automated fault diagnosis

8/19/2019 Automated Fault Diagnosis

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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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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("*#&%


?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("*#'%


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("*#.%


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("*#/%


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$


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$


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

48

Application of Decision 2ree"#&%


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Vibration signals for $& fault classes at Speed


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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


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


!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


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


1 2 3 4 5 ! " # 1$ 1135.$$

4$.$$

45.$$

5$.$$

55.$$

$.$$

5.$$

!$.$$

!5.$$

"$.$$

"5.$$



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


1 2 3 4 5 ! " # 1$ 115$.$$

55.$$

$.$$

5.$$

!$.$$

!5.$$

"$.$$



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


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


1 2 3 4 5 !3$.$$

4$.$$

5$.$$

$.$$

!$.$$

"$.$$

#$.$$

1$$.$$


lassification efficienc( of D2 0ith 7A in dimensionalit( reduction

62

Application of 7A #'%


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Application of 7A"#'%

3/12/16



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



1 2 3 4 5 !3$.$$

35.$$

4$.$$

45.$$

5$.$$

55.$$

$.$$

5.$$

!$.$$

!5.$$

"$.$$


64

Application of 7A #/%


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Application of 7A"#/%

3/12/16



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"#;%

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1 2 3 4 5 ! "

4$.$$

45.$$

5$.$$

55.$$

$.$$

5.$$

!$.$$


66

Application of 7A #@%


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Application of 7A"#@%

3/12/16

Sound signals for &. fault classes


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

3/12/16 70

Application of !A #&%


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Application of !A"#&%

1 2 3 4 5 !3$.$$

4$.$$

5$.$$

$.$$

!$.$$

"$.$$

#$.$$

1$$.$$


lassification efficienc( of D2 0ith !A in dimensionalit( reduction


3/12/16 71

Application of !A #'%


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Application of !A"#'%


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 #.%


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Application of !A"#.%

1 2 3 4 5 ! "1$.$$

2$.$$

3$.$$

4$.$$

5$.$$

$.$$

!$.$$

"$.$$




3/12/16 73

Application of !A #/%


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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 ; ; ; ;


Sound signal for $& fault classes

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Application of !A #?%


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Application of !A"#?%


1 2 3 4 5 !1$.$$

2$.$$

3$.$$

4$.$$

5$.$$

$.$$

!$.$$



3/12/16 75

Application of !A #;%


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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-

; ; ; ;


Sound signal for &. fault classes

3/12/16 76

Application of !A #@%


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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


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Selection of dimensionalit( reduction techni)ue"#$%


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( ) # %

omparison of dimensionalit( reduction techni)ues


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Selection of dimensionalit( reduction techni)ue"#&%


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( ) # %

'he five most discriminating ability features are

7$ Standard error#

C$ Sample variance#

$ Median#

=$ Standard deviation and

>$ S&ewness$


Selection of dimensionalit( reduction techni)ue"#'%


80/174

( ) # %



3/12/16 80

Selection of dimensionalit( reduction techni)ue"#.%


81/174

( ) # %

'he four most discriminating ability features are

7$ S&ewness#

C$ Standard error#

$ Minimum and

=$ Median$


Selection of dimensionalit( reduction techni)ue"#/%


82/174

( ) # %



3/12/16 82

Selection of dimensionalit( reduction techni)ue"#?%


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$


Fault classification


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"#$%


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


3/12/16 85

Fault lassification - Decision tree"#&%


86/174

Fault lassification Decision tree"#&%

a$ a& a' a. a/ a? a; a@ a< a$: a$$ a$&

a$


87/174

Fault lassification Decision tree"#'%


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:



3/12/16 87

Fault lassification - Decision tree"#.%


88/174

# %

onfusion matri4 of decision tree at $$:: rpm -


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"#/%


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$8C 9>$;



3/12/16 89

Fault lassification - Decision tree"#?%


90/174

Fault lassification Decision tree"#?%

a$ a& a' a. a/ a? a; a@ a< a$: a$$ a$&

a$


91/174

Fault lassification Decision tree"#;%


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



3/12/16 91

Support Vector Machine"#$%


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"#&%


93/174

pp # %

3/12/16 93

Support Vector Machine"#'%


94/174

pp # %

3/12/16 94

Support Vector Machine"#.%


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"#/%


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"#$%


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


3/12/16 97

Fault lassification B SVM"#&%


98/174


2otal number of


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


3/12/16 98

Fault lassification B SVM"#'%


99/174

onfusion matri4 of SVM at $$:: rpm


3/12/16 99

a$ a& a' a. a/ a? a; a@ a< a$: a$$ a$&

a$ $:: ; ; ; ; ; ; ; ; ; ; ;

a& ; $:: ; ; ; ; ; ; ; ; ; ;

a' ; ;


100/174


Mean/:: ;:: = 7C C7; 77 78$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



3/12/16 100

Fault lassification B SVM"#/%


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 -


Fault lassification B SVM"#?%


102/174

# %

2esting 7arameter Speed in rpm Mean/:: ;:: C ==$9

2otal number of


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>



3/12/16 102

Fault lassification B SVM"#;%


103/174

a$ a& a' a. a/ a? a; a@ a< a$: a$$ a$&

a$


104/174


Mean/:: ;:: ;C C9: :


orrectl( classified instances 779 :9C 8=; 7;;8 888

Misclassified instances 7CC9 7>C: 7=; 787 7=;7

lassification efficienc( > =:$:: $ 8$79 =C$;= =7$;



