Condition monitoring and fault diagnosis of induction machine using artificial intelligence methods and empirical mode decomposition

L IST OF S YMBOLS &A CRONYMSa i: non-zero Lagrange multipliers BMU: Best Matching Unit of SOM b o: SVM bias BRG: Bearing fault BRB: Broken rotor bar C: slack factor of SVM D b: is the

ACKNOWLEDGEMENT

I would like to convey my most sincere thanks to my project supervisors, Prof Xu Jianxin and A/Prof Sanjib Kumar Panda for their encouragement and advices Their profound knowledge and experiences in the field of machine learning techniques and machine system are my source of inspiration I also appreciate the opportunity to work in the field of Empirical Mode Decomposition, which is the most versatile and powerful signal processing tool I have read

I would like to thank Mr Woo Ying Chee and Mr Mukaya Chandra from the Electrical Machine and Drives Laboratory, who helped in setting up the Machine Fault Simulator, DAQ measurement systems and preparing workstations for MATLAB simulations used in the project, and their help in booking meeting room for project briefing

Lastly, I would like to thank Dr N Rehman and Dr D.P Mandic for making the Noise-Assisted Multi-variate Empirical Mode Decomposition MATLAB code publicly

available at http://www.commsp.ee.ic.ac.uk/~mandic/research/emd.htm, and Dr G Rilling and Dr P Flandrin for making the mono-variate Empirical Mode Decomposition

MATLAB code publicly available at http://perso.ens-lyon.fr/patrick.flandrin/emd.html

