Vibration-based Condition Monitoring of Rotating Machines

Vibration-based Condition

Monitoring of Rotating

Machines

A thesis submitted to

The University of Manchester

for the degree of

Doctor of Philosophy (PhD)

in the Faculty of Engineering and Physical Sciences

2015

Akilu Yunusa-Kaltungo

School of Mechanical, Aerospace and Civil

Engineering

Vibration-based Condition Monitoring of Rotating Machines

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Akilu Yunusa-Kaltungo 2

PhD in Mechanical Engineering (2015) University of Manchester (UK)

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Table of Contents

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TABLE OF CONTENTS ----------------------------------------------------------------------------------------------

TABLE OF CONTENTS ...................................................................................................................... 3

LIST OF FIGURES ............................................................................................................................ 12

LIST OF TABLES .............................................................................................................................. 19

ABBREVIATIONS ............................................................................................................................. 21

NOMENCLATURE ............................................................................................................................ 23

LIST OF PUBLICATIONS ................................................................................................................. 25

ABSTRACT ....................................................................................................................................... 28

DECLARATION ................................................................................................................................. 29

COPYRIGHT STATEMENT .............................................................................................................. 30

ACKNOWLEDGEMENTS ................................................................................................................. 32

DEDICATION .................................................................................................................................... 33

SCIENTIFIC QUOTE ........................................................................................................................ 34

CHAPTER 1 INTRODUCTION ........................................................................... 35

1.1 Overview .............................................................................................................. 35

1.2 Research Objectives ........................................................................................... 39

1.3 Research Review ................................................................................................. 40

1.4 Outline of Thesis ................................................................................................. 42

CHAPTER 2 LITERATURE REVIEW ................................................................. 47

2.1 Typical VCM Process Framework ...................................................................... 47

2.1.1 Data collection ............................................................................................................... 49

2.1.2 Data processing ............................................................................................................ 52

2.1.2.1 Time domain analysis ............................................................................................... 52

2.1.2.2 Frequency domain analysis ...................................................................................... 53

2.1.2.3 Time-frequency analysis ........................................................................................... 53

2.1.3 Faults diagnosis ............................................................................................................ 54

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2.2 Standard Approaches to Vibration-based Fault Detection ............................... 55

2.2.1 Spectrum analysis ......................................................................................................... 56

2.2.1.1 Unbalance fault ......................................................................................................... 56

2.2.1.2 Shaft bow .................................................................................................................. 57

2.2.1.3 Shaft misalignment .................................................................................................... 58

2.2.1.4 Mechanical looseness ............................................................................................... 59

2.2.1.5 Shaft crack ................................................................................................................ 61

2.2.1.6 Shaft rub .................................................................................................................... 62

2.2.2 Rotor orbit analysis........................................................................................................ 63

2.2.3 Full spectrum analysis ................................................................................................... 65

2.2.4 Order tracking ................................................................................................................ 67

2.3 Overview of Standard Vibration Based Fault Detection Approaches .............. 68

2.4 Emerging Approaches to Vibration Based Fault Detection ............................. 70

2.4.1 Model-based approaches .............................................................................................. 70

2.4.2 Artificial intelligence and faults classification ................................................................ 74

2.4.3 Higher order signal processing tools ............................................................................. 77

2.4.4 Data Fusion ................................................................................................................... 80

2.4.4.1 Sensor level data fusion ............................................................................................ 83

2.4.4.2 Parameter level data fusion ...................................................................................... 85

2.5 Summary.............................................................................................................. 92

CHAPTER 3 EXPERIMENTS ............................................................................. 94

3.1 Experimental Rig and Components ................................................................... 94

3.1.1 Electric motor and speed controller............................................................................... 96

3.1.2 Anti-friction ball bearings ............................................................................................... 98

3.1.3 Couplings ...................................................................................................................... 99

3.1.4 Threaded bars ............................................................................................................. 100

3.2 Instrumentation ................................................................................................. 100

3.2.1 Accelerometers ........................................................................................................... 101

3.2.2 Proximity probes.......................................................................................................... 102

3.2.3 Measurement microphones ......................................................................................... 102

3.2.4 Instrumented hammer ................................................................................................. 103

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3.2.5 Signal conditioning units ............................................................................................. 105

3.2.6 Analogue-to-digital converter (ADC) ........................................................................... 107

3.2.7 Data acquisition software ............................................................................................ 108

3.3 Experimental Rig Foundations ......................................................................... 109

3.3.1 Rigid support (RS) ....................................................................................................... 109

3.3.2 Flexible supports ......................................................................................................... 111

3.4 Dynamic Characterisation ................................................................................ 114

3.5 Experimentally Simulated Faults ..................................................................... 122

3.5.1 Rigid support (RS) ....................................................................................................... 122

3.5.1.1 Case 1: Healthy ....................................................................................................... 122

3.5.1.2 Case 2: Misalignment .............................................................................................. 122

3.5.1.3 Case 3: Cracked shaft ............................................................................................. 123

3.5.1.4 Case 4: Shaft rub .................................................................................................... 124

3.5.2 Flexible supports (FS1 and FS2) ................................................................................ 125

3.6 Summary............................................................................................................ 126

CHAPTER 4 EXPERIMENTAL OBSERVATIONS OF ROTOR ORBIT

ANALYSIS IN ROTATING MACHINES ............................................................. 128

ABSTRACT ........................................................................................................ 128

4.1 Introduction ....................................................................................................... 129

4.2 Experimental Rigs ............................................................................................. 130

4.3 Vibration Experiments ...................................................................................... 131

4.3.1 Case 1: Healthy with residual misalignment (HRM) .................................................... 132

4.3.2 Case 2: Unbalance (UNB) ........................................................................................... 132

4.3.3 Case 3: Shaft crack (SC) ............................................................................................ 133

4.3.4 Cases 5-8: Shaft misalignment (SM) .......................................................................... 133

4.3.5 Case 9: Shaft rub (SR) ................................................................................................ 134

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4.4 Results and Observations ................................................................................ 135

4.5 Spectrum Analyses ........................................................................................... 137

4.6 Summary............................................................................................................ 139

CHAPTER 5 A COMPARISON OF SIGNAL PROCESSING TOOLS: HIGHER

ORDER SPECTRA VERSUS HIGHER ORDER COHERENCES ...................... 141

ABSTRACT ........................................................................................................ 142

5.1 Introduction ....................................................................................................... 142

5.2 Computational Approaches for Spectra and Coherences.............................. 144

5.3 Simulated Example ........................................................................................... 147

5.4 CSD and Ordinary Coherence Analysis ........................................................... 149

5.5 Bispectrum and Bicoherence Analysis ........................................................... 151

5.6 Trispectrum and Tricoherence Analysis ......................................................... 153

5.7 Signals with Noise ............................................................................................ 155

5.8 Summary............................................................................................................ 157

CHAPTER 6 COMBINED BISPECTRUM AND TRISPECTRUM FOR FAULTS

DIAGNOSIS IN ROTATING MACHINES ........................................................... 158

ABSTRACT ........................................................................................................ 159

6.1 Introduction ....................................................................................................... 159

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6.2 PSD and HOS Computations ............................................................................ 161

6.3 Experimental Setup ........................................................................................... 162

6.4 Simulation of Faults .......................................................................................... 164

6.5 Data Analysis .................................................................................................... 165