3/12/16 104

lonal Selection lassification Algorithm


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 "#$%


106/174


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


3/12/16 106

Fault lassification B SA "#&%


107/174

a$ a& a' a. a/ a? a; a@ a< a$: a$$ a$&

a$ $:: ; ; ; ; ; ; ; ; ; ; ;

a& ; $:: ; ; ; ; ; ; ; ; ; ;

a' ; ;


108/174


Mean/:: ;::


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>



3/12/16 108

Fault lassification B SA "#.%


109/174

2esting 7arameter Speed in rpm Mean

/:: ;:: $97 7;$; :$99 7;$;> :$=


orrectl( classified instances =>C >> : >; 7;

Misclassified instances 9=: >=> >79 >>; >8;

lassification efficienc( > 9$9 >=$>: >$8C >=$79 >;$:



3/12/16 109

7ro4imal Support Vector Machine


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 "#$%


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 "#&%


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


3/12/16112

Fault lassification B 7SVM "#'%


113/174

ondition


/:: 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


Fault classification results of 7SVM

Fault lassification B 7SVM "#.%S i f $& f


114/174

ondition


/:: 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



3/12/16 114

Fault lassification B 7SVM "#/%Sound signal for &. fault classes


115/174

ondition


/:: 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



3/12/16 115

Fault diagnosis using statistical features


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


117/174

Fault Diagnosis using

5avelet Features

5avelet features"#$%


118/174

7rocedure of four level 0avelet decomposition #9ao and an6 &:$$%

3/12/16 118

5avelet features"#&%


119/174

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&$

3/12/16 119

5avelet features"#'%


120/174

'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

3/12/16 120

Fault Diagnosis using 5avelet featuresF t t ti


121/174

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"#$%


122/174

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


S = 5 l t



123/174

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


124/174

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

3/12/16 124

Selection of 0avelet"#.%Vibration signal for $& fault classes


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Ma4imum classification efficienc( of each 0avelet famil(


3/12/16 125

Selection of 0avelet"#/%Vibration signal for &. fault classes


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3/12/16 126

Selection of 0avelet"#?%Sound signal for $& fault classes


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3/12/16 127

Selection of 0avelet"#;%Sound signal for &. fault classes


128/174

Ma4imum classification efficienc( of each 0avelet famil( -


3/12/16 128

Feature Selection"#$%Vibration signal for $& fault classes


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Decision tree representation using 'rbio3.9' 0avelet energ( features at /:: rpm


3/12/16 129

Feature Selection"#&%Vibration signal for $& fault classes


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Decision tree representation using 'rbio3.9' 0avelet energ( features at ;:: rpm


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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


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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


3/12/16 133

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.$$


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.$$


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.$$


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


139/174


Mean/:: ;::


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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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/:: ;::


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


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

3/12/16 145

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

/:: ;::


orrectl( classified instances 78: C; 7879 79 787:

Misclassified instances =79 = =: = =:C

lassification efficienc( > :C$ :=$: 98$:9> 9C$ 98$8C


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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orrectl( classified instances 777: 77:9 77:C 7788 779C

Misclassified instances :C 7 7: 7 >:

lassification efficienc( > 8$79 8:$8C 8:$>; 88$8C 89$


seven 'coif4' 0avelet energ( features

3/12/16 149

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@ ; ; ; ; ; ; ;


151/174


Mean

/:: ;:: C> CC 778 78


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>


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

3/12/16 152

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


154/174

2esting 7arameter Speed in rpm Mean/:: ;:: C:$7 C$>9


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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Mean/:: ;::


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


156/174


Mean

/:: ;:: 8$79 ;$9 >$87 >$: =>$>9


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


/:: 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


1583/12/16

Fault classification B 7SVM"#'%




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ondition


/:: 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

3/12/16 159

Fault classification B 7SVM"#.%ondition


/:: 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


3/12/16 160

Fault classification using 0avelet features


161/174

lassification

algorithm


Vibration Signals Sound Signals


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

3/12/16 161


162/174

Major ontributions

Major ontributions"#$%

+ll the critical rotating elements such as shaft rotor bearing and gear with


163/174

+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$


166/174

onclusion


167/174

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$

3/12/16 169

onclusion"#.%


170/174

Mean classification efficienc( of the classifier using

statistical features and 0avelet features

lassifier


Vibration signals Sound signals


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

3/12/16 170

onclusion"#/% 'he "S,M with discrete wavelet energy features was selected as a best


171/174

feature-classifier pair to automate the multi component fault diagnosis of

rotating machine using both sound and vibration signals.

3/12/16 171

Scope for Future 5or1"#$% 'he features such as wavelet pac&et features and fractal analysis may


172/174

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$

3/12/16 172

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$

3/12/16 173


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2han1 ou

automated fault diagnosis

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