T ABLE OF C ONTENTS

CHAPTER 1:INTRODUCTION 1

1.1 Objectives 2

1.2 Thesis Organization 3

1.3 Fault Mode Statistics Survey 6

1.4 Literature Survey 8

1.4.1 Vibration Signature Analysis 8

1.4.2 Motor Current Signature Analysis 9

CHAPTER 2:MECHANICS OF MACHINE FAULT MODES 14

2.1 Eccentricity 15

2.1.1 Static Eccentricity 15

2.1.2 Dynamic Eccentricity 16

2.1.3 Mixed Eccentricity Motor Current Signature 17

2.2 Unbalanced Rotor Fault 18

2.2.1 Unbalanced Rotor Fault Motor Current Signature 20

2.3 Bearing Faults 20

2.3.1 Bearing Faults Vibration Signatures 22

2.3.2 Bearing Faults Motor Current Signatures 25

2.4 Bearing General Roughness 26

2.5 Broken Rotor Bar Motor Current Signature 27

2.6 Shorted Stator Winding Fault Motor Current Signature 28

2.7 Healthy Machine Signature 29

2.8 Dynamic Estimation of the Machine Slip 30

CHAPTER 3:MOTOR CURRENT SIGNATURE AND VIBRATION SIGNATURE ANALYSIS 32

3.1 Motor Current signal Analysis or Vibration Analysis? 32

3.2 Challenges of Motor Current Signature Analysis 33

3.3 Discussions: Proposed Ensemble Spectrum Approach 35

CHAPTER 4:ARTIFICIAL INTELLIGENCE TECHNIQUES FOR MACHINE FAULT DIAGNOSIS 37

4.1 k-Nearest Neighbour (k-NN) 37

4.1.1 k-NN Algorithm 38

4.2.1 Structure and Operation of SOM 39

4.2.2 SOM Algorithm 41

4.3 Support Vector Machine (SVM) 42

4.3.1 Multi-Class SVM (M-SVM) 44

4.3.2 M-SVM Algorithm 45

4.4 Empirical Mode Decomposition (EMD) 46

4.4.1 EMD Algorithm 47

4.4.2 Mode Mis-alignment 48

4.4.3 Multi-variante EMD 57

4.4.4 Mode Mixing 57

4.4.5 Noise-assisted Multi-variate EMD (N-A M-EMD) 57

CHAPTER 5:ASTUDY ON AUTOMATIC DIAGNOSIS OF BEARING AND UNBALANCED ROTOR FAULTS 59

5.1 Fault Diagnosis using Time-Domain Vibration Signatures 59

5.1.1 Similarity measures by Cross-Correlation Operator 60

5.2 Machine Fault Simulator 66

5.3 Machine Signatures Collection 69

5.4 Experimental Results 70

5.5 Discussions: Difficulty in choosing a suitable value for k 71

5.6 Discussions: Larger Training Samples 72

5.7 Visualization of Classification Results by k-NN 72

5.8 Fault Diagnosis using Frequency-Domain Vibration Signatures 75

5.8.1 Discrete Wiener Filter 76

5.8.2 Frequency Analysis of Vibration Signatures 78

5.8.2.1 Frequency content of Healthy Machine 78

5.8.2.2 Frequency content of Unbalanced Rotor fault 78

5.8.2.3 Frequency content of Bearing fault 78

5.8.2.4 Discussion on vibration frequency analysis 78

5.8.3 Feature Extraction of Frequency domain information 83

5.8.4 Cluster Analysis of Vibration Feature Vectors 84

5.8.5 Further Feature Extraction 85

5.8.6 Multi-class SVM (M-SVM) for Classifying Machine Fault Data 86

5.9 Discussions: Frequency-domain Analysis of Vibration Signatures 88

CHAPTER 6:ASTUDY ON MOTOR CURRENT SIGNATURE USING EMPIRICAL MODE DECOMPOSITION 89

6.1 Fourier Transform 89

6.2 Wavelet Transform 91

6.3 Hilbert-Huang Transform 92

6.3.1 Hilbert Spectrum 93

6.3.2 Marginal Hilbert Spectrum 94

6.4 Discussion: EMD as a suitable Analysis Tool 94

6.5 N-A M-EMD Experiment Results 95

6.5.1 Discussions: IMF Derived by EMD 97

6.5.2 Discussions: Filter-bank Property of EMD Algorithm 99

6.5.3 Discussions: Significance of IMF1, IMF2, IMF3, IMF4 101

6.5.4 Discussions: Significance of IMF10, IMF11 103

6.5.5 Discussions: Significance of IMF5, IMF6, IMF7, IMF8, IMF9 104

6.6 Visualization of the Comparison results by SOM 107

6.7 Discussions: Discovery of Unique Features by SOM 107

CHAPTER 7:CONCLUSION 111

REFERENCES 113

APPENDIX A:INTRINSIC MODE FUNCTIONS DERIVED BY N-AMEMDALGORITHM FOR MACHINE SPEED AT 20HZ 124

APPENDIX B:HILBERT SPECTRUM AND MARGINAL HILBERT SPECTRUM OF MACHINE SIGNATURE (AT MACHINE SPEED OF 20HZ)INTRINSIC MODE FUNCTION 5 TO 9 131

APPENDIX C:PSEUDO CODE FOR 2-CLASS SVM LEARNING 135

APPENDIX D:PSEUDO CODE FOR MULTI-CLASS SVM LEARNING 140

APPENDIX E:PSEUDO CODE FOR SOM LEARNING 147

APPENDIX F: PSEUDO CODE FOR K-NN LEARNING 160

S UMMARY

Induction machine are used widely in industrial process e.g., steel mills, chemical plants etc it is therefore vital to condition monitor the health of the machine to prevent unexpected and untimely failure Their untimely downtime have significant economic and social impact, such as, disruption to production process, spoilage to work-in-progress, costly plant process re-start etc It is therefore useful to investigate automatic machine fault detection and diagnosis techniques This creates the motivation for this study Why condition monitoring? Incipient machine faults can be detected by continuous monitoring [1] As such, condition-based maintenance has become a new maintenance methodology that has rapidly been adopted by the industry as the standard operating procedure In the past, it is essentially a routine periodic machine shutdown for servicing and inspection This method has proved to be inefficient In condition-based maintenance, the machine is carefully and continuously condition monitored for symptoms of failure Based on such continuous tracking of the machine health-states, imminent failures is detected and planned shutdown made, only when necessary This way, machine downtime and maintenance costs are reduced, and asset security and reliability increased, both achieving efficiency and profitability for the organization With this in view, this project investigates the various machine condition monitoring techniques, with the objective to implement effective automatic fault detection and diagnosis methods, to reveal developing incipient faults, so that timely intervention is made to prevent sudden catastrophic failures

L IST OF T ABLES

Table 1.1: Summary of percentage of each of the failure mode 6

Table 1.2: Fault statistics on 8 surveyed articles (*MC denotes Most Common fault) 7

Table 1.3: Percentage of each of the failure mode derived from Table 1.2 7

Table 5.1: Similarity Measure for v 1 , v 2 and v 3 66

Table 5.2: Training and test sets for k-NN classification 69

Table 5.3: Fault classification confusion matrix 70

Table 5.4: Classification result summary 70

Table 5.5: Tabulated results of error rate (%) with various k-neighbor values 71

Table 5.6: Distribution of spectrum of machine vibration signatures 83

Table 5.7: Fault classification confusion matrix of vibration signature 87

Table 5.8: M-SVM classification of vibration signatures result summary 88

Table 6.1: Similarity measures of same-indexed pair of machine current IMFs at 20Hz 98 Table 6.2: Similarity measures of same-indexed pair of machine current IMFs at 30Hz 98 Table 6.3: Similarity measures of same-indexed pair of machine current IMFs at 40Hz 98 Table 6.4: Frequency band for HTY30 (IMF 5-9) machine current signature 100

L IST OF F IGURES

Figure 1.1: Approaches of this project to investigate machine fault diagnosis 13

Figure 2.1: Perturbation force (Fc) created by unbalanced mass (m) rotating at Ω 19

Figure 2.2: Unbalanced rotor fault signatures at various machine speeds 19

Figure 2.3: Bearing assembly 21

Figure 2.4: Defective rolling elements (adopted from [93]) 21

Figure 2.5: Raceway faults (adopted from [93]) 22

Figure 2.6: Rolling element pitch, diameter and contact angle of a bearing 23

Figure 2.7: Rolling element fault signatures at various machine speeds 24

Figure 2.8: Inner raceway fault signatures at various machine speeds 24

Figure 2.9: Outer raceway fault signatures at various machine speeds 25

Figure 2.10: Healthy machine signatures at various machine speeds 29

Figure 4.1: Connections between the input and output neurons of SOM 39

Figure 4.2: Linear decaying learning rate versus learning steps of a SOM 40

Figure 4.3: Support vectors, decision boundary and margin of 2-class SVM 43

Figure 4.4: Multi-class SVM using one-versus-all learning strategy 45

Figure 4.5: Mono-variate EMD of BRG signature 49

Figure 4.6: Mono-variate EMD of UBR signature 50

Figure 4.7: Mono-variate EMD of HTY signature 51

Figure 4.8: Extremum of two signals x 1 (t) and x 2 (t) 52

Figure 4.9: Mean of 3D ―tube‖ of complex signal signals zb (t) 53

Figure 4.10: Evolution of bi-variate complex signal for (|HTY40(t)|,|BRG40(t),t) 53

Figure 4.11: Mean of complex signal signals zt (t) 54

Figure 4.12: Evolution of tri-variate complex signal for (|HTY40(t)|,|BRG40(t)|,|BRB40(t)|) 55

