2 86 0 0 0 0 0 0 2 0 0 8
A1
5 0 0 0 0 0 0 0 0 0 0 0 0 1 0 74 17 0 0 0 0 0 1 6 1A1
Fault lassification - Decision tree"#/%
8/19/2019 Automated Fault Diagnosis
89/174
# %
2esting 7arameter Speed in rpm Mean/:: ;::
2otal number of
instances7C;; 7C;; 7C;; 7C;; 7C;;
orrectl( classified
instances9= 89 8= 8>8 8;7
Misclassified instances = C C>9 C=7 C88
lassification
efficienc( > 7$7 :;$>: 9:$>: 98$8C 9>$;
Fault classification results of decision tree
Sound signal for $& fault classes
3/12/16 89
Fault lassification - Decision tree"#?%
8/19/2019 Automated Fault Diagnosis
90/174
Fault lassification Decision tree"#?%
a$ a& a' a. a/ a? a; a@ a< a$: a$$ a$&
a$
8/19/2019 Automated Fault Diagnosis
91/174
Fault lassification Decision tree"#;%
2esting 7arameter Speed in rpm Mean/:: ;::
2otal number of
instancesC=;; C=;; C=;; C=;; C=;;
orrectl( classified
instances87; = 99: :7C 987
Misclassified instances 7=8; 79 7CC 7>:: 7;8
lassification
efficienc( > 9$8C C9$9 C$=C $: C$8
Fault classification results of decision tree
Sound signal for &. fault classes
3/12/16 91
Support Vector Machine"#$%
8/19/2019 Automated Fault Diagnosis
92/174
pp # %
belongs to a class of supervised learning algorithm
constructs an optimal hyperplane for linearly separable
patterns to classify the data into two categories$
extends to patterns that are not linearly separable by
transformations of original data to map into new space with
the help of &ernel functions$
Support Vector Machine"#&%
8/19/2019 Automated Fault Diagnosis
93/174
pp # %
3/12/16 93
Support Vector Machine"#'%
8/19/2019 Automated Fault Diagnosis
94/174
pp # %
3/12/16 94
Support Vector Machine"#.%
8/19/2019 Automated Fault Diagnosis
95/174
pp # %
'he ob2ective function of the problem is to maximi(es the
margin and minimi(es the error$
e combine this and form a single minimi(ation problem$
+ ye
C
w
''
yw#ν
w Min
Support Vector Machine"#/%
8/19/2019 Automated Fault Diagnosis
96/174
pp # %
S,M Model
!-S,! and nu-S,!
?ernel Functions
Linear
'hree degree polynomial
%adial basis function and
Sigmoid
Fault lassification B SVM"#$%
8/19/2019 Automated Fault Diagnosis
97/174
# %
Sl* =o
SVM
Cernel
Function
lassification 3fficienc( >
Speed /:: rpm Speed ;:: rpm Speed $>: 88$79 8:$879 88$: 88$9
C'hree degree
polynomial8:$: 8:$879 8: 8$879 88$> 89$: 88$: 88$:
%adial 0asis
Function
@%0FA
88$ 88$ 8:$C> 89$: 88$=79 88$ 88$879 88$:
= Sigmoid 8:$879 8:$C> 8:$;: 8 88$79 8=$879 88$: 8:$>
7erformance of SVM 1ernel functions
Vibration signal for $& fault classes
3/12/16 97
Fault lassification B SVM"#&%
8/19/2019 Automated Fault Diagnosis
98/174
2esting 7arameter Speed in rpm Mean/:: ;::
2otal number of
instances7C;; 7C;; 7C;; 7C;; 7C;;
orrectl( classified
instances77:8 7798 778C 778: 778;
Misclassified instances 77 C7 : C 7;
lassificationefficienc( >
88$;: 8:$C> 88$ 88$: 88$7C
Fault classification results of SVM
Vibration signal for $& fault classes
3/12/16 98
Fault lassification B SVM"#'%
8/19/2019 Automated Fault Diagnosis
99/174
onfusion matri4 of SVM at $$:: rpm
Vibration signal for $& fault classes
3/12/16 99
a$ a& a' a. a/ a? a; a@ a< a$: a$$ a$&
a$ $:: ; ; ; ; ; ; ; ; ; ; ;
a& ; $:: ; ; ; ; ; ; ; ; ; ;
a' ; ;
8/19/2019 Automated Fault Diagnosis
100/174
2esting 7arameterSpeed in rpm
Mean/:: ;:: = 7C C7; 77 78$C>
2otal number of instances C=;; C=;; C=;; C=;; C=;;
orrectl( classified instances C7=; C;C9 C; 787 C;C:
Misclassified instances C; 9 9 =:9 9C
lassification efficienc( > :8$79 :=$= :=$9 98$97 :=$>7
Fault classification results of SVM
Vibration signal for &. fault classes
3/12/16 100
Fault lassification B SVM"#/%
8/19/2019 Automated Fault Diagnosis
101/174
A1 A2 A3 A4 A5 A6 A7 A8 A9 A10
A1
1
A1
2
A1
3
A1
4
A1
5
A1
6
A1
7
A1
8
A1
9
A2
0
A2
1
A2
2
A2
3
A2
4
A1 70 14 1 14 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
A2 14 65 6 14 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
A3 0 1 94 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
A4 8 9 4 79 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
A5 2 0 0 0 76 19 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0
A6 2 1 0 0 13 84 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
A7 0 0 0 0 0 0 97 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
A8 0 0 0 0 0 0 3 97 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