6.5.1 Spectrum analysis ....................................................................................................... 165

6.5.2 Bispectrum analysis .................................................................................................... 168

6.5.3 Trispectrum analysis ................................................................................................... 171

6.5.4 Diagnostic Features .................................................................................................... 176

6.6 Summary............................................................................................................ 178

CHAPTER 7 USE OF COMPOSITE HIGHER ORDER SPECTRA FOR FAULTS

DIAGNOSIS OF ROTATING MACHINES WITH DIFFERENT FOUNDATION

FLEXIBILITIES ................................................................................................... 179

ABSTRACT ........................................................................................................ 180

7.1 Introduction ....................................................................................................... 180

7.2 Composite Spectra Computations ................................................................... 183

7.3 Experimental Rig with Different Foundations ................................................. 185

7.3.1 Modal tests and data analysis ..................................................................................... 190

7.4 Experiments ...................................................................................................... 190

7.5 Data Analysis .................................................................................................... 192

7.6 CS Analysis and Observations ........................................................................ 192

7.7 CB Analysis and Observations ........................................................................ 193

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7.8 CT Analysis and Observations ......................................................................... 198

7.9 Combined Diagnostic Features ........................................................................ 203

7.9.1 Sensitivity analysis ...................................................................................................... 205

7.9.2 Practical application .................................................................................................... 206

7.10 Summary............................................................................................................ 207

CHAPTER 8 AN IMPROVED DATA FUSION TECHNIQUE FOR FAULTS

DIAGNOSIS OF ROTATING MACHINES .......................................................... 208

ABSTRACT ........................................................................................................ 208

8.1 Introduction ....................................................................................................... 209

8.2 Earlier Composite Spectrum ............................................................................ 210

8.3 Proposed poly-Coherent Composite Spectrum (pCCS) ................................. 211

8.4 Experiments and Observations ........................................................................ 212

8.4.1 Diagnosis features....................................................................................................... 215

8.5 Diagnosis with Earlier Composite Spectrum Method ..................................... 216

8.6 Summary............................................................................................................ 218

CHAPTER 9 A NOVEL FAULTS DIAGNOSIS TECHNIQUE FOR ENHANCING

MAINTENANCE AND RELIABILITY OF ROTATING MACHINES .................... 220

ABSTRACT ........................................................................................................ 220

9.1 Introduction ....................................................................................................... 221

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9.2 Composite Spectra Computations ................................................................... 225

9.2.1 Earlier method ............................................................................................................. 225

9.2.2 Improved method ........................................................................................................ 227

9.3 Proposed Fault Diagnosis Method ................................................................... 228

9.3.1 Concept of PCA........................................................................................................... 230

9.3.2 Computational approach of the proposed FD technique ............................................ 232

9.4 Experimental Example ...................................................................................... 234

9.4.1 Rig and faults simulation ............................................................................................. 236

9.4.2 Experimental modal analysis ...................................................................................... 238

9.4.3 Signal processing ........................................................................................................ 242

9.5 Faults Diagnosis ............................................................................................... 245

9.5.1 Data preparation.......................................................................................................... 245

9.5.2 Results and discussions .............................................................................................. 247

9.5.3 Comparison with Earlier Method ................................................................................. 249

9.6 Practical application of the proposed FD technique ...................................... 251

9.7 Summary............................................................................................................ 253

CHAPTER 10 SENSITIVITY ANALYSIS OF HIGHER ORDER COHERENT

SPECTRA IN MACHINE FAULTS DIAGNOSIS ................................................ 255

ABSTRACT ........................................................................................................ 255

10.1 Introduction ....................................................................................................... 256

10.2 poly-Coherent Composite Spectra ................................................................... 258

10.3 Example 1: Laboratory Scale Experimental Rig .............................................. 261

10.3.1 Earlier Faults Detection Method [251] ......................................................................... 264

10.4 Sensitivity Analysis Based on Experimental Data .......................................... 266

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10.5 Example 2: Industrial Fan ................................................................................. 270

10.5.1 The Case Study (RKIDF) ............................................................................................ 270

10.5.2 On-site vibration measurements ................................................................................. 272

10.5.3 Detection and Classification of RKIDF Operating Conditions using Earlier Method ... 273

10.6 Sensitivity Analysis Based on Industrial Data ................................................ 275

10.7 Summary............................................................................................................ 277

CHAPTER 11 CONCLUDING REMARKS AND FUTURE RESEARCH .......... 279

11.1 Overall Summary ............................................................................................... 279

11.2 Achieved Objectives ......................................................................................... 282

11.3 Concluding Remarks ........................................................................................ 287

11.4 Future Research ................................................................................................ 287

REFERENCES ................................................................................................... 289

APPENDIX A THEORETICAL BACKGROUND OF SPECTRUM BASED SIGNAL

PROCESSING TOOLS ....................................................................................... 311

A.1 Overview of Frequency Domain Signal Processing ....................................... 311

A.2 Power Spectrum ................................................................................................ 311

A.3 Cross-power Spectrum ..................................................................................... 313

A.4 Ordinary Coherence .......................................................................................... 313

A.5 Higher Order Signal Processing Tools ............................................................ 314

A.5.1 Bispectrum .................................................................................................................. 315

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A.5.2 Trispectrum ................................................................................................................. 315

A.6 Normalisation of Higher Order Signal Processing Tools ............................... 316

A.6.1 Bicoherence ................................................................................................................ 316

A.6.2 Tricoherence ............................................................................................................... 316

List of Figures

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LIST OF FIGURES ----------------------------------------------------------------------------------------------

Figure 1.1 Maintenance philosophies and their characteristics ............................. 36

Figure 1.2 Multi-shaft coal mill drive assembly layout, with locations and

orientations of VCM sensors. HO represents horizontal orientation, VO vertical

orientation and AO axial orientation [8], [9]. .......................................................... 38

Figure 1.3 Thesis chapters and contents .............................................................. 43

Figure 2.1 Basic stages of a typical VCM process ................................................ 49

Figure 2.2 Vibration data collection process for a typical rotating machine [20] .... 50

Figure 2.3 Typical spectrum-based VCM fault tree for a rotating machine ........... 55

Figure 2.4 Typical amplitude-spectrum of a rotating machine at 2040 RPM,

showing dominant 1x RPM peak as a result of unbalance fault. ........................... 57

Figure 2.5 A typical amplitude-spectrum of a rotating machine at 1200 RPM,

showing the appearance of several higher harmonics of machine speed due to

rotor bow. .............................................................................................................. 58


showing dominant 1x RPM and 2x RPM peaks due to misalignment. .................. 59



bearing looseness. ................................................................................................ 60


showing the appearance of several harmonics of machine speed due to rotor

crack. .................................................................................................................... 62


showing the appearance of sub-harmonics of machine speed due to rotor rub. ... 63

Figure 2.10 Rotor orbit plot of a typical rotating machine ...................................... 64

Figure 2.11 3D model of a typical rotating machine. ............................................. 71

Figure 2.12 Typical ANN-based model ................................................................. 75

Figure 2.13 Data fusion at sensor level ................................................................. 84

Figure 2.14 Multi-sensor data fusion [122]–[126] .................................................. 85

Figure 2.15 Data fusion at parameter level ........................................................... 86