Figure 4.13: Mode mixing 56

Figure 4.14: N-A M-EMD on signal with Guassian white noise added 58

Figure 5.1: Template matching using cross-correlation of machine signatures 60

Figure 5.2: Deterministic signals v 1 (t), v 2 (t) and v 3 (t) 61

Figure 5.3: Normalized cross-correlation sum coefficients of a pair signature 64

Figure 5.4: Machinery Fault Simulator (MFS) by SpectraQuest®, Inc 66

Figure 5.5: Schematic of machine signature acquisition using DAQ by Dewetron® 67

Figure 5.6: Bearing fault simulation using MFS 68

Figure 5.7: Unbalanced rotor fault simulation using MFS 68

Figure 5.8: Error rate (%) versus k-neighbor values 71

Figure 5.9: Unbalanced rotor fault misclassified as healthy machine 73

Figure 5.10: Healthy machine signatures correctly classified 73

Figure 5.12: Unbalanced rotor signature correctly classified 75

Figure 5.13: Wiener Filter 77

Figure 5.14: Filtered machine signatures at f r=15Hz and 31Hz 77

Figure 5.15: Frequency content of HTY signatures at f r=15Hz 79

Figure 5.16: Frequency content of HTY signatures at f r=31Hz 79

Figure 5.17: Frequency content of UBR signatures at f r=16Hz 80

Figure 5.18: Frequency content of UBR signatures at f r=32Hz 80

Figure 5.19: Frequency content of BRG signatures at f r=15Hz 81

Figure 5.20: Frequency content of BRG signatures at f r=32Hz 82

Figure 5.21: 11-dimensional feature vector at f r=15Hz and 31Hz 84

Figure 5.22: Semantic map of vibration signatures from two SOM different simulations 85

Figure 5.23: 2-dimensional feature vector 86

Figure 5.24: M-SVM classification (Gaussian kernel h svm =8.0, slack factor C=0.1) of vibration signature 87

Figure 6.1: Fourier Series (a finite sum of a 10Hz square wave with n=3 and n=10) 90

Figure 6.2: Different wavelet basis functions 92

Figure 6.3: A 7-channel Motor Current Signature decomposition by N-A MEMD 96

Figure 6.4: EMD as filter-banks for HTY30 (IMF 5 – 9) machine current signature 99

Figure 6.5: IMF1, IMF2, IMF3, IMF4 of the machine signatures at 20Hz 101

Figure 6.6: IMF1, IMF2, IMF3, IMF4 of the machine signatures at 30Hz 102

Figure 6.7: IMF1, IMF2, IMF3, IMF4 of the machine signatures at 40Hz 102

Figure 6.8: IMF10 and IMF11 (residue) of the machine signatures at 20Hz 103

Figure 6.9: IMF10 and IMF11 (residue) of the machine signatures at 30Hz 103

Figure 6.10: IMF10 and IMF11 (residue) of the machine signatures at 40Hz 103

Figure 6.11: IMF5-9 of the HTY machine signatures at 20Hz 104

Figure 6.12: IMF5-9 of the BRG machine signatures at 20Hz 105

Figure 6.13: IMF5-9 of the BRB machine signatures at 20Hz 105

Figure 6.14: IMF5-9 of the UBR machine signatures at 20Hz 106

Figure 6.15: IMF5-9 of the SWF machine signatures at 20Hz 106

Figure 6.16: Feature map using fea_IMF vector at fs=20Hz 108

Figure 6.17: Feature map using fea_IMF vector at fs=30Hz 109

Figure 6.18: Feature map using fea_IMF vector at fs=40Hz 110

L IST OF S YMBOLS &A CRONYMS

a i: non-zero Lagrange multipliers

BMU: Best Matching Unit of SOM

b o: SVM bias

BRG: Bearing fault

BRB: Broken rotor bar

C: slack factor of SVM

D b: is the diameter of the rolling element

D c: is the rolling element pitch

d i , d j: data label for OVA learning strategy for M-SVM

"EMD": Empirical Mode Decomposition

f r: rotor frequency

F R: rotor mechanical frequency

f s: fundamental supply frequency

g 0: radial air-gap length in the case of a uniform air-gap

h svm: Guassian kernel width

h: inverter harmonic order

HTY: healthy machine

IMF: Intrinsic Mode Function

i sD: instantaneous values of direct-axis component of monitored stator current

i sQ: instantaneous values of quadrature-axis component of the monitored stator current k-NN: k-Nearest Neighbor

L m: three-phase magnetizing inductance

L r: three-phase self-inductance of the rotor winding

L s ’

: stator transient inductances

m: rotor unbalanced mass

MFS: machine fault simulator

MMF: magneto motive force

MCSA: Motor Current Signature Analysis

M-SVM: multi-class Support Vector Machine

N: is the number of rotor bars

N B: is the number of rolling elements

n d: eccentricity order number, (static eccentricity=0, dynamic eccentricity=1)

N-A MEMD: noise-assisted MEMD

OVA: one-versus-all learning strategy for M-SVM

P: number of pole-pairs

P 0: average air-gap permeance

r: distance between the centre of rotation and the centre of gravity of the rotor

R r: resistance of rotor phase winding

s: machine slip

SOM: Self-Organizing Map

SWF: Shorted stator winding fault

SVM: support vector machine

T r : open-circuit rotor time constant given by L r /R r

UBR: Unbalanced rotor fault

w_som(i,j): SOM output neuron‘s weight vector

w_svm i: SVM weight term

w k [i]: Wiener filter weights at instant i th

x i: support vectors for a SVM

z b (t): complex signal in space (|x 1 (t)|, |x 2 (t)|,t)

z t (t): complex signal in space (|x 1 (t)|, |x 2 (t)|, |x 3 (t)|)