A9 0 0 0 0 0 0 3 0 75 22 0 0 0 0 0 0 0 0 0 0 0 0 0 0
A10 0 0 0 0 0 0 1 0 29 70 0 0 0 0 0 0 0 0 0 0 0 0 0 0
A11 0 0 0 0 0 0 0 0 0 0
10
0 0 0 0 0 0 0 0 0 0 0 0 0 0
A12 0 0 0 0 0 0 0 0 0 0 0
10
0 0 0 0 0 0 0 0 0 0 0 0 0
A13 0 0 0 0 0 0 0 0 0 0 0 0 69 13 0 0 0 0 0 0 0 0 11 7
A14 0 0 0 0 0 0 0 0 0 0 0 0 8 79 0 0 0 0 0 1 0 0 7 5
A15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 97 3 0 0 0 0 0 0 0 0
A16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 86 0 0 0 2 0 0 0 0
A17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 92 8 0 0 0 0 0 0
A18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 94 0 0 0 0 0 0
A19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0100 0 0 0 0 0
A20 0 0 0 0 2 0 0 0 0 0 0 0 0 5 0 0 0 0 0 69 1 22 1 0
A21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 89 8 0 0
A22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 6 85 4 0
A23 0 0 0 0 0 0 0 0 0 0 0 0 4 2 0 2 0 0 0 1 0 2 86 3
A24 0 0 0 0 0 0 0 0 0 0 0 0 7 4 0 0 0 0 0 0 0 0 6 83
onfusion matri4 of SVM at $$:: rpm -
Vibration signal for &. fault classes
Fault lassification B SVM"#?%
8/19/2019 Automated Fault Diagnosis
102/174
# %
2esting 7arameter Speed in rpm Mean/:: ;:: C ==$9
2otal number of
instances7C;; 7C;; 7C;; 7C;; 7C;;
orrectl( classified
instances:98 7;97 7;77 7;7> 88=
Misclassified instances C7 7C8 7:8 7:> C;
lassification
efficienc( > 9$C> :8$C> :=$C> :=$>: :C$:C>
Fault classification results of SVM
Sound signal for $& fault classes
3/12/16 102
Fault lassification B SVM"#;%
8/19/2019 Automated Fault Diagnosis
103/174
a$ a& a' a. a/ a? a; a@ a< a$: a$$ a$&
a$
8/19/2019 Automated Fault Diagnosis
104/174
2esting 7arameterSpeed in rpm
Mean/:: ;:: ;C C9: :
2otal number of instances C=;; C=;; C=;; C=;; C=;;
orrectl( classified instances 779 :9C 8=; 7;;8 888
Misclassified instances 7CC9 7>C: 7=; 787 7=;7
lassification efficienc( > =:$:: $ 8$79 =C$;= =7$;
Fault classification results of SVM
Sound signal for &. fault classes
3/12/16 104
lonal Selection lassification Algorithm
8/19/2019 Automated Fault Diagnosis
105/174
Supervised learning algorithm
0ased on natural immune system ur biological immune system protects our body against
foreign cells called antigens$
'o recogni(e and eliminate the antigens# each 0-cell secretes
variety of antibodies $
0 cells produce large numbers of antigen-specific antibodies
Each antibody recogni(e and bind to antigens$
Fault lassification B SA "#$%
8/19/2019 Automated Fault Diagnosis
106/174
2esting 7arameterSpeed in rpm
Mean
/:: ;:: 7
2otal number of instances 7C;; 7C;; 7C;; 7C;; 7C;;
orrectl( classified instances 88 7;> 89> 7;7 7;;:
Misclassified instances C7 7== CC> 78 78C
lassification efficienc( > :;$9> ::$;; :7$C> :>$8C :$8:
Fault classification results of SA
Vibration signal for $& fault classes
3/12/16 106
Fault lassification B SA "#&%
8/19/2019 Automated Fault Diagnosis
107/174
a$ a& a' a. a/ a? a; a@ a< a$: a$$ a$&
a$ $:: ; ; ; ; ; ; ; ; ; ; ;
a& ; $:: ; ; ; ; ; ; ; ; ; ;
a' ; ;
8/19/2019 Automated Fault Diagnosis
108/174
2esting 7arameterSpeed in rpm
Mean/:: ;::
2otal number of instances C=;; C=;; C=;; C=;; C=;;
orrectl( classified instances 7=> 7=C= 7C:9 7;7 7C8>
Misclassified instances 8== 89 777 7:9 77;>
lassification efficienc( > ;$9 >8$7 >$ =C$C7 >$8>
Fault classification results of SA
Vibration signal for &. fault classes
3/12/16 108
Fault lassification B SA "#.%
8/19/2019 Automated Fault Diagnosis
109/174
2esting 7arameter Speed in rpm Mean
/:: ;:: $97 7;$; :$99 7;$;> :$=
2otal number of instances 7C;; 7C;; 7C;; 7C;; 7C;;
orrectl( classified instances =>C >> : >; 7;
Misclassified instances 9=: >=> >79 >>; >8;
lassification efficienc( > 9$9 >=$>: >$8C >=$79 >;$:
Fault classification results of SA
Sound signal for $& fault classes
3/12/16 109
7ro4imal Support Vector Machine
8/19/2019 Automated Fault Diagnosis
110/174
'he S,M design the hyperplane to divide the space into two half spaces
which separate the data points into two different classes$
'he computational complexity increases when the number of classes and
the training samples will increase$
In proximal support vector machine# the data points are assigned according
to the proximity to the hyperplanes that are separated as far as possible$
"S,M is a fast and simple algorithm to generate a linear or nonlinear
classifier by solving the linear e)uations.