List of Figures

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Figure 2.16 A typical multiple speeds cement plant roots blower with various

foundation options [132]–[136]. ............................................................................. 89

Figure 2.17 A unified data fusion approach .......................................................... 91

Figure 3.1 Typical experimental set-up ................................................................. 95

Figure 3.2 Picture of electric motor and speed controller ...................................... 97

Figure 3.3 Anti-friction ball bearings (a) Plummer block (b) Flange-mounted ....... 98

Figure 3.4 Couplings (a) Flexible (b) Rigid ............................................................ 99

Figure 3.5 Threaded bars for flexible foundations ............................................... 100

Figure 3.6 Accelerometers with their brass mounting studs ................................ 101

Figure 3.7 (a) MTN/ECPD+24V Proximity probes (b) EP080 drivers .................. 102

Figure 3.8 (a) Condenser microphone (b) Single channel power supply (c) sound

amplifier .............................................................................................................. 103

Figure 3.9 ICP-PCB 086C03 instrumented hammer ........................................... 104

Figure 3.10 PCB 482C signal conditioning unit ................................................... 106

Figure 3.11 NI 6229/16-bit/16-channel ADC ....................................................... 107

Figure 3.12 Picture of RS experimental rig ......................................................... 110

Figure 3.13 Schematic of RS experimental rig with dimensions ......................... 111

Figure 3.14 Picture of FS experimental rig .......................................................... 112

Figure 3.15 Schematic of FS experimental rig .................................................... 113

Figure 3.16 Picture of flexible supports (a) FS1 (b) FS2 ..................................... 114

Figure 3.17 Modal test setup for determining FS1 and FS2 natural frequencies 116

Figure 3.18 Typical FRF plots for FS1, measured at bearing 2 in the vertical

direction (a) FRF amplitude, (b) FRF phase ....................................................... 117

Figure 3.19 Typical FRF plots for FS1, measured at bearing 2 in the horizontal






Figure 3.22 Modal test setup for determining FS1 and FS2 mode shapes ......... 119

Figure 3.23 Locations of ICP accelerometers for mode shapes’ determination .. 120

List of Figures

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Figure 3.24 FS1experimentally determined mode shapes (a) 50.66Hz, dominant in

vertical direction (b) 56.76Hz, dominant in horizontal direction ........................... 121

Figure 3.25 Cracked shaft ................................................................................... 124

Figure 3.26 Shaft rub .......................................................................................... 124

Figure 4.1 Experimental rig with flexible bearing foundation ............................... 131

Figure 4.2 Flexible anti-friction ball bearings foundations (a) FS1 (b) FS2 ......... 131

Figure 4.3 Unbalance case ................................................................................. 132

Figure 4.4 Loose bearing case............................................................................ 133

Figure 4.5 Shaft misalignment cases (a) SM1 (b) SM2 ....................................... 134

Figure 4.6 Shaft rub case .................................................................................... 135

Figure 4.7 Rotor orbit plots for FS1 (a) HRM (b) UNB (c) SC (d) LB (e) SM1 (f)

SM2 (g) SM3 (h) SM4 (i) SR ............................................................................... 136


SM2 (g) SM3 (h) SM4 (i) SR ............................................................................... 137

Figure 4.9 Typical amplitude spectra for FS1 at 2400RPM (a) HRM (b) SC (c) SM4

(d) SR ................................................................................................................. 138

Figure 4.10 Typical amplitude spectra for FS2 at 2400RPM (a) HRM (b) SC (c)

SM4 (d) SR ......................................................................................................... 139

Figure 5.1 Typical amplitude spectra (a) Case 1 (healthy) and (b)-(d) Case 2-

Case 4 (different faulty conditions) ...................................................................... 149

Figure 5.2 Typical CSD plots (a) Signals 1&2, (b) Signals 1&4, (c) Signals 2&4,

and (d) Signals 3&4 ............................................................................................ 150

Figure 5.3 Typical ordinary coherence plots (a) Signals 1&2, (b) Signals 1&4, (c)

Signals 2&4, and (d) Signals 3&4 ....................................................................... 151

Figure 5.4 Typical amplitude-bispectra plots (a) Case 1 (healthy) and (b)-(d) Case

2-Case 4 (different fault conditions) .................................................................... 152

Figure 5.5 Typical bicoherence plots (a) Case 1 (healthy) and (b)-(d) Case 2-Case

4 (different fault conditions) ................................................................................. 153

Figure 5.6 Typical amplitude-trispectra plots (a) Case 1 (healthy) and (b) Case 2

(faulty) ................................................................................................................. 154

Figure 5.7 Typical tricoherence plots (a) Case 1 (healthy) and (b) Case 2 (faulty)

............................................................................................................................ 155

List of Figures

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Figure 6.1 Photographic representation of the experimental rig.......................... 163

Figure 6.2 Schematic representation of the experimental rig .............................. 164

Figure 6.3 Typical amplitude spectra at 34Hz for bearing 1 ................................ 166

Figure 6.4 Typical amplitude spectra at 50Hz for bearing 1 ................................ 167

Figure 6.5 Typical normalised amplitude spectrum components at 34Hz ((a)-(b))

and at 50Hz ((c)-(d)) for all the simulated cases ................................................. 168

Figure 6.6 Typical amplitude bispectra plots at 34Hz (a) healthy (b) misalignment

(c) cracked shaft (d) shaft rub ............................................................................. 169


(c) cracked shaft (d) shaft rub ............................................................................. 169

Figure 6.8 Typical amplitude trispectra plots at 34Hz for bearings 1 (a-d) and 3 (e-

h); (a and e) healthy, (b and f) misalignment, (c and g) cracked shaft, (d and h)

shaft rub .............................................................................................................. 172

Figure 6.9 Typical amplitude trispectra at 50Hz (a) healthy (b) misalignment (c)

cracked shaft (d) shaft rub .................................................................................. 173

Figure 7.1 Abstract representation of rotating machine and foundation .............. 183

Figure 7.2 Photograph of the experimental rig .................................................... 187

Figure 7.3 Schematic of the experimental rig ...................................................... 188

Figure 7.4 Different rig supports (a) FS1 (b) FS2 ................................................ 189

Figure 7.5 Experimentally simulated cases (a) SC (b) LB (c) SM (d) SR ............ 191

Figure 7.6 Typical composite spectra at 1200RPM (a) HRM for FS1 (b) HRM for

FS2 (c) LB for FS1 (d) LB for FS2 ....................................................................... 193

Figure 7.7 Typical coherent composite bispectra (CB) at 1200RPM (a) HRM for

FS1 (b) HRM for FS2 (c) LB for FS1 (d) LB for FS2 ........................................... 194

Figure 7.8 Typical B11 CB component magnitude and phase (a) FS1 (1200RPM)

(b) FS2 (1200RPM) (c) FS1 (1800RPM) (d) FS2 (1800RPM) (e) FS1 (2400RPM)

(f) FS2 (2400RPM) .............................................................................................. 196



(f) FS2 (2400RPM) .............................................................................................. 197

Figure 7.10 Typical coherent composite trispectra (CT) at 1200RPM (a) HRM for

FS1 (b) HRM for FS2 (c) LB for FS1 (d) LB for FS2 ........................................... 199

List of Figures

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Figure 7.11 Typical T111 CT component magnitude and phase (a) FS1 (1200RPM)