β: rolling element contact angle

γ: ―nudge-to-zero‖ constant for Wiener filter

η 0: initial learning rate of SOM

θ: angular position of r

θ r: angular position of the rotor with respect to the stator reference

μ: constant to adjust the rate of convergence of the weights for Wiener filter

ν: order of the stator time harmonics present in the power supply

ρ: degree of eccentricity

Φ: particular angular position along the stator inner surface

Φ n : phase delay

ψrd: instantaneous values of direct-axis component of the rotor flux linkage

ψrq: instantaneous values of quadrature-axis component of the rotor flux linkage

Ω: rotor shaft rotational speed

ω 1: angular stator frequency

ω sl: angular slip frequency

ω v : frequency of the kth vibration due to bearing defect

L IST OF R ELEVANT P UBLICATIONS

1 W.-Y Chen, J.-X Xu, S.K Panda, ―A Study on Automatic Machine Condition Monitoring and Fault Diagnosis for Bearing and Unbalanced Rotor Faults‖, IEEE International Symposium on Industrial Electronics (ISIE‘2011), Poland, Gdansk, 28-

30 Jun 2011, Accepted for publication

2 W.-Y Chen, J.-X Xu, S.K Panda, ―Application of Artificial Intelligence Techniques

to the Study of Machine Signatures‖, IEEE International Symposium on Industrial Electronics (ISIE‘2012), China, Hangzhou, 28-31 May 2012, Manuscript submitted for publication

C HAPTER 1: I NTRODUCTION

The field of machine condition monitoring and fault diagnosis is vast A literature survey; which is presented subsequently, has shown wide ranging diagnostic techniques Various machine operation quantities may be used for monitoring the health of a motor, e.g., partial discharge, thermo-graphic monitoring of hot-spots, chemical content; such as, oil degradation detection, wear debris detection, machine axial leakage flux, acoustic, torque, machine power efficiency, machine vibration signal, and motor current signature [2, 3] Among these, the technique by analyzing machine stator current is known as Motor Current Signature Analysis (MCSA) is the state-of-the-art technique [102] It is a popular research area where many algorithms have been proposed, but a single effective method that is able to detect and diagnosis multiple classes of machine fault still elude researchers

The current harmonics that is present in the motor current is mainly created by the machine asymmetries and vibrations due to machine faults Hence, this project focuses on two fault detection techniques, namely, vibration signature and MCSA There are a number of issues to address in the formulation of a reliable fault detection and diagnosis scheme [4]:

 definition of a single diagnostic procedure for any type of faults

 insensitive to and independent of operating conditions

 reliable fault detection for position, speed and torque controlled drives

 reliable fault detection for drives in time-varying conditions

 quantify a stated fault threshold independent of operating conditions

1.1 Objectives

With the above issues in mind, this project aims to accomplish two main objectives, namely,

Objective 1: To investigate and formulate an automatic machine condition monitoring

scheme to detect and diagnose the most common machine fault modes, namely, bearing and unbalanced rotor fault, that is insensitive to machine operating speed

Objective 2: To investigate and study the use of MCSA to cover a wider range of

machine fault modes; apart from bearing and unbalanced rotor faults, to include broken rotor bars and shorted winding faults as well, where vibration analysis is difficult to diagnose, and to discover unique nonlinear and non-stationary features for automatic fault classifications

In these studies, computational intelligence are applied Of particular interests, are the Self-Organizing Map (SOM), multi-class Support Vector Machine (M-SVM), k-Nearest Neighbor (k-NN) case-based learning and the Empirical Mode Decomposition (EMD)

On the first objective, this project has formulated and implemented a simple and effective data-based scheme, using time-domain vibration data, for the continuous automatic condition monitoring and diagnosis of bearing and unbalanced rotor faults is

similarity measure, and in combination with the use k-NN algorithm for the effective automatic classification of machine faults This technique is both noise-tolerant and shift-invariant., It also has a low error rate and insensitive to machine operating speed, as shown subsequently in this thesis Further, the diagnosis of these two mechanical faults using vibration frequency-domain information is also shown, where SOM is used to discover cluster information on the extracted features in an unsupervised fashion, and an M-SVM is next used to derive the clusters globally optimal separating hyperplanes for the automatic classification of the fault modes

On the second objective, this project use EMD technique to study the motor current signatures harmonic contents of a healthy machine (HTY), a machine with bearing fault (BRG), unbalanced rotor fault (UBR), broken rotor bar fault (BRB) and shorted stator winding fault (SWF) In this project, new unique non-linear and non-stationary features are discovered for these fault modes at machine operating speed of 20Hz and 30Hz However, it is also observed in this project that uniqueness of these features is not obvious at higher speed of 40Hz With the newly discovered unique features at 20Hz and 30Hz, future works on automatic fault classifications by a single effective fault detection and diagnosis scheme based on EMD technique is achievable

1.2 Thesis Organization

This thesis consists of seven chapters

Chapter 1: Introduction on the issues of formulating a reliable machine fault diagnostic

scheme, and the rationale for condition monitoring using MCSA and vibration

analysis, and sets the stage for stating the objectives of this research Fault

statistics and literature survey are also carried out to compile the fault

statistics and identifies the most common failure modes This allows research effort to be directed at the most common failure modes Fault diagnostic technique literature survey is next conducted, to understand how various novel diagnostic techniques are formulated and the difficulties encountered This identifies niche research area where this project adds values

Chapter 2: Mechanics of machine fault elucidates the origin of different type of

machine faults, presents the various fault vibration signatures and the expected motor current fault spectrum for MCSA

Chapter 3: Motor Current Signature and Vibration Signature Analysis explain the

difficulties, challenges and issue of vibration analysis and MCSA techniques and a new approach is proposed