Fault lassification B 7SVM "#$%
8/19/2019 Automated Fault Diagnosis
111/174
ondi
tion lassification Method
!7 a7 ,s aC a a= a> a a9 a: a8 a7; a77 a7C!C aC ,s a a= a> a a9 a: a8 a7; a77 a7C
! a ,s a= a> a a9 a: a8 a7; a77 a7C
!= a= ,s a> a a9 a: a8 a7; a77 a7C
!> a> ,s a a9 a: a8 a7; a77 a7C
! a ,s a9 a: a8 a7; a77 a7C
!9 a9 ,s a: a8 a7; a77 a7C
!: a: ,s a8 a7; a77 a7C
!8 a8 ,s a7; a77 a7C
!7; a7; ,s a77 a7C
!77 a77 ,s a7C
Method of classification in 7SVM
3/12/16 111
Fault lassification B 7SVM "#&%
8/19/2019 Automated Fault Diagnosis
112/174
ondition
lassification 3fficienc(
/:: rpm ;:: rpm 7;; 7;; 7;; 7;;
! 7;; 7;; 7;; 7;;
!9 8>$ 7;; 7;; 88$8
!: 7;; 7;; 7;; 7;;
!8 7;; 7;; 7;; 7;;
!7; 7;; 7;; 7;; 7;;
!77 7;; 7;; 7;; 8:$;;
Mean 8$9; 89$C8 8$>; 89$:8
'ime@secA 7C 7C 7C 7CFault classification results of 7SVM
Vibration signal for $& fault classes
3/12/16112
Fault lassification B 7SVM "#'%
8/19/2019 Automated Fault Diagnosis
113/174
ondition
lassification 3fficienc(
/:: rpm ;:: rpm $: 8>$: 8>$: 8>$:
!C 8>$> 8>$> 8>$> 8>$>
! 8>$=> 8>$=> 8>$=> 8>$=>
!= 8>$C= 8>$C= 8>$C= 8>$C=
!> 8>$;; 8>$;; 8>$;; 8>$;;
! 8=$9= 8=$9= 8=$9= 8=$9=
!9 8=$== 8=$== 8=$== 8=$==
!: 8=$7C 8=$7C 8=$7C 8=$7C
!8 8$9> 8=$;; 89$C> 8$9>
!7; 8$ 8$ 8$:; 8:$8
!77 8C$: 8C$: 8C$: 8C$>9
!7C 7;;$;; 7;;$;; 7;;$;; 7;;$;;
!7 87$9 8C$9 8C$9 87$9
!7= 8>$C9 8:$87 7;;$;; 8:$87
!7> 8;$=; 8:$;; 8C$:; :8$;
!7 7;;$;; 7;;$;; 7;;$;; 7;;$;;
!79 7;;$;; ::$;; 8>$;; 87$>;
!7: :$C8 7;;$;; 7;;$;; 7;;$;;
!78 7;;$;; 89$ :>$ 8;$;;
!C; 7;;$;; 8:$=; :;$;; 8$:;
!C7 7;;$;; 7;;$;; 7;;$;; 8=$;;
!CC 8$ C$9 8C$;; 8:$9
!C 9;$;; C$;; 9:$;; :$;;
Mean 8=$C 8C$8: 8=$;> 8=$7C
'ime@secA >= >> >= 7
3/12/16 113
Vibration signal for &. fault classes
Fault classification results of 7SVM
Fault lassification B 7SVM "#.%S i f $& f
8/19/2019 Automated Fault Diagnosis
114/174
ondition
lassification 3fficienc( >
/:: rpm ;:: rpm 87$>; 8C$>; 8C$>; 88$>;
! 8:$C8 8:$: 89$7= 7;;$;;
!9 7;;$;; 88$ 7;;$;; 8:$9
!: 8:$=; 88$C; 7;;$;; 7;;$;;
!8 88$;; 8:$;; 7;;$;; 7;;$;;
!7; 8:$9 89$ 8$ 8:$9
!77 :=$;; 8=$;; 8$;; 8$;;
Mean 8$8 8>$78 8>$89 8$79
'ime@secA 7 7C 7 7C
Fault classification results of 7SVM
Sound signal for $& fault classes
3/12/16 114
Fault lassification B 7SVM "#/%Sound signal for &. fault classes
8/19/2019 Automated Fault Diagnosis
115/174
ondition
lassification 3fficienc(
/:: rpm ;:: rpm $: 8>$: 8>$: 8>$:!C 8>$> 8>$> 8>$> 8>$>
! 8>$=> 8>$=> 8>$=> 8>$=>
!= 8>$C= 8>$C= 8>$C= 8>$C=
!> 8>$;; 8>$;; 8>$C; 8>$;;
! 8=$9= 8=$9= 8=$9= 8=$9=
!9 8=$== 8=$== 8=$== 8=$==
!: 8=$7C 8=$7C 8=$7C 8>$C8
!8 8$9> 8$9> 8=$C> 8=$C>
!7; 8$ 8$ 8$ 8$
!77 8C$: 8C$: 8C$: 8C$:
!7C 89$:> 8C$7 8=$7> 8$C
!7 87$9 87$9 87$9 87$9
!7= 88$C9 8$=> 8=$>> 87$=
!7> 8=$;; 8$C; 8$; 8C$;;
!7 7;;$;; 7;;$;; 7;;$;; 7;;$;;
!79 ::$;; :9$;; :9$>; ::$>;
!7: 8$97 89$97 8=$C8 8=$C8
!78 :=$;; 8=$;; 8$ 8>$
!C; :8$; 8$;; 89$; 8$;;
!C7 :;$;; 89$;; 8=$;; 89$;;
!CC 89$ 8$ 8:$9 8=$9
!C ;$;; ::$;; 8:$;; 8$;;
Mean 87$88 8=$;8 8=$9C 8=$=>
'ime@secA >8 >: C
Fault classification results of 7SVM
Sound signal for &. fault classes
3/12/16 115
Fault diagnosis using statistical features
8/19/2019 Automated Fault Diagnosis
116/174
lassification
algorithm
Mean lassification 3fficienc( >
Vibration signals Sound Signals
$& classes &. classes $& classes &. classes
D2 8:$;7 :7$C: 9>$; C$8
SVM 88$7C :=$>7 :C$: =7$7
SA :$8: >$8> >;$: -
7SVM 89$;; 8$:> 8>$7 8$:7
Mean classification efficienc( of the classification algorithm using statistical features
116
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Fault Diagnosis using
5avelet Features
5avelet features"#$%
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7rocedure of four level 0avelet decomposition #9ao and an6 &:$$%
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5avelet features"#&%
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avelet family for performing D' are
3aar wavelet#
Meyer wavelet#
Daubechies wavelet#
!oiflet wavelet#
Symlet wavelet#
0iorthogonal and
%everse biorthogonal wavelet$
>8 wavelets are considered in this wor&$
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5avelet features"#'%
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'he wavelets are selected on the basis of following criteria*
7$ 'he wavelet that extracts large amount of energy from
the signal
6a$elet energy features
C$ 'he wavelet that minimi(es the shanon entropy of thewavelet coefficients
$ 'he wavelet that has produced the maximum energy to
shanon entropy ratio should be chosen as the most
appropriate wavelet
6a$elet energy to entropy ratio features
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Feature extraction -
avelet features - Energy features
- Energy to Entropy featuresavelet Selection -
Decision 'ree$
Feature selection -Decision 'ree$
Feature !lassification-
Decision 'ree#
Support ,ector Machine#
!lonal selection classification algorithm and
"roximal support vector machine$