(f) FS2 (2400RPM) .............................................................................................. 201



(f) FS2 (2400RPM) .............................................................................................. 202

Figure 7.13 Typical combined magnitudes of B11 CB and T111 CT components

(a) FS1 (1200RPM) (b) FS2 (1200RPM) (c) FS1 (1800RPM) (d) FS2 (1800RPM)

(e) FS1 (2400RPM) (f) FS2 (2400RPM) ............................................................. 204

Figure 7.14 Typical combined magnitudes of B11 CB and T111 CT components at

1200RPM for FS2 foundation (a) scenario 1 (b) scenario 2 (c) scenario (d)

scenario 4 ........................................................................................................... 206

Figure 8.1 Photograph of experimental rig [128] ................................................. 213

Figure 8.2 Typical pCCS and phase plots at 2040RPM (a)-(b) Healthy and (c)-(d)

crack ................................................................................................................... 214


crack ................................................................................................................... 214

Figure 8.4 Typical 1x and 2x pCCS amplitudes and phases for all four cases at

2040RPM ............................................................................................................ 215


3000RPM ............................................................................................................ 216

Figure 8.6 Typical normalised CS amplitudes for all four cases at 2040RPM ..... 217

Figure 8.7 Typical normalised CS amplitudes for all four cases at 3000RPM ..... 218

Figure 9.1 Proposed faults diagnosis process flow chart .................................... 230

Figure 9.2 Experimental rig ................................................................................. 235

Figure 9.3 Different rig supports (a) FS1 (b) FS2 ................................................ 236

Figure 9.4 Experimentally simulated cases (a) SC (b) LB (c) SM (d) SR ............ 238

Figure 9.5 Experimental setup for modal test ..................................................... 239

Figure 9.6 Typical FRF amplitude and phase plots for FS1, measured at bearing 2

(a) vertical direction (b) horizontal direction ........................................................ 240


(a) vertical direction (b) horizontal direction ........................................................ 241

List of Figures

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Figure 9.8 Typical CB plots for FS1 and FS2 at 1200RPM (a) HRM (FS1), (b)

HRM (FS2), (c) LB (FS1), (d) LB (FS2) ............................................................... 243

Figure 9.9 Typical CT plots for FS1 and FS2 at 1200RPM (a) HRM (FS1), (b) HRM

(FS2), (c) LB (FS1), (d) LB (FS2) ........................................................................ 244

Figure 9.10 Proposed faults diagnosis (a) multiple speeds – FS1 setup (b) multiple

speeds – FS2 foundation (c) multiple speeds and multiple foundations ............. 248

Figure 9.11 Faults diagnosis with earlier CB and CT method (a) multiple speeds –

FS1 setup (b) multiple speeds – FS2 setup (c) multiple speeds and multiple

foundations ......................................................................................................... 250

Figure 9.12 Continuous faults diagnosis, (a) Multiple speeds - FS1 setup (b)

Multiple speeds - FS2 foundation (c) Multiple speeds and multiple foundations . 252

Figure 10.1 Schematic representation of pCCS computational process ............. 260

Figure 10.2 Laboratory scale experimental rig .................................................... 262

Figure 10.3 Typical pCCB plots (a) C1 (b) C2..................................................... 265

Figure 10.4 Typical pCCT plots (a) C1 (b) C2 ..................................................... 265

Figure 10.5 Typical combined magnitudes of B11 pCCB and T111 pCCT

components for all cases under ideal laboratory scenario (LS0) of complete data

............................................................................................................................ 266


components for all cases under different laboratory scenarios of missing data (a)

LS1 (b) LS2 (c) LS3 (d) LS4 .................................................................................. 268


components for individual cases for all scenarios (a) C1 (b) C2 (c) C3 (d) C4 (e)

C5 ....................................................................................................................... 269

Figure 10.8 Schematic representation of RKIDF assembly [262] ....................... 271

Figure 10.9 Schematic representation of the burning line ................................... 272

Figure 10.10 Limestone deposits on RKIDF impeller and blades [263] .............. 272

Figure 10.11 Photograph of on-site vibration measurement setup [263] ............. 273

Figure 10.12 Typical pCCB plots (a) faulty (b) healthy ........................................ 274

Figure 10.13 Typical pCCT plots (a) faulty (b) healthy ........................................ 274


components for all cases under ideal industrial scenario (IS0) of complete data 275

List of Figures

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components for all cases under different industrial scenarios of missing data (a)

IS1 (b) IS2 (c) IS3 (d) IS4 ...................................................................................... 276


components for individual cases for all scenarios (a) all faulty (b) all healthy ..... 277

List of Tables

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LIST OF TABLES ----------------------------------------------------------------------------------------------

Table 2.1 Roots blower scenarios for 2 cement plants ......................................... 90

Table 3.1 Technical specifications of the electric motor ........................................ 97

Table 3.2 Technical specifications of the speed controller .................................... 97

Table 3.3 Technical specifications of anti-friction ball bearings ............................ 99

Table 3.4 Technical specifications of accelerometers ......................................... 101

Table 3.5 Technical specifications of condenser microphone and power supply 103

Table 3.6 Technical specifications of ICP-PCB 086C03 instrumented hammer . 105

Table 3.7 Technical specifications of ICP-PCB 086C03 instrumented hammer . 106

Table 3.8 Technical specifications of NI 6229/16-bit/16-channel ADC ................ 108

Table 3.9 LABVIEW-based (version 2.0) data acquisition software settings ....... 109

Table 3.10 Experimentally identified natural frequencies for FS1 and FS2 ......... 119

Table 3.11 Experimentally simulated cases, abbreviations, severities and locations

............................................................................................................................ 126

Table 4.1 Shaft misalignment severities and locations ....................................... 134

Table 5.1 Simulated amplitudes and phases ...................................................... 148

Table 5.2 Magnitudes of CSD components ........................................................ 151

Table 5.3 Magnitudes of bispectrum and bicoherence components ................... 156

Table 6.1 Summary of the diagnostic features for bispectrum and trispectrum .. 174

Table 7.1 Experimentally identified natural frequencies for FS1 and FS2 ........... 190

Table 7.2 Summary of cases, locations and abbreviations ................................. 192

Table 7.3 CB components for HRM and LB cases (FS1 and FS2) at 1200RPM 195

Table 7.4 CT components for HRM and LB cases (FS1 and FS2) at 1200RPM 199

Table 7.5 Different scenarios of signal processing parameters .......................... 205

Table 9.1 Experimentally identified natural frequencies for FS1 and FS2 ........... 239

Table 9.2 Experimental scenarios for FS1 and FS2 ............................................ 242

Table 10.1 Experimental rig components and their specifications ...................... 263

Table 10.2 Experimentally simulated cases ........................................................ 264

Table 10.3 Signal processing parameters for experimental data ........................ 267

Table 10.4 Description of laboratory scenarios ................................................... 267

List of Tables

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Table 10.5 Technical specifications of RKIDF [262] ............................................ 270

Abbreviations

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ABBREVIATIONS ----------------------------------------------------------------------------------------------