Chapter 4: Application of Artificial Intelligence (AI) techniques for fault diagnosis

presents the various AI techniques used in this project

Chapter 5: A study on Automatic Diagnosis of Bearing and Unbalanced Rotor faults

presents the results of the data-based machine fault detection and diagnosis

scheme using time-domain vibration data It explains how cross-correlation sum operation in time-domain data series is a suitable similarity measure for the vibration signatures for the purpose of automatic pattern classification using k-NN classifier, and presents the fault classification error rate and confusion matrix It also presents feature extraction using vibration frequency-domain information, fault-class clusters study and discovery using unsupervised learning by SOM, the clusters globally optimal separating hyperplane derived from a M-SVM using one-versus-all learning strategy, and the M-SVM classification error rate and confusion matrix

Chapter 6: A study on Motor Current Signature using Empirical Mode

Decomposition explains the disadvantages of the traditional analysis tool for

MCSA using Fourier-based and Wavelet transform, the rationale for using EMD techniques as an effective tool for the analysis of machine current signatures, with a view to discover new information that Fourier and Wavelet transform may not be able to reveal

Chapter 7: Conclusion

In the next, a fault mode statistics survey is carried out with a view to identify the most commonly occurring machine fault modes The survey article in 1985 [5] reveals that bearing fault is the most common machine fault mode The followings further survey and present the situation in the 1990s

1.3 Fault Mode Statistics Survey

In [1], a detail survey on fault statistics was done in 2008 In this comprehensive survey, several sources; including the private communication between the author and an original equipment manufacturer, referenced about 80 journal papers published in IEEE and IEE on the subject over the past 26 years since 2008, were used The table below summaries the survey result

Table 1.1: Summary of percentage of each of the failure mode

Table 1.2: Fault statistics on 8 surveyed articles (*MC denotes Most Common fault)

By taking the average across the rows of Table 1.2, the following table is derived

Table 1.3: Percentage of each of the failure mode derived from Table 1.2

1.4.1 Vibration Signature Analysis

Vibration signature analysis is the most commonly monitored operation parameter for detection and diagnosis of mechanical fault modes e.g., bearing defects and eccentricities [14] Using Wavelet techniques to preprocess the vibration signal is popular The articles [15-17] presented such a study where the wavelet coefficients were the feature vectors It is interesting to note that, in Elsevier collection of articles, the use

of Morlet wavelet basis function is common, whereas in IEEE collection of articles, Daubechies wavelet is popular Higher order spectral analysis using Bispectral transform,

is used for noise suppression, detection of non-Gaussian data, and to detect nonlinearity

of the fault information in [18] Envelope analysis is used in [19, 20] for feature extraction Article [21] showed that combining features extracted from Mel-frequency Cepstral Coefficients (MFCC) and Kurtosis, are effective for diagnosing bearing faults Independent component analysis can be used to extract features from vibration signatures for bearing fault diagnosis [22] After feature extraction, AI techniques e.g., neural network, SVM, SOM, are next used to predict fault modes Excellent examples of works

However, the most interesting technique is the use of EMD for the analysis of machine vibration signatures, where the basis function is derived based on empirical data

in terms of Intrinsic Mode Functions (IMFs) Articles [27-31] presented such a study The IMFs thus derived are the feature vectors for fault diagnosis

1.4.2 Motor Current Signature Analysis

A survey on MCSA technique reveals that the approaches are numerous and wide-ranging The articles maybe broadly categorized into: reviews, model construction for fault modes, feature extraction techniques, and the use of computational intelligence for machine fault diagnosis

Over the years, a series of reviews have been made by [1, 4, 7, 32-37] They offer

a good overview on how progress has been made A notable change is the progress from the use of traditional Fourier transform e.g., Fast Fourier Transform (FFT), to analyze motor current signatures, and the increasingly popular use of Wavelet transform e.g., Discrete Wavelet Packet transform, to identify fault spectrum and extract unique features for fault diagnosis FFT is the traditional tool for MCSA where by locating individual fault spectrum, the machine fault is diagnosed This approach is successful for broken rotor bars and eccentricities faults [11, 38, 39]

In [40, 41], a good comparative study of the various techniques for MCSA for broken rotor bar and air-gap eccentricities is presented In [42], a good review is given on the various diagnosis methods for stator voltage asymmetry and rotor broken bars However, these techniques are mainly Fourier based It is worth to note that, as the fault

spectrum in low slip situation Further, since motor current signature is non-linear and non-stationary in nature [43], as such, Wavelet multi-resolution decomposition approach

is popular In [44-52], Wavelet transform is used to decompose the motor current into various approximate and detail levels wavelet coefficients, and features are extracted from these coefficients for fault diagnosis Diagnoses of bearing, broken rotor bar, eccentricities faults were reported However, careful selection of a wavelet basis function

is not trivial [40, 49], as wavelet decomposition is a convolution computation of machine signature with wavelet basis function and hence a different choice of basis function produces different results

Beside wavelet technique, other high resolution frequency-domain techniques e.g., Eigen-analysis Multiple Signal Classification (MUSIC) spectrum Estimator, Welch, Burg [53] are used In [54], these techniques are applied for the detection of rotor cage faults

In [8], a detail study using different auto-regressive parametric methods e.g., Walker, and the possibility of using a lower sampling rate were explored The article [55], showed that a sliding window ROOT-MUSIC algorithm for bearing fault diagnosis is possible, and in [56] a novel combination of maximum covariance method for frequency tracking and Zoom-FFT technique, to selectively increase the frequency resolution of the frequency range of interest for fault diagnosis were demonstrated Other methods incorporating temporal information of the motor current using higher order statistic, such

Yule-as, spectral kurtosis is used in [57]