3/12/16
Selection of 0avelet"#$%
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2he 0avelet decomposition of vibration signal for good conditions of $& fault classes
using 'rbio3.9' 0avelet at $$:: rpm*
122
Selection of 0avelet"#&%S = 5 l t
lassification 3fficienc( >
S = 5 l t
lassification 3fficienc( >
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S*=o 5avelet S*=o 5aveletSpeed /::
rpm
Speed ;::
rpm
Speed $9C 7 D08 8$=C 8>$;: :9$7C :$> 87$C8
C bior7$ 8=$79 8$8C :9$>= :9$;= 8;$9 C D07; 8=$9 8$;; :9$97 :>$== 8;$C;
bior7$> 8>$79 8>$8C :9$C7 :$ 87$7 D077 8>$79 8C$: :9$9 :$=> 8;$== biorC$C :8$;; 98$;; :7$7 99$C9 :7$> = D07C 8=$>; 8$8C :9$98 :9$C8 8;$::
> biorC$= 8$;: 8;$=C 8;$=; :$>8 8;$7C > D07 8>$9> 8=$8C :9$ :8$9 8C$;7
biorC$ 8$>: 8C$=C 87$ :$9: 87$9: D07= 8$;; 8C$>; :$=> 8;$=; 87$=
9 biorC$: 8$79 87$>: 8;$C :9$7C 87$; 9 D07> 8>$;; 8$79 ::$9C ::$7 87$C>
: bior$7 9$>; >$9> >9$>: :$7; C$=: : rbio7$7 :8$79 :8$79 :=$:> 98$97 :>$9C
8 bior$ :=$9 :>$=C 98$89 :7$>9 :C$8; 8 rbio7$ 87$: :$=C :>$7; :=$: :9$;7
7; bior$> 87$9 87$ :9$:: :9$>= :8$7 =; rbio7$> 8$C> :8$9> :=$;8 :=$; :9$8C
77 bior$9 87$9> 8$8C 8;$>9 :9$7C 8;$:= =7 rbioC$C 8=$8C 8$;: :>$8 :9$C7 8;$CC
7C bior$8 8$>; 8C$: 8;$7> :>$8= 8;$7 =C rbioC$= 8>$: 8$8C 8;$=8 ::$=9 8C$7:
7 bior=$= 89$>; 87$>; :8$:7 :9$98 87$> = rbioC$ 8>$9> 8$79 ::$=9 ::$; 87$=C
7= bior>$> 89$9 8$;; ::$89 :8$8: 8C$=7 == rbioC$: 8$8C 8>$8C ::$:; :9$97 8C$=
7> bior$: 8:$;: 8C$C> ::$89 :8$7= 8C$77 => rbio$7 8$=C 8>$> 8;$=8 :9$C7 8C$=;
7 coif7 8=$ :8$>; :$; :>$C9 ::$9: = rbio$ 8$C> 8$9> 8;$9= ::$>> 8C$C
79 coifC 8$C> 8C$>; ::$7 :$9: 8;$8C =9 rbio$> 8>$8C 8>$C> 8;$88 :$C 8C$78
7: coif 8$;; 8C$9 ::$;> :$=> 8;$98 =: rbio$9 8$79 8$;; :8$:7 :$9; 8C$79
78 coif= 8$;; 8C$9 ::$= ::$: 87$> =8 rbio$8 89$C> 8>$9 87$;: ::$= 8$7
C; coif> 8=$=C 8=$C> ::$; ::$;> 87$C> >; rbio=$= 8$>: 8$9> :8$7= :9$8 87$:
C7 dmey 8$: 8>$ :$9: :8$> 8C$7> >7 rbio>$> 89$>; 8$79 ::$:8 :>$7; 87$7
CC 3aar :8$79 :8$79 :=$:> 98$97 :>$9C >C rbio$: 89$=C 8$ ::$:; ::$; 87$8
C D07 :8$79 :8$79 :=$:> 98$97 :>$9C > symC 8>$;: ::$>: :=$8 :$>8 ::$;>
C= D0C 8>$;: ::$>: :=$8 :$>8 ::$;> >= sym 8>$>: 8C$> ::$>> :>$78 8;$=
C> D0 8>$>: 8C$>; ::$>> :>$78 8;$= >> sym= 8$79 8=$9> ::$:; :>$8= 8;$9
C D0= 8>$=C 8$9> :$8> :=$9 8;$CC > sym> 8$>: 8>$8C :9$ :8$7 8C$
C9 D0> 8=$79 8$;; :=$ :9$98 :8$:8 >9 sym 8>$8C 8=$9 :9$8 :9$:: 87$7
C: D0 8$;: 8=$=C :$=> :$ 8;$: >: sym9 8$79 8>$;: :8$9 :>$8 87$9
C8 D09 8>$: 8$>; :>$99 :$ 8;$9 >8 sym: 8$>; 8=$79 :8$> :8$8: 8C$>>
; D0: 8$C> 8$=C :$C: :$9; 8;$
lassification efficienc( for the 0avelet energ( features - Vibration signal for $& fault classes3/12/16 123
Selection of 0avelet"#'%S =o 5avelet
!lassification Efficiency B
S =o 5avelet
!lassification Efficiency B
S d /:: S d ;:: S d
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S*=o 5avelet S*=o 5aveletSpeed /::
rpm
Speed ;::
rpm
Speed 7 D08 8;$=C 8C$> :9$;: :$> :8$7
C bior7$ 87$8C 87$C> :$8C :$C> ::$ C D07; 8C$;: 8C$79 :$C> :: :8$
bior7$> 87$> 8;$C> :9$;: :$79 :: D077 :8$> 8;$C> :9$=C :8$ :8$7
= biorC$C :: :>$;: :7$9> :;$=C :$:7 = D07C :8$ 87$> :$;: ::$=C ::$:
> biorC$= 8C 87$9 :8$9> :>$79 :8$> > D07 87$ 87$>: :=$79 :8$8C :8$C>
biorC$ 8C$79 8;$=C :$C> :>$79 ::$> D07= ::$ :8$>: := :8$: :9$8=
9 biorC$: 8C :8$>: :: :=$=C ::$> 9 D07> ::$8C :8$C> :$8C :8$>: :9$8C
: bior$7 >8 >7$> =9$9 >:$ >=$7 : rbio7$7 87$C> :9$;: ::$79 ::$;: ::$>
8 bior$ :9 :$ 98$=C :=$9> :$ 8 rbio7$ 87$: 87$ :$;: :C :9$:7
7; bior$> 87$: :8$: :>$> :$> ::$=C =; rbio7$> 87$>: :8$: :=$: :C$8C :9$C8
77 bior$9 8C$8C 8;$: ::$C> :$ :8$>: =7 rbioC$C 8 8C$C> :8$;: :9$> 8;$=
7C bior$8 8C$ 87 :9$9> :=$> ::$8 =C rbioC$= 8;$9 8C$ :$8C :$9> :8$79
7 bior=$= 8;$>: 8;$: :$9> :9$79 ::$: = rbioC$ 8;$=C 8;$> :>$9> :$79 ::$C77= bior>$> 8;$C> 8;$9> :=$9> :$9 ::$7 == rbioC$: 87 87$> :=$=C :: ::$9
7> bior$: 87$C> 8;$C> : ::$ ::$8 => rbio$7 8=$9 87$=C 8$;: 87$> 8C$9
7 coif7 87$;: 87$>: :$: :$=C ::$8: = rbio$ 8C$;: 87$8C :8 :8 8;$>
79 coifC 87$C> 8C :>$9> :$ ::$: =9 rbio$> :8$9 87$>: :$=C :9$9 ::$:
7: coif 87$> 87$=C :=$8C :$9> ::$> =: rbio$9 8;$ 87$79 :>$8C :$79 ::$=
78 coif= 8;$C> 8;$;: :$;: :9$> ::$=: =8 rbio$8 8;$9 8;$8C :> :$C> ::$C7
C; coif> ::$9 :8$>: :$;: :$9 :9 >; rbio=$= 8;$=C 87$ :9$ ::$=C :8$:
C7 dmey :9$> ::$8C :C :$> :$C >7 rbio>$> 8C$;: 87 :>$8C :9$>: :8$7>
CC 3aar 87$C> :9$;: ::$79 ::$;: ::$> >C rbio$: 87$9 8;$ :>$>: :9$9> ::$:
C D07 87$C> :9$;: ::$79 ::$;: ::$> > symC 87$>: 87$9> 8;$C> :>$>: :8$98
C= D0C 87$>: 87$9> 8;$C> :>$>: :8$98 >= sym 87$>: 87$;: ::$;: ::$79 :8$9
C> D0 87$>: 87$;: ::$;: ::$79 :8$9 >> sym= 8C$>: 8;$: :8$9> :9$8C 8;$C9
C D0= 8C$> 87$;: :=$=C :>$C> ::$7 > sym> 87$>: 8C$>: :$ :$;: :8$7>
C9 D0> 87$ 87$79 :>$9> :>$C> ::$: >9 sym 8C$> 8C$>: :9$: ::$9 8;$=
C: D0 8;$: 87$9> :$: :$79 ::$8 >: sym9 8C$=C 87$9> :$ :>$8C :8$7
C8 D09 :8$8C 87$79 :9$9 :9$C> :8 >8 sym: 87$8C 87$ :=$9> :9$9> ::$8=