AI

artificial intelligence

ANN artificial neural networks

BM breakdown maintenance

BS bent shaft

CB composite bispectrum

CI condition indicator

CM condition monitoring

CS composite spectrum

CSD cross-power spectral density

CT composite trispectrum

EDM electric discharge machining

FC flexible coupling

FD fault diagnosis

FDS

FE

fault diagnosis scenario

finite element

FRF frequency response function

FS flexible support

FT

HOC

HOS

Fourier transformation

higher order coherences

higher order spectra

HRM

IP

ISO

healthy with residual misalignment

input parameters

international standards organisation

LB

MMF

MSMF

OEM

loose bearing

magneto motive force

multi-speed multi-foundation

original equipment manufacturer

PC principal components

PCA principal component analysis

Abbreviations

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PCB printed circuit board

pCCS poly coherent composite spectrum

PMR planned maintenance regions

PPM

PSD

RB

planned preventive maintenance

power spectrum density

roots blower

RC rigid coupling

RMS root mean square

RPM revolutions per minute

SC shaft crack

SM shaft misalignment

SR

STFT

shaft rub

short time Fourier transformation

SVM

TM

UMA

support vector machine

target moduli

unified multi-speed analysis

VFD vibration-based fault diagnosis

WEC wind energy converter

Nomenclature

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NOMENCLATURE ----------------------------------------------------------------------------------------------

A orthogonal matrix

B number of bearings

B number of flexible supports

composite bispectrum at frequencies and

composite bispectrum at engine orders and

, , ..., experimentally simulated cases

covariance matrix of p

, , , frequencies

, ,.....,

feature matrices for different experimentally simulated cases at rotor speed

,

, ..., feature matrices at rotor speeds , ,.....,

respectively

, , ..., identical ‘as installed’ rotating machines with flexible supports 1, 2, ..., B

ns number of equal segments for Fourier transformation

n1 n2

observations variables

P number of measured data sets at a particular rotor speed

, ,....., rotor speeds in revolutions per minute

coherent composite spectrum at frequency

poly Coherent composite spectrum at frequency

,

coherent cross-power spectrum of the rth segment between bearings 1 and 2; bearings 2 and 3 at frequency

Nomenclature

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_________________________________________________________________



coherent cross-power spectrum of the rth segment between bearings (b-1) and b at frequency

T number of principal components

composite trispectrum at frequencies , and

, Fourier transformation of rth segment at frequency for

bearings (b-1) and b respectively

,

, ,

coherent composite Fourier transformation of rth segment at frequency , , and

,

complex conjugate of the Coherent composite Fourier transformation of rth segment at frequency and

complex conjugate of the Coherent composite Fourier transformation of rth segment at frequency

, poly coherent composite Fourier transformation of rth

segment at frequencies and

,

complex conjugate of poly coherent composite Fourier transformation of rth segment at frequencies and

,

, ,

Fourier transformation of rth segment at frequency for measurement locations 1-4 respectively

X1, X2, X3, ...., Xq individual features for “p” number of observations for a

particular case at rotor speed

, and engine orders

, ,

coherence between bearings 1 and 2; 2 and 3; ... (b-1) and b

diagonal matrix

List of Publications

_________________________________________________________________

_________________________________________________________________



LIST OF PUBLICATIONS ----------------------------------------------------------------------------------------------

Journal Publications

1. Paper title:- A comparison of signal processing tools: higher order spectra

versus higher order coherences

Authors: - A. Yunusa-Kaltungo, J.K. Sinha

Journal Name: - Journal of Vibration Engineering and Technologies

Status: - Published, Volume 3, Issue 4, August 2015

2. Paper title:- Combined bispectrum and trispectrum for faults diagnosis in

rotating machines


Journal Name: - Proceedings of the Institution of Mechanical Engineers, Part

O: Journal of Risk and Reliability

Status: - Published, Volume 228, Issue 4, February 2014

3. Paper title:- An improved data fusion technique for faults diagnosis in rotating

machines

Authors: - A. Yunusa-Kaltungo, J.K. Sinha, K. Elbhbah

Journal Name: - Measurement

Status: - Published, Volume 58, August 2014

4. Paper title:- Use of composite higher order spectra for faults diagnosis of

rotating machines with different foundation flexibilities

Authors: - A. Yunusa-Kaltungo, J.K. Sinha, A.D. Nembhard

Journal Name: - Measurement

Status: - Published, Volume 70, March 2015

5. Paper title:- A novel faults diagnosis technique for enhancing maintenance and

reliability of rotating machines



_________________________________________________________________

_________________________________________________________________



Journal Name: - Structural Health Monitoring

Status: - Available online (DOI: 10.1177/1475921715604388)

6. Paper title:- Sensitivity analysis of higher order coherent composite spectra in

machine faults diagnosis


Journal Name: - Structural Health Monitoring

Status: - Under review

Peer-reviewed Conference Publications

1. Paper title:- HOS analysis of measured vibration data on rotating machines

with different simulated faults

Authors: - A. Yunusa-Kaltungo, J.K. Sinha, K. Elbhbah

Conference Name: - 3rd

International Conference on Condition Monitoring of

Machinery in Non-Stationary Operations (CMMNO 2013), Ferrara/Italy, May 8-

10 2013

Status: - Published

2. Paper title:- Faults diagnosis in rotating machines using higher order spectra


Conference Name: - ASME Turbo Expo 2014: Turbine Technical Conference

and Exposition (GT2014), Dusseldorf/Germany, June 16-20 2014

Status: - Published

3. Paper title:- Coherent composite HOS analysis of rotating machines with

different support flexibilities


Conference Name: - 10th International Conference on Vibration Engineering

Technology of Machinery (VETOMAC X 2014), Manchester/United Kingdom,

September 9-11 2014

Status: - Published


_________________________________________________________________

_________________________________________________________________



4. Paper title:- Experimental observations of rotor orbit analysis in rotating

machines

Authors: - A. Yunusa-Kaltungo, A.D. Nembhard, J.K. Sinha

Conference Name: - 9th IFToMM International Conference on Rotor Dynamics

(IFToMM ICORD 2014), Milan/Italy, September 22-25 2014

Status: - Published

5. Paper title:- Study on rotating machine vibration behaviour using measured

vibro-acoustic signals


Conference Name: - 4th International Conference on Condition Monitoring of

Machinery in Non-Stationary Operations (CMMNO 2014), Lyon/France,

December 15-17 2014

Status: - Published

Abstract

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ABSTRACT ------------------------------------------------------------------------------------------------ The University of Manchester Akilu Yunusa-Kaltungo PhD Mechanical Engineering Vibration-based Condition Monitoring of Rotating Machines (2015)

Vibration-based condition monitoring (VCM) is an accepted approach for classifying machines as healthy or faulty. Although tangible advancements have been made with acceptable VCM techniques such as amplitude spectrum analysis, phase analysis, orbits analysis, etc. This often warrants the acquisition of vibration data from all orthogonal directions using multiple sensors at each bearing pedestal. Consequently, the number of data sets to be processed and interpreted could become overwhelming, especially when dealing with large industrial rotating machines.

Rotating machine faults are generally detected by the presence of harmonics of rotating speed in vibration response. Several studies indicate that higher order spectrum (HOS) and higher order coherence (HOC) possess the capabilities to establish the amplitude and phase interactions of frequency components in measured vibration signals. Hence HOS or HOC may be useful for detecting rotating machine faults. However, applications of HOC dominate the literature, with no clarification on which class is more useful. A comparative study was conducted with numerically simulated (with and without noise) and experimental data from a rig. These studies clearly indicate that HOS offers more meaningful results than HOC, owing to the significant dependence of HOC on the signal noise content. Hence HOS was used for further research studies.