With the popular use of inverter speed controller for machine, the effect of PWM inverter harmonics on MCSA was investigated in [58, 59] In [60], inverter input and output current were studied with a view to detect the twice fundamental frequency

harmonics for diagnosis of rotor faults It is shown that detection of these harmonics is possible using inverter input current near zero frequency

To extend the type of fault coverage, stator winding faults are investigated as well

In [61], a novel diagnostic indicator for stator winding fault, that does not involve ground fault, is formulated using positive and negative sequence line-voltage and line-current information The key idea is that various indicators were determined at various machine speeds, and a kind of lookup table was created for diagnosis at different machine operating speed However, the use of line-voltage, made the method invasive, where potential transformer (PT) is required The article [62] presented a method using Extended Park‘s Vector Approach (EPVA), where instead of observing the ovality of the signature in the D-Q plane, the frequency-domain information revealed the presence of fault for stator winding This approach may be used for bearing fault as well [10]

Survey also revealed other innovative approaches Instead of using steady-state information, transient start-stop information may be used for diagnosis as well, as shown

in [63, 64] In [6], monitoring instantaneous power factor and motor efficiency [65] are possible approaches too An interesting approach is presented in [66], where a noise cancellation technique was used for diagnosing general roughness fault The scheme assumed that all frequencies that are not related to the bearing faults, e.g., supply frequency, supply unbalance harmonics, the eccentricity harmonics, the slot harmonics, saturation harmonics and interferences from environmental sources are regarded as noise and are estimated by a Wiener Filter All these noise components are then cancelled out

by their estimate in a real-time manner The remaining components are hence related to

bearing fault, and the RMS value of this noise-cancelled signal is next calculated online

as fault index, with impending fault as an increase in fault index

Model-based approach aims to construct a mathematical model of the machine and thereby using the model to analysis and predict fault mode [67-74] Finite element analysis is popular for simulating and studying of fault mode; especially for broken rotor bar Winding-Function model is specially formulated for modeling air-gap eccentricity as shown in [75, 76]

Data-based approach collects real machine fault data rather than using sophisticated mathematical model to calculate them, and uses these data as examples for fault diagnosis These examples are collected from fault simulator With the fault data available, AI techniques e.g., SOM, neural network, fuzzy logic, M-SVM etc., are used to automatically classify the faults [77-81] Other modeling approaches are possible, such as, [12] use Autoregressive (AR) Spectrum Estimation; a form of parametric spectrum estimation technique to model a healthy motor signature, and deviation from this baseline indicates a bearing general roughness fault However, this method requires the use of notch-filter to remove the dominant fundamental frequency and a series of filter banks to remove the harmonics of other possible faults e.g., unbalance voltage source, cyclical load torque, eccentricities, broken rotor bars, rotor slotting effects etc This adds to the complexity of this method Recently, the use of Independent Component Analysis (ICA) has achieved remarkable results, where the diagnostic procedure is independent of machine operation speed for the diagnosis of bearing and broken rotor bars [82-84]

EMD is applied for the diagnosis of shorted stator winding fault and broken rotor bars in [85, 86] However, in each of the study, only one fault mode was covered This runs the risk of mis-diagnosing a fault, as another fault signatures not covered in the study, may produce similar features This project aims to widen the scope of motor current signature study to cover more fault modes Figure 1.1 illustrates the approaches of this project to investigate the automatic fault diagnosis of AC synchronous machine In the next, the mechanics of machine fault mode is presented

Figure 1.1: Approaches of this project to investigate machine fault diagnosis

AC synchronous machine fault diagnosis

Motor current signatures Broken Rotor Bar fault Unbalanced Rotor Bar fault Bearing fault Shorted Winding fault

Empirical Mode Decomposition

Fast Fourier Transform

C HAPTER 2: M ECHANICS OF M ACHINE F AULT

Machine is a moving magnetic apparatus Its various parts are subject to kinetic energy, magnetic energy, operational thermal stress and harsh environmental conditions e.g., humidity and chemical corrosion, causing wear and tear, and ultimately numerous types of fault may develop Faults are categorized as electrical or mechanical faults Electrical failure modes are mostly insulation failure of core, stator winding, rotor winding and rotor bar breakage Mechanical failure modes are mostly bearing failure, rotor eccentricities e.g., unbalanced rotor; caused for example by wear and tear, accumulation of deposits and temperature changes etc., and creating unequal distribution

of rotor mass

An ideal healthy machine has physical constructional symmetry, such as, an equally spaced and constant air-gap length, equal rotor resistances in the rotor and stator windings and a balanced rotor However, there are inherent construction asymmetries and imperfections in an actual healthy machine, for example, the air-gap length is not perfectly spaced and as the rotor rotates the air-gap length varies, and the rotor and stator winding resistances for each phase are not the same These minor physical asymmetries generate unequal magnetic flux and as a result magnetic force induced vibrations are caused Hence, a healthy machine is expected to generate some low magnitude vibrations

A faulty machine has much more severe physical and electrical asymmetries, generating larger unequal magnetic flux, and the resultant magnetic force creates larger

cause variations in magnetic permanence of the air-gap The stator windings, acting like a transducer, pick up these stray magnetic fluxes and induce current harmonics into the stator current In the next presents the detail mechanics of some major fault modes, namely, 1) eccentricity, 2) unbalanced rotor, 3) bearing general roughness, 6) bearings faults, 5) broken rotor bar, and 6) shorted stator winding fault

2.1 Eccentricity

Induction machine may fail due to air-gap eccentricity Air-gap eccentricity occurs due to shaft deflection, inaccurate positioning of the rotor with respect to stator, bearing wear, stator core movement etc Air-gap eccentricity creates unbalanced radial forces and hence unbalanced magnetic pull that may cause rotor-to-stator rub, and ultimately results in damage of the stator core and stator windings