; D0: 8;$ 8;$9> :$: :> ::$Classification efficienc( for the 0avelet energ( to entrop( features - Vibration signal for $& fault classes
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Selection of 0avelet"#.%Vibration signal for $& fault classes
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Ma4imum classification efficienc( of each 0avelet famil(
Vibration signal for $& fault classes
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Selection of 0avelet"#/%Vibration signal for &. fault classes
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Ma4imum classification efficienc( of each 0avelet famil(
Vibration signal for &. fault classes
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Selection of 0avelet"#?%Sound signal for $& fault classes
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Ma4imum classification efficienc( of each 0avelet famil(
Sound signal for $& fault classes
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Selection of 0avelet"#;%Sound signal for &. fault classes
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Ma4imum classification efficienc( of each 0avelet famil( -
Sound signal for &. fault classes
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Feature Selection"#$%Vibration signal for $& fault classes
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Decision tree representation using 'rbio3.9' 0avelet energ( features at /:: rpm
Vibration signal for $& fault classes
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Feature Selection"#&%Vibration signal for $& fault classes
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Decision tree representation using 'rbio3.9' 0avelet energ( features at ;:: rpm
Vibration signal for $& fault classes
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Feature Selection"#'%Vibration signal for $& fault classes
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Decision tree representation using 'rbio3.9' 0avelet energ( features at
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Decision tree representation using 'rbio3.9' 0avelet energ( features at $$:: rpm
Vibration signal for $& fault classes
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Feature Selection"#/%Vibration signal for $& fault classes
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Sl* =o =umber offeatures
Decision tree - lassification 3fficienc( >Mean
classification
efficienc( >Speed /::
rpm
Speed ;::
rpm
Speed 8>$9 8$;: 8=$=C 8>$:>
C : 89$C> 8>$: 8$=C 8$9> 8>$:7
9 89$79 8$;: 8$> 8$> 8>$:7
= 89$79 8>$8C 8$;: 8$79 8>$>8
> > 8$>; 8=$9 8>$>; 8;$9 8=$=
= 8$;: :8$ 8C$: 8;$79 8C$7;
9 8=$;: :8$79 8C$: :8$9> 87$=
: C 8;$ :>$79 :9$9 :>$> :9$79
8 7 7$;; >:$8C >C$>: =$>: >8$C9
7erformance of D2 using 'rbio3.6' 0avelet energ( features in dimensionalit( reduction
Vibration signal for $& fault classes
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Feature Selection"#?%Vibration signal for $& fault classes
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Dimensionalit( reduction of Erbio'*
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Dimensionalit( reductions of 'dmey' 0avelet energ( features
1 2 3 4 5 ! " #
4$.$$
45.$$
5$.$$
55.$$
$.$$
5.$$
!$.$$
!5.$$
Mean Classification Efficiency %
g
3/12/16 135
Feature Selection"#@%Sound signal for $& fault classes
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Dimensionalit( reduction of 'coif4' 0avelet energ( features
1 2 3 4 5 ! " #
45.$$
5$.$$
55.$$
$.$$
5.$$
!$.$$
!5.$$
"$.$$
"5.$$
#$.$$
#5.$$
Mean Classification Efficiency %
g
3/12/16 136
Feature Selection"#
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Dimensionalit( reduction of 'DB14' 0avelet energ( features
1 2 3 4 5 ! " #
35.$$
4$.$$
45.$$
5$.$$
55.$$
$.$$
5.$$
!$.$$
!5.$$
"$.$$
"5.$$
Mean Classification Efficiency %
g
3/12/16 137
Feature Selection"#$:%
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onditions 5avelet =umber of prominent features
7C fault conditions of vibration signal %bio$8 Six
C= fault conditions of vibration signal Dmey Five
7C fault conditions of sound signal !oif= Seven
C= fault conditions of sound signal D07= Six
est 0avelet and its number of prominent features
Fault classification B Decision 2ree"#$%Vibration signal for $& fault classes
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2esting 7arameterSpeed in rpm
Mean/:: ;::
2otal number of instances 7C;; 7C;; 7C;; 7C;; 7C;;
orrectl( classified
instances77 77>7 77> 777: 77=9
Misclassified instances = =8 =9 :C >
lassification efficienc( > 89$79 8>$8C 8$;: 8$79 8>$>8
Fault classification results of decision tree using si4 'rbio3.9' 0avelet energ( features
1393/12/16
g
Fault classificationBDecision2ree"#&%Vibration signal for $& fault classes
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a$ a& a' a. a/ a? a; a@ a< a$: a$$ a$&
a$
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Decision tree representation using si4 'rbio3.9' 0avelet energ( features at $$:: rpm