Earlier studies tried to eliminate the rigour of analysing separate spectrum per measurement location by constructing single composite spectrum (CS) and bispectrum (CB) irrespective of measurement locations. Observations were encouraging but confined to a rig with relatively rigid foundation. Since several industrial rotating machines possess flexible foundations, the current study examined a wider range of faults on identical rigs with different flexible foundations. Composite trispectrum (CT) was also introduced to enhance robustness and it was observed that fault classification was possible at all speeds by combining just one CB and CT components. Despite the encouraging results obtained from earlier CS, it was limited by phase information loss at intermediate measurement locations. Also, the power spectrum density (PSD) computational approach adopted for the final CS makes it phase blind, thereby relying solely on the amplitudes at individual frequencies. Consequently, an improved poly-coherent composite spectrum (pCCS) was developed which retained phase information at all measurement locations. By building upon the earlier successes achieved with CB and CT, poly-coherent composite bispectrum (pCCB) and trispectrum (pCCT) were similarly developed which provided better diagnosis features.

Equipment standardisation as a cost-effective means of rationalising maintenance spares has become a very common industrial strategy. As a consequence of this, the existence of several identical rotating machines with different natural frequencies due to variations in their foundation flexibilities is also common. The development of a reliable method that permits the application of measured vibration data from one machine on another identical machine is likely to be appreciated by the industry. Hence, this was achieved by fusing pCCB and pCCT components in a novel hybrid data fusion algorithm on the identical rigs with different flexible foundations. The insensitivity of the proposed method to various scenarios of data availability was also confirmed with experimental and industrial data.

Declaration

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DECLARATION ------------------------------------------------------------------------------------------------

I hereby declare that no portion of the work referred to in the thesis has been

submitted in support of an application for another degree or qualification of this or

any other university or other institute of learning.

Copyright Statement

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_________________________________________________________________



COPYRIGHT STATEMENT ------------------------------------------------------------------------------------------------

I. The author of this thesis (including any appendices and/or schedules to this

thesis) owns certain copyright or related rights in it (the “Copyright”) and he

has given The University of Manchester certain rights to use such Copyright,

including for administrative purposes.

II. Copies of this thesis, either in full or in extracts and whether in hard or

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appropriate, in accordance with licensing agreements which the University

has from time to time. This page must form part of any such copies made.

III. The ownership of certain Copyright, patents, designs, trademarks and other

intellectual property (the “Intellectual Property”) and any reproductions of

copyright works in the thesis, for example graphs and tables

(“Reproductions”), which may be described in this thesis, may not be owned

by the author and may be owned by third parties. Such Intellectual Property

and Reproductions cannot and must not be made available for use without

written permission of the owner(s) of the relevant Intellectual Property and/or

Reproductions.

IV. Further information on the conditions under which disclosure, publication and

commercialisation of this thesis, the Copyright and any Intellectual Property

and/or Reproductions described in it may take place is available in the

University IP Policy (see

http://www.campus.manchester.ac.uk/medialibrary/policies/intellectual-

property.pdf), in any relevant Thesis restriction declarations deposited in the

University Library, The University Library’s regulations (see

http://www.campus.manchester.ac.uk/medialibrary/policies/intellectual-property.pdf

http://www.campus.manchester.ac.uk/medialibrary/policies/intellectual-property.pdf

Copyright Statement

___________________________________________________________________

_________________________________________________________________



http://www.manchester.ac.uk/library/aboutus/regulations) and in The

University’s Policy on presentation of Theses.

http://www.manchester.ac.uk/library/aboutus/regulations

Acknowledgements

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_________________________________________________________________



ACKNOWLEDGEMENTS ------------------------------------------------------------------------------------------------

My colossal gratitude goes to the Almighty Allah for the strength and wisdom I

received through His infinite mercies during my PhD research.

I would like to express my sincere appreciation to the Petroleum Technology

Development Fund (Federal Government of Nigeria) for wholly sponsoring each

element of my PhD research at the University of Manchester (UK).

I am also indebted to my friends and former colleagues at Lafarge Cement PLC

(Ashaka Plant, Nigeria) for providing all of the equipment technical specifications and

data used for the industrial validation aspect of this study.

I would also like to thank Dr. Jyoti Kumar Sinha (my PhD supervisor) for his

unabated support, guidance and drive during my PhD research, which transmogrified

into an extremely wonderful research environment at the University of Manchester

(UK). I am also indebted to all members of the School of Mechanical, Aerospace and

Civil Engineering (MACE) workshop team for accurately producing all the

components of my experimental rigs.

I extend my thanks to my colleagues and friends at D-Floor students’ village (Pariser

Building) and the Dynamics Laboratory at the School of MACE (University of

Manchester). In particular, Dr. Adrian D. Nembhard and Dr. Keri Elbhbah with whom

I built a formidable and result-oriented relationship during the last 3 years.

Finally, I would like to thank my family (immediate and extended) and friends for their

moral support and stoicism during more than 3 years of sedulous efforts committed

to this research, especially when the chips appeared to be down.

Dedication

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DEDICATION ------------------------------------------------------------------------------------------------

I dedicate this work to my late father (died 26/12/2005), my mother, my wife, my kids,

my sisters and my brothers who supported and encouraged me during this PhD

research.

Scientific Quote

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SCIENTIFIC QUOTE ------------------------------------------------------------------------------------------------

“The measure of greatness in a scientific idea is the extent to which

it stimulates thought and opens up new lines of research.”

- Paul A.M. Dirac

Introduction

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1 Chapter 1 INTRODUCTION

----------------------------------------------------------------------------------------------

1.1 Overview

A significant number of modern industrial operations rely on various rotating

machines including pumps, compressors, induction motors, turbo-generators,

crushers, etc. Owing to the recent advances in design and manufacturing

technologies, the configurations and complexities of these rotating machines have

risen tremendously, which has correspondingly increased their failure modes. In

general, the attainment of the end of useful operating life of one or more rotating

machine components (e.g. rotors, discs, bearings, couplings, blades, gears, etc.)

can be either age-related (gradual) or random [1]. In most cases, age-related and

systematic failures are often tolerable, owing to the fact that they are more

predictable and offer appreciable lead time to failure [2]. On the contrary, random

failures are often associated with a significant degree of uncertainty, which makes

them less desirable to any operational process [1], [3], especially when they can

potentially lead to huge production downtimes and in extreme cases loss of human

life. For instance, previous statistics had indicated that as much as 20% of

accidents that occur in aircraft transmission systems are random in nature [4], [5],

which further emphasizes the need for early and accurate rotating machine faults

detection techniques.

For several decades, maintenance activities (repair or replace) have always

served as remedies to rotating machine failures, although earlier maintenance

strategies accommodated larger tolerances for equipment failure. However, owing

to increasingly tough sanctions associated with operational inefficiencies,

maintenance strategies have significantly transformed from the age of waiting for

Introduction

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_________________________________________________________________



failures to occur before repair/replace actions are initiated (breakdown

maintenance (BM)) or assuming that all failures are gradual and time-based (time-

driven or planned preventive maintenance (PPM)) to the prediction of failures prior

to their occurrence (condition monitoring). Figure 1.1 presents an outline of the

popular maintenance philosophies and some of their characteristic features.