2.1.1 Static Eccentricity

There are two types of air-gap eccentricity: static and dynamic eccentricity In static air- gap eccentricity, the position of the minimal radial air-gap length is fixed in space For example, static air-gap eccentricity may be caused by the ovality shaped of the core, or by incorrect positioning of the stator or rotor during commissioning stage The

air-gap of static eccentricity is independent of θr, the angular position of the rotor with respect to the stator reference, and is given by [87]

(2.1)

where ρ is the degree of eccentricity and g 0 is the radial air-gap length in the case of a

)1,0(cos

)(  g0 g0  

g

2.1.1.1 Static Eccentricity Motor Current Signature

With the motion of the air-gap given in (2.1), it can be shown that the harmonic frequency components in the stator currents of an induction machine with static air-gap eccentricity are given by [87],

(2.2)

where f s is the fundamental supply frequency, k an integer, N number of rotor slots, n d

eccentricity order number, (static eccentricity is n d=0, dynamic eccentricity is n d =1), P is the number of pole-pairs, ν is the order of the stator time harmonics that are present in the power supply driving the motor, taking the values ±1, ±3, ±5, …etc, and s the slip

2.1.2 Dynamic Eccentricity

In the case of dynamic eccentricity, the centre of the rotor is not at the centre of rotation and the position of minimum air-gap rotates and varies with the rotor This

misalignment maybe caused for example by, a bent rotor shaft, bearing wear or

misalignment, mechanical resonance at critical speed, etc The air-gap of dynamic eccentricity is given by [59]

(2.3)

where ρ is the degree of eccentricity, θ r is the angular position of the rotor with respect to

the stator reference, g 0 is the radial air-gap length in the case of a uniform air-gap, and Φ

)1,0()

cos(

),( r  g0 g0 r 

g

3 , 2 , 1

1

_        f k 

P

s kN

is the particular angular position along the stator inner surface The corresponding permeance variation due to dynamic eccentricity is [59],

(2.4)

where P 0 is the average air-gap permeance and Φ n is the phase delay

2.1.2.1 Dynamic Eccentricity Motor Current Signature

Due to permeance variation as a result of eccentricity, side-band components appear around the slot harmonics in the stator line current frequency spectrum The frequency components in the stator currents of an induction machine with to dynamic air-gap eccentricity are given by [3, 88],

(2.5)

where f s is the fundamental supply frequency, k an integer, N number of rotor slots, n d

eccentricity order number, (static eccentricity is n d=0, dynamic eccentricity is n d =1), P is the number of pole-pairs, ν is the harmonic of the stator magneto motive force (MMF) time harmonics, given by ±1, ±3, ±5, …etc., and s the slip

2.1.3 Mixed Eccentricity Motor Current Signature

However, in a practical machine, both static and dynamic eccentricities are present This mixed eccentricity creates the following harmonics in the machine current [4],

3 , 2 , 1

1 ) (

_         f k 

P

s n

kN

3 , 2 , 1

1 1

_   k  s f k 

) ) (

cos(

) ,

n n r

With the use of VSI, additional harmonics are introduced [59, 89],

(2.7)

where h is the inverter harmonic order, f s is the fundamental supply frequency and f r is the rotor frequency It is hence possible to detect air-gap eccentricity by monitoring motor current

2.2 Unbalanced Rotor Fault

Unbalance rotor is a type of eccentricity fault where the off-center rotation of the rotor is caused by unbalanced mass rather than bent rotor shaft It is the most common source of excessive vibration [90, 91] Possible causes are, asymmetrical mass distribution of the rotating element as a result of wear, erosion, material buildup, thermal expansion or contraction, causing shaft bending or misalignment As a result, the centre

of gravity of the rotating element does not coincide with the centre of rotation, and at the

point of unbalanced mass creates a synchronous radial perturbation force (F c), causing a forced vibration This phenomenon is described by the following expression, assuming a rigid isotropic rotor system [14],

(2.8)

where m is the unbalanced mass, r is the distance between the centre of rotation and the centre of gravity of the rotor, Ω is the shaft rotational speed, θ is the angular position of r and j is the complex operator Figure 2.1 illustrates this

) (

_  h f  k f h k 

Figure 2.1: Perturbation force (F c ) created by unbalanced mass (m) rotating at Ω

Figure 2.1 shows some sample vibration signatures of unbalanced rotor fault at various machine speeds A characteristic oscillatory sine wave is observed

Figure 2.2: Unbalanced rotor fault signatures at various machine speeds

2.2.1 Unbalanced Rotor Fault Motor Current Signature

With the motion of the rotor described by Eq (3.8), the expected current harmonics for a machine with unbalanced rotor is given by [92],

3 , 2 , 1

Figure 2.3: Bearing assembly

Bearing and raceway wear and tear present initially as general roughness and progresses to metal fatigue, and ultimately spall and chip on the surface of the rolling elements [93] Figure 2.4 and 2.5 show severely chipped rolling elements and spalled raceway faults These defective surfaces on these components are a source of machine vibration A chipped rolling element spins as it revolves around the raceway When it is

in contact with the defective surface of the raceway, an impact pulse is produced, creating

a free vibration In the absence of significant damping medium in the bearing assembly, the impact pulses decay exponentially

Figure 2.4: Defective rolling elements (adopted from [93])

a Outer raceway fault e Inner raceway

b Rolling element fault f Shaft

c Inner raceway fault g Rolling element

d Retainer h Outer raceway

Figure 2.5: Raceway faults (adopted from [93])