3/12/16 141
Fault classification B Decision 2ree"#.%Vibration signal for &. fault classes
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2esting 7arameter Speed in rpm Mean/:: ;:: ; = =; 9;8 >:9
lassification efficienc( > 99$8C :;$>: 9$ 9;$= 9>$>9
Fault classification results of decision tree using five 'dmey' 0avelet energ( features
3/12/16 142
Fault classificationBDecision 2ree"#/%Sound signal for $& fault classes
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2esting 7arameter Speed in rpm Mean/:: ;::
2otal number of instances 7C;; 7C;; 7C;; 7C;; 7C;;
orrectl( classified instances 7;; 77C8 777: 779 77CC
Misclassified instances 7= 97 :C C= 9:
lassification efficienc( > ::$:; 8=$77 8$7: 89$8: 8$>C
Fault classification results of decision tree using seven 'coif4' 0avelet energ( features
3/12/16 143
Fault classificationBDecision 2ree"#?%Sound signal for &. fault classes
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2esting 7arameter
Speed in rpm
Mean/:: ;::
2otal number of instances 7C;; 7C;; 7C;; 7C;; 7C;;
orrectl( classified instances C;: 7:8C C;; C7C; C;C
Misclassified instances 7= >;: 8= C:; 9=
lassification efficienc( > :$8C 9:$: :$>: ::$ :=$=C
Fault classification results of decision tree using si4 'DB14' 0avelet energ( features
3/12/16 144
Fault classification B SVM"#$%Vibration signal for $& fault classes
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2esting 7arameter Speed in rpm Mean/:: ;:: C$;7 8$C: C$C C9$;7
2otal number of instances 7C;; 7C;; 7C;; 7C;; 7C;;
orrectl( classified instances 77: 7799 77=8 77= 77>
Misclassified instances 7= C >7 >= >
lassification efficienc( > 8:$: 8>$9> 8:$;: 8>$> 89$;=
Fault classification results of support vector machine using
si4 'rbio3.9' 0avelet energ( features
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Fault classification B SVM"#&%Vibration signal for $& fault classes
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a$ a& a' a. a/ a? a; a@ a< a$: a$$ a$&
a$ $:: ; ; ; ; ; ; ; ; ; ; ;
a& ; $:: ; ; ; ; ; ; ; ; ; ;
a' ; ; ;; ; C ; ; ; ; ; ; ;
a. ; ; ;
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2esting 7arameter Speed in rpm Mean
/:: ;::
2otal number of instances C=;; C=;; C=;; C=;; C=;;
orrectl( classified instances 78: C; 7879 79 787:
Misclassified instances =79 = =: = =:C
lassification efficienc( > :C$ :=$: 98$:9> 9C$ 98$8C
Fault classification results of support vector machine using
five 'dmey' 0avelet energ( features
3/12/16 147
Fault classification B SVM"#.%Vibration signal for &. fault classes
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onfusion matri4 of support vector machine using five 'dmey' 0avelet energ( features
Fault classification B SVM"#/%Sound signal for $& fault classes
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2esting 7arameter Speed in rpm Mean/:: ;::
2otal number of instances 7C;; 7C;; 7C;; 7C;; 7C;;
orrectl( classified instances 777: 77:9 77:C 7788 779C
Misclassified instances :C 7 7: 7 >:
lassification efficienc( > 8$79 8:$8C 8:$>; 88$8C 89$
Fault classification results of support vector machine using
seven 'coif4' 0avelet energ( features
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Fault classification B SVM"#?%Sound signal for $& fault classes
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a$ a& a' a. a/ a? a; a@ a< a$: a$$ a$&
a$ $:: ; ; ; ; ; ; ; ; ; ; ;
a& ; $:: ; ; ; ; ; ; ; ; ; ;
a' ; ; $:: ; ; ; ; ; ; ; ; ;
a. ; ; ; $:: ; ; ; ; ; ; ; ;
a/ ; ; ; ; $:: ; ; ; ; ; ; ;
a? ; ; ; ; ; $:: ; ; ; ; ; ;
a; ; ; ; ; ; ; $:: ; ; ; ; ;
a@ ; ; ; ; ; ; ;
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2esting 7arameterSpeed in rpm
Mean
/:: ;:: C> CC 778 78
2otal number of instances C=;; C=;; C=;; C=;; C=;;
orrectl( classified instances C788 C;98 C7; CC= C7>:
Misclassified instances C;7 C7 C8= 7>= C=C
lassification efficienc( > 87$ :$C :9$9> 8$>: :8$8;Fault classification results of support vector machine using
si4 'DB14' 0avelet energ( features
3/12/16 151
Fault classification B SA"#$%Vibration signal for $& fault classes
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2esting 7arameter Speed in rpm Mean/:: ;:: 8$=9 $8= :$9C>
2otal number of instances 7C;; 7C;; 7C;; 7C;; 7C;;
orrectl( classified instances 7798 77 77=C 777; 77=:
Misclassified instances C7 9 >: 8; >C
lassification efficienc( > 8:$C> 8$8C 8>$79 8C$>; 8>$97
Fault classification results of clonal selection classification algorithm using
si4 'rbio3.9‘ 0avelet energ( features
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Fault classification B SA"#&%Vibration signal for $& fault classes
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a$ a& a' a. a/ a? a; a@ a< a$: a$$ a$&
a$ $:: ; ; ; ; ; ; ; ; ; ; ;
a& ; $:: ; ; ; ; ; ; ; ; ; ;
a' ; ; ?< ; 7 ; ; ; ; ; ; ;
a. ; ; 7
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2esting 7arameter Speed in rpm Mean/:: ;:: C:$7 C$>9