Figure 1.1 Maintenance philosophies and their characteristics

Condition monitoring (CM) of rotating machines fundamentally involves the

continuous application of measured and trended operational parameters (which

are often compared to pre-established baseline values) such as temperature,

pressure, sound, vibration, motor current, etc., to predict machine health [6].

Amongst all the CM techniques (infrared thermography (IRT), wear debris analysis

(WDA), vibration-based condition monitoring (VCM), acoustic emission (AE),

motor current analysis (MCA), etc.), VCM is the most established and most

tangible [7], owing to the fact that most rotating machine faults (unbalance,

misalignment, looseness, broken rotor bars, worn/damaged gears, damaged

Introduction

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_________________________________________________________________



couplings, damaged bearings, etc.) exhibit their peculiar defect characteristics,

which often provide very strong indications of the sources of machine faults [7].

Although several VCM techniques have been used for detecting faults related to

rotating machines, however, spectrum analysis is the most commonly applied in

practice. A major drawback of the application of spectrum analysis alone is the

possibility to generate identical features for different rotating machine operating

conditions. This drawback is owing to the fact that spectrum analysis simply

compares the amplitudes at individual frequencies for different machine

conditions, since all phase information have been lost during the magnitude

squared operation leading to its computation. This is why additional analysis such

as rotor orbits and phase analysis are often required, which significantly increase

the complexity and subjectivity of the fault diagnosis process. The problem

becomes even bigger and more complicated when dealing with one or more large

multi-shaft rotating machines with several bearings and operating at multiple

speeds, such as large turbo generator sets for power generation or the coal mill

drive assembly schematically shown in Figure 1.2.

Introduction

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Figure 1.2 Multi-shaft coal mill drive assembly layout, with locations and

orientations of VCM sensors. HO represents horizontal orientation, VO vertical

orientation and AO axial orientation [8], [9].

According to the provisions of popular vibration monitoring standards such as ISO

10816 [10], VCM faults diagnosis on a typical rotating machine such as that shown

in Figure 1.2 would entail the analysis of approximately 28 data sets (i.e. 10 VO

accelerometers, 10 HO accelerometers, 3 AO accelerometers, 4 proximity probes

and 1 tachometer), which will require separate analysis (e.g. amplitude spectra,

rotor orbits, phase plots, etc.). Therefore, taking advantage of the recent

advancements in computational technology, the development of a VCM technique

that will significantly minimise sensor/data requirements without necessarily

compromising the faults diagnosis process is highly desirable. Besides reducing

the rigour, complexity and subjectivity associated with the application of

Introduction

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_________________________________________________________________



conventional VCM techniques such as spectrum analysis, the current approach

will foster the realisation of the global need for sensor reduction and management

of big data (especially when it can be applied to several identical rotating

machines irrespective of their foundation flexibilities and speeds), which has

topped the list of several research councils for the past decade [11].

1.2 Research Objectives

The aim of this research is to simplify the currently existing rotating machines’

faults diagnosis process, so that the influence of subjectivity and engineering

judgements can be significantly minimised. Hence, the objectives are:

Objective 1: Compare Higher order spectra and higher order coherences

in order to determine the usefulness of either class of signal processing

tools.

Objective 2: Observe the dynamics of different rotating machine faults with

reduced sensors, using higher order spectra.

Objective 3: Improve the existing frequency domain data fusion technique

used for constructing a single composite spectrum for a rotating machine,

so as to ease and enhance the accuracy of fault diagnosis.

Objective 4: Develop a fault diagnosis method that is independent of

machine speeds and foundation flexibilities, using composite spectra.

Objective 5: Determine the sensitivity of composite higher order spectra to

various scenarios of data availability.

Introduction

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1.3 Research Review

As earlier mentioned, the aim of the current research is to simplify the VCM of

rotating machines by reducing the number of sensors required, and hence the

data sets to be analysed as well as developing a faults diagnosis approach that

will aid faults classification in identically configured rotating machines irrespective

of their operating speeds and foundation types. General vibration guidelines (e.g.

ISO 10816 [10]) commonly used in practice often recommend that vibration

measurements at each bearing location of a typical rotating machine should be

recorded from all orthogonal directions (i.e. vertical, horizontal and axial

directions), thereby resulting to the installation of approximately 3 vibration

sensors (and a corresponding number of vibration data sets to be analysed) per

bearing location. In order to realise the objective of reduced sensors and

measured vibration data, the current research only employs the use of a single

vibration sensor (accelerometer) per bearing location. The measured vibration

data are then processed using the higher order signal processing tools, which

exhibit a valuable faults diagnosis characteristic of establishing the relationships

that exist between the various frequency components of a signal. Besides

expressing the relationship that exists between frequency components of a

measured vibration signal (which is very vital for rotating machines’ faults

diagnosis, since measured vibration signals from practical rotating machines often

contain several harmonic components due to different faults), each higher order

signal processing component contains both amplitude and phase information,

thereby eliminating the need for additional analysis of phase information often

associated with the conventional spectrum analysis technique.

There are two very popular classes of higher order signal processing techniques,

higher order spectra (HOS) and its normalised form, higher order coherences

(HOC). The decision to select HOS for the current research was based on the

results of an initial sensitivity analysis conducted on both experimental and

numerically simulated vibration data. From these analyses, it was observed that

HOC components were significantly influenced by variations in measurement

Introduction

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_________________________________________________________________



noise, while the HOS components remained relatively stable at different noise

levels.

Besides the aim of minimising the number of rotating machines’ VCM sensors and

data requirements, currently employed faults diagnosis approaches such as

spectrum analysis often entail the analysis of numerous amplitude spectra (which

are directly proportional to the number of vibration measurement locations on the

machine) prior to establishing the machine’s state of health. This implies that

routine establishment of the operating condition of large rotating machines

characterised by several measurement locations could be extremely rigorous and

costly, which may hinder the timely detection of incipient faults. Therefore, an

approach that generates a single composite spectrum (CS) that represents the

entire dynamics of a rotating machine irrespective of the number of vibration

measurement locations has been developed by an earlier study. The approach

entails the fusion of measured vibration data in the frequency domain, which

provided different composite spectral features for several experimentally simulated

rotor-related faults of an experimental rig. Despite the encouraging results

observed from the earlier CS approach, its absolute reliance on the amplitudes of

harmonic components limited its robustness. Hence, an improved frequency

domain data fusion approach has been developed in the current study, which

clearly offered better fault diagnosis results when compared to the earlier

approach.

It is a very common practical scenario to have identically configured rotating

machines (either installed at different locations in a particular plant or installed at

different plants) with varying foundation flexibilities and operating at various

speeds. Based on existing VCM techniques, faults classification under such

scenarios usually entail the conduction of separate analysis for individual

machines at different speeds, which is extremely demanding. Therefore, based on

the combination of a few composite HOS components, the current approach was

used to diagnose several rotor-related faults irrespective of machine foundation

and speed. Finally, the sensitivity of the current method was also tested against

Introduction

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_________________________________________________________________



different signal processing parameters and measured vibration data availability,

and the faults diagnosis features under each case remained relatively stable.