2.3.1 Bearing Faults Vibration Signatures

There are four basic motions that describe the dynamics of faulty bearing movement, namely, cage, outer race, inner race or rolling elements Each fault generates

a unique natural frequency The following equations show the natural frequencies associated with each of the bearing single-point defect, where the cage fault, outer race

fault, inner race fault and rolling element fault frequencies are F C , F O , F I and F B

C

D

D F

1 2 1

B O

D

D F

N

1 2

D

D F

N

1 2

(2.14)

where F R is the rotor mechanical frequency, N B is the number of rolling elements, D c is

the rolling element pitch, D b is the diameter of the rolling element, and β is the rolling

element contact angle Figure 2.6 illustrates this Therefore, these fault frequencies are functions of the bearing geometry, the number of rolling elements, and the bearing rotational speed

Figure 2.6: Rolling element pitch, diameter and contact angle of a bearing

Figure 2.7, 2.8 and 2.9 show the fault vibration signatures, measured in acceleration (m/s2), of a faulty rolling element, inner raceway and outer raceway at different machine operating speeds

c

b R

b

c B

D

D F

D

D

Rolling Element diameter (D b )

Pitch (D c ) Contact Angle (β)

Figure 2.7: Rolling element fault signatures at various machine speeds

Figure 2.9: Outer raceway fault signatures at various machine speeds

2.3.2 Bearing Faults Motor Current Signatures

Bearing defect causes minute radial movement of the rotor, and hence is a kind of dynamic eccentricity However, the difference between dynamic eccentricity and bearing fault is the characteristic of the mechanical oscillations For the former, an eccentric rotor causes a non-uniform sinusoidal air-gap, but for the latter, bearing defect causes an instantaneous mechanical impulse displacement in the air-gap, giving rise to vibrations that cause air-gap permeance variation that is a complex sum of an infinite number of rotating eccentricities [94] With instant eccentricities generated by the bearing fault, the air-gap is given by [59],

where ω v is the frequency of the kth vibration due to bearing defect, and the permeance variation are of the machine is [59],

(2.16) Therefore, the periodical changes in the machine permeance, in turn, creates harmonics in the stator current shown below [59],

(2.17)

where f s is the supply frequency and f v is F C , F O , F I or F B With the use of inverter, there

is interaction between the inverter harmonics and bearing fault induced harmonics and the expected bearing fault spectrum is [59],

(2.18)

where h is the inverter harmonic order

2.4 Bearing General Roughness

It was reported in the literature that, there should be a distinction between bearing fault and general roughness of the bearing [12] General roughness of bearing is an early sign of impending bearing fault However, it does not show a distinctive failure mode like bearing fault whereby clear and visible point-faults are developed e.g., cracks, pitting and other localized damages Normally, general roughness is simulated by de-greasing the bearing, thus causing great friction of bearing movement and hence general roughness Whereas for bearing faults, it is simulated by creating holes e.g., drilling, on the raceway assembly Different level of fault severity can be created by creating holes of various diameters General roughness is reported to cause a general increase in the noise level in the motor signature, and does not exhibit any particular frequency spikes Generalized

n k n r

3,2,1





roughness fault is subtle and does not have clear distinguishable defects Therefore, it does not have a unique fault frequency, but rather, it manifests as a general and unpredictable increase in magnitude and broadband changes in vibration and stator current frequencies However, general roughness is considered as a kind of eccentricity fault [95] Therefore, instead of measuring the vibration frequencies, the machine condition can be monitored by stator current harmonics to detect harmonics created by the minute variations in the machine permeance

2.5 Broken Rotor Bar Motor Current Signature

Rotating machine subjects its rotor to prolong kinetic, electrical and thermal stresses, and breakage results as material fatigue develops over time Breakage increases the rotor resistance of the broken rotor bars and causes electrical asymmetry and distortion of the rotor bar currents, and hence distorts the three-phase magnetic field The rotor MMF is distorted as well This distorted rotor MMF consists of a forward and backward rotating wave with respect to the rotor fixed reference frame The former is the main magnetic field and the latter is due to the rotor electrical asymmetry caused by the breakage The backward travelling wave induces a stator voltage harmonic component at

the frequency (1−2s)f s where f s is the stator supply frequency and s is the slip This stator

voltage harmonics in turns creates a stator current harmonic of the same frequency [72],

(2.19) The interaction of these side band currents with flux and the speed ripple creates additional harmonics at frequency [72],

where f s is the supply frequency, s is the machine slip, the difference gives the lower

sideband and the sum gives the upper sideband These frequencies are a function of the

machine slip (s) Therefore, these frequencies are dynamic in nature and vary as the

operational condition of the motor varies At higher slip, and spectra are further away

from f s , and at lower slip the spectrum lines are close to f s and are difficult to detect

2.6 Shorted Stator Winding Fault Motor Current Signature

The most common kind of fault related to stator winding of induction motors are: phase-to-ground, phase-to-phase and short-circuit of coils of the same or different phase (―turn-to-turn‖ fault) These insulation faults maybe caused by hot spots in the stator winding, oil contamination, moisture, dirt, electrical discharges, slack core lamination, cooling system failure [2]

In this fault mode, the winding turn-to-turn fault is the subject of interest for condition monitoring, as such short-circuit fault involving different phase is difficult detected by the usual machine protection relays If it persists undetected, causes heating and ultimately progress rapidly to phase-ground or phase-phase faults with little warnings, damaging the machine core permanently Short-circuited turns on the stator of the induction motor causes asymmetry of the three-phase stator winding, and the effect is the presence of three-phase negative sequence currents The diagnosis of shorted turns using MCSA is to detect the frequency components in Eq (2.21) since the rotating flux induces corresponding harmonics in the stator winding [96],

(2.21)

3 , 2 , 1 1