2otal number of instances C=;; C=;; C=;; C=;; C=;;
orrectl( classified instances 7=> 7>; 7=;; 7;8> 79;
Misclassified instances 8=9 :9; 7;;; 7;> 7;;
lassification efficienc( > ;$>= $9> >:$ =>$ >9$;
Fault classification results of clonal selection classification algorithm using
five 'dmey‘ 0avelet energ( features
3/12/16 154
Fault classification B SA"#.%Sound signal for $& fault classes
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2esting 7arameterSpeed in rpm
Mean/:: ;::
2otal number of instances 7C;; 7C;; 7C;; 7C;; 7C;;
orrectl( classified instances :8C 7;>; 7;99 77=> 7;=7
Misclassified instances ;: 7>; 7C >> 7>8
lassification efficienc( > 9=$ :9$= :8$9 8>$=> :$9=
Fault classification results of clonal selection classification algorithm usingseven 'coif4‘ 0avelet energ( features
3/12/16 155
Fault classification B SA"#/%Sound signal for &. fault classes
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2esting 7arameterSpeed in rpm
Mean
/:: ;:: 8$79 ;$9 >$87 >$: =>$>9
2otal number of instances C=;; C=;; C=;; C=;; C=;;
orrectl( classified instances 7>8 7=7 79C> 7: 7>:=
Misclassified instances 7;=7 8:= 9> >= :7
lassification efficienc( > >$ >8$;; 97$:: 9$> $;;
Fault classification results of clonal selection classification algorithm usingsi4 'DB14‘ 0avelet energ( features
3/12/16 156
Fault classification B 7SVM"#$%Vibration for $& fault classes
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Conditionlassification 3fficienc( >
/:: rpm ;:: rpm $= 87$= 7;; 7;;
, 7;; 7;; 7;; 7;;
- 7;; 7;; 7;; 88$77
/ 7;; 7;; 7;; 7;;
5 7;; 89$9C 7;; 7;;
1 7;; 7;; 7;; 7;;
2 7;; 7;; 89$; 7;;
3 7;; 7;; 7;; 7;;
4 7;; 7;; 7;; 7;;
* 7;; 7;; 7;; 7;;
** 7;; 7;; 7;; 7;;
Mean 88$; 88$; 88$9: 88$8CTime!sec# 77 8 8 7
Fault classification results of 7SVM using si4 'rbio3.9' 0avelet energ( features
3/12/16 157
Fault classification B 7SVM"#&%ondition
lassification 3fficienc( >
/:: rpm ;:: rpm $> 8>$> 8>$> 8>$>
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!7 8>$> 8>$> 8>$> 8>$>
!C 8>$=> 8>$=> 8>$=> 8>$=>
! 8>$C= 8>$C= 8>$C= 8>$C=
!= 8>$;; 8>$;; 8>$;; 8>$;;!> 88$>: 8=$9= 8=$9= 8=$9=
! 8=$== 8=$== 8=$== 8=$==
!9 8=$> 8=$> 8=$7C 8=$7C
!: 8$9> 8$9> 8$9> 8$9>
!8 8=$7 88$C; 8$:; 8=$=;
!7; 7;;$;; 7;;$;; 7;;$;; 7;;$;;
!77 8C$7 8C$7 8C$7 8C$7
!7C 7;;$;; 7;;$;; 7;;$;; 7;;$;;
!7 8$=> 88$= 8C$9 8C$;;
!7= 8:$;; 7;;$;; 88$; 7;;$;;
!7> 87$> 8>$77 8=$9 89$9:
!7 7;;$;; 7;;$;; 7;;$;; 7;;$;;
!79 7;;$;; :>$97 ::$>9 :>$97
!7: 8:$;; 7;;$;; 7;;$;; 7;;$;;
!78 88$C; 8$:; ::$;; 7;;$;;!C; 7;;$;; 7;;$;; 8:$;; 7;;$;;
!C7 8$;; 8;$9 :8$ 7;;$;;
!CC :$;; 9$;; :=$;; ;$;;
!C 9C$;; 9C$;; =$;; =$;;
Mean 8=$8 8=$7: 8$C 8$C=
'ime@secA >: >8 7 >9Fault classification results of 7SVM using five 'dmey' 0avelet energ( features B
Vibration signal for &. fault classes
1583/12/16
Fault classification B 7SVM"#'%
lassification 3fficienc( >
Sound signal for $& fault classes
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ondition
lassification 3fficienc( >
/:: rpm;::
rpm 7;; 89$
!= 7;; 7;; 7;; 7;;
!> 8>$= 7;; 88$= 8:$C8
! 7;; 7;; 7;; 7;;
!9 7;; 7;; 89$ 7;;
!: 7;; 7;; 7;; 7;;
!8 7;; 7;; 7;; 7;;
!7; 7;; 7;; 7;; 7;;
!77 7;; 7;; 7;; 7;;
Mean 88$=C 88$:8 88$8> 88$;
'ime@secA 7 77 7C 7;
Fault classification results of 7SVM using seven 'coif4' 0avelet energ( features
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Fault classification B 7SVM"#.%ondition
lassification 3fficienc( >
/:: rpm ;:: rpm $> 8>$> 8>$> 8>$>
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!C 8>$=> 8>$=> 8>$=> 8>$=>
! 8>$C= 8>$C= 8$78 7;;$;;
!= 8>$; 8:$C; 7;;$;; 7;;$;;!> 8=$9= 8=$9= 8$C7 8=$9=
! 8=$== 8=$== 8=$== 8=$==
!9 8=$7C 8=$7C 8=$7C 8=$7C
!: 8$9> 8$9> 8$9> 8$9>
!8 8$ 8$ 8$ 8$
!7; 8C$: 8C$: 89$7= 8=$:
!77 8C$7 8C$7 8C$7 8C$7
!7C 8C$ 87$9 7;;$;; 7;;$;;
!7 8:$>> 8>$C9 8$9 8=$7:
!7= 88$; 7;;$;; 8:$:; 88$C;
!7> ::$:8 ::$:8 ::$:8 :8$
!7 7;;$;; 7;;$;; 7;;$;; 7;;$;;
!79 7;;$;; 8:$: 8>$= :8$7=
!7: 88$ 7;;$;; 7;;$;; 7;;$;;
!78 7;;$;; :9$C; 8C$:; 8$:;
!C; 88$;; 7;;$;; 7;;$;; 7;;$;;
!C7 7;;$;; :C$9 8C$;; 7;;$;;
!CC 7;;$;; 8=$;; 8:$;; 7;;$;;
!C 7;;$;; 7;;$;; 7;;$;; 7;;$;;
Mean 8$7 8=$9C 8$7= 8$=;
'ime@secA 9> >8 77: 9CFault classification results of 7SVM using si4 'DB14' 0avelet energ( features B
Sound signal for &. fault classes
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Fault classification using 0avelet features
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lassification
algorithm
Mean lassification 3fficienc( >
Vibration Signals Sound Signals
$& classes &. classes $& classes &. classes
D2 8>$>8 9>$>9 8$>C :=$=C
SVM 89$;= 98$8C 89$ :8$8;
SA 8>$97 >9$; :$9=
7SVM 88$>: 8$8 88$9C 8>$:8
Mean classification efficienc( of the classification algorithm using 0avelet features
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Major ontributions
Major ontributions"#$%
+ll the critical rotating elements such as shaft rotor bearing and gear with