1.4 Outline of Thesis

This thesis is not presented in the classical PhD thesis format, but rather

presented in the alternative format where the core context is provided in the form

of published/submitted research journal and peer-reviewed conference papers.

However, it should be noted that as in the classical PhD thesis format, the

alternative format requires that all cited references are compiled and grouped

under “References” at the end of the thesis. Figure 1.3 shows a graphical abstract

of the various chapters and their associated contents, which is further elaborated

in the subsequent paragraphs.

Introduction

_______________________________________________________________________________________________________

________________________________________________________________________________________________________

Akilu Yunusa-Kaltungo 43 PhD in Mechanical Engineering (2015) University of Manchester (UK)

Figure 1.3 Thesis chapters and contents

Introduction

___________________________________________________________________

_________________________________________________________________



Chapter 2 presents a review of academic and commercial research works related to

the general concepts of rotating machines’ VCM, as well as some of the common

causes of vibration in rotating machines. Owing to the alternative format adopted for

this thesis, the literature review conducted in Chapter 2 has been limited to a

general overview of rotating machines’ VCM process and the characteristics of some

of the most common causes of abnormal rotor-related vibrations. However, since

each of the “results” chapters (i.e. Chapters 4-10) is self-contained, a more specific

review of literature related to the questions addressed by that chapter is again

provided, so that it can be read without reference to the rest of the thesis.

In Chapter 3, detailed descriptions of the experimental rigs and experimentally

simulated cases are provided, including the technical specifications and settings of

the equipment, tools and instrumentation used for data collection and processing.

Prior to the simulation of different machine faults on the rigs, the natural frequencies

of each rig were experimentally determined through modal analysis, so as to

adequately understand the dynamic behaviours of the studied rotating machines.

With the exception of Chapter 5 and Chapter 11, the subsequent chapters are

constituted of the results obtained from the various experiments conducted and their

corresponding explanations. Although full details of the experimental setups and

faults simulation are provided in Chapter 3, however, the alternative format adopted

in this thesis (based on published/submitted research papers) may sometimes be

characterised by the repetition of information (in this case, the experimental setups

and faults simulation sections) in some chapters (i.e. Chapter 4 and Chapters 6-10),

especially when the same experimental rigs and faults were used to generate all the

analysed data. However, this approach enhances readability, as it eliminates the

need for constant reference to Chapter 3. Also, it preserves the original contents of

the already published/submitted research papers as much as possible.

Chapter 4 provides initial experimental observations on the detection of different

rotor-related faults, using common VCM techniques (spectrum and rotor orbits

analyses), so as to justify the need for the currently proposed approaches.

Introduction

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_________________________________________________________________



Based on some of the limitations observed to be associated with the commonly

applied VCM techniques studied in Chapter 4, a comparison of the faults diagnosis

abilities of the 2 most popular classes of higher order signal processing tools (i.e.

Higher Order Spectra and Higher Order Coherences) is provided in Chapter 5. The

results of the comparisons indicated that HOS (bispectrum and trispectrum) features

were unaffected by variations in measurement noise, which eventually led to the use

of HOS for diagnosing different faults associated with a rigidly supported rotating

machine in Chapter 6.

Once the ability of HOS to distinguish between different rotating machines’ operating

conditions was established in Chapter 6, the possibilities of simplifying faults

diagnosis through the construction of a single coherent composite higher order

spectrum (i.e. bispectrum and trispectrum) that represents the entire dynamics of a

typical rotating machine with various foundation flexibilities was then investigated in

Chapter 7. This investigation exposed the prospects of significantly reducing the

subjectivities and engineering judgements associated with faults diagnosis of rotating

machines, especially when dealing with large industrial rotating machines that are

supported by numerous bearings (e.g. large turbo generators).

Although the coherent composite higher order spectrum (CCS) data fusion technique

proposed in Chapter 7 provided encouraging rotating machines’ faults diagnosis

results, however, it was later observed that the cross-power spectral density (CSD)

approach adopted for the fusion of the measured vibration data from all

measurement locations led to the loss of phase information at successive bearing

locations, which eventually restricted the technique to faults diagnosis based on only

the amplitudes of several higher machine harmonics. In order to address this

limitation, an improved data fusion technique (i.e. poly-Coherent Composite

Spectrum) that retains all the amplitude and phase information at all the

measurement locations of a typical rotating machine was developed in Chapter 8.

The results obtained in Chapter 8 clearly indicated that faults diagnosis with the

improved poly-Coherent Composite Spectrum (pCCS) can be done based on just the

amplitudes and phase of the first or second harmonic alone, thereby eliminating the

need for investigating the higher harmonic components.

Introduction

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Chapter 9 presents a novel faults diagnosis technique that is capable of detecting

and classifying different rotating machines’ conditions, irrespective of the machine

speed or foundation flexibility. In this chapter, pCCS components computed for

different machine conditions (i.e. operating speed, different foundation flexibility and

state of health) were used as the features in a principal components analysis (PCA)

based algorithm, so as to develop a multiple faults/multiple speeds/multiple

foundations faults diagnosis technique for enhancing maintenance and reliability of

industrial rotating machines. This approach aims to eliminate the current practice of

conducting separate faults diagnosis for identical rotating machines installed at

different plant locations and operating under different conditions of speed and health.

A comparison of the multiple faults/multiple speeds/multiple foundations faults

classification capabilities of features computed based on the earlier CCS and the

improved pCCS was also conducted in this chapter.

Based on the premise that industrial rotating machines often operate under severe

adverse conditions that sometimes lead to VCM sensors’ damage and eventual loss

of vibration data, Chapter 10 examines the ability of the proposed pCCS faults

diagnosis technique to classify machine faults under different scenarios of measured

vibration data availability.

Finally, Chapter 11 provides the concluding remarks (i.e. an overall summary of the

main findings from each chapter), and discusses the possibilities for future research.

Literature Review

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2 Chapter 2 LITERATURE REVIEW

----------------------------------------------------------------------------------------------

This chapter commences by presenting a general overview of rotating machines

and the VCM framework, including detailed explanations of the vital stages (i.e.

data collection, data processing and faults diagnosis) of the VCM process. The

chapter then proceeds to discuss some of the most commonly encountered rotor-

related faults in practice. Reviews of previously reported research studies on VCM

techniques that are commonly used to diagnose such rotor-related faults are

provided, as well as highlights of the need for more robust and simplified

approaches.

2.1 Typical VCM Process Framework

As previously mentioned, rotating machines form the heart of most industrial

activities, and more often than not, a reasonable amount of industrial failures are

usually associated with one or more components of these rotating machines. A

rotating machine may be simply described as an assembly of different

components (e.g. bearings, shafts, gears, couplings, impellers, blades, etc.) with

at least one of these components subjected to rotational motion, so as to aid the

achievement of a specific operational purpose [12]. The class of rotating machines

is quite enormous and vast, of which some of the most commonly used ones

across different industries include compressors, induction motors, fans, turbo-

generators, bucket elevators, belt conveyors, drag chains, crushers, drills, pumps,

etc. Owing to the extreme relevance of rotating machines, varying degrees of

Literature Review

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_________________________________________________________________



design and complexities have emerged over the years. These complexities and

sophistications correspondingly increase their proneness to failures, due to

increased failure modes. The implications of rotating machines