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+ll the critical rotating elements such as shaft# rotor# bearing and gear with
twenty four fault conditions were considered in this study$
'he sound based automated fault diagnosis was well explored in this study$
'he behavior of statistical features and wavelet features of the sound
signals were studied in detail$
'he sound and vibration based fault diagnosis were studied and compared$
'he sound signal based fault diagnosis is better than vibration signal whendiscrete wavelet energy features are used$
Major ontributions"#&% 'he classification algorithm results showed that the difficulty in
id tifi ti f f lt d th ti t & i d h th b
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identification of faults and the time ta&en are increased when the number
of components or fault classes increases$
'he classification accuracy of classifier using wavelet energy features was
improved when compared to the statistical features in both sound and
vibration signals$
'he use of three dimensionality reduction techni)ues such as decision tree#
principal component analysis and independent component analysis on
rotating machine fault diagnosis was discussed and compared in this
research wor&$
Major ontributions"#'% 'he decision tree algorithm was extensively used for selection of wavelet#
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choosing the optimum number of prominent features and classification of
the faults$
'he "erformance of c-S,! model with the %0F &ernel function in support
vector machine is better than nu-S,! and other &ernel functions$
'he clonal selection classification algorithm was used as a classifier in
machinery fault diagnosis$ 'he !S!+ is not very efficient in multi
component fault diagnosis of rotating machine.
"S,M effectively classify the C= fault classes using wavelet features of
both sound and vibration signals within a short period$
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onclusion
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onclusion"#&% 'he following features were used in this study
Statistical features
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Statistical features
avelet energy features and
avelet energy to entropy features
'he dimensionality reduction techni)ues such as Decision 'ree @D'A#
"rincipal !omponent +nalysis@"!+A and Independent !omponent
+nalysis@I!+A were used for feature selection in fault diagnosis using
statistical features$
168
onclusion"#'%
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'he selected features were used for classification of faults$
'he classifiers used in the present wor& are
Decision 'ree @D'A#
Support ,ector Machine @S,MA#
!lonal selection classification algorithm @!S!+A and"roximal support vector machine @"S,MA$
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onclusion"#.%
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Mean classification efficienc( of the classifier using
statistical features and 0avelet features
lassifier
Mean lassification 3fficienc( >
Vibration signals Sound signals
$& classes &. classes $& classes &. classes
Statistical
Features
5avelet
Features
Statistical
Features
5avelet
Features
Statistical
Features
5avelet
Features
Statistical
Features
5avelet
Features
D2 8:$;7 8>$>8 :7$C: 9>$>9 9>$; 8$>C C$8 :=$=C
SVM 88$7C 89$;= :=$>7 98$8C :C$: 89$ =7$7 :8$8;
SA :$8: 8>$97 >$8> >9$; >;$: :$9= - $;;
7SVM 89$;; 88$>: 8$:> 8$8 8>$7 88$9C 8$:7 8>$:8
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onclusion"#/% 'he "S,M with discrete wavelet energy features was selected as a best
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feature-classifier pair to automate the multi component fault diagnosis of
rotating machine using both sound and vibration signals.
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Scope for Future 5or1"#$% 'he features such as wavelet pac&et features and fractal analysis may
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increase the classification ability of the machine learning algorithm$
'he &ernel principal component analysis# factor analysis# fisherJs linear
discriminant analysis can be tried out for dimensionality reduction$
'he gene expression programming# 3idden Mar&ov model etc$# may be
used to increase the classification efficiency for the large number of fault
classes$
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Scope for Future 5or1"#&% 'he development of new classification algorithm for machinery fault
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diagnosis$
'he machine learning process can be tried with feature fusion or decision
fusion of sound and vibration signals$
'he portable hardware &it can be fabricated using best feature-classifier for
the automated fault diagnosis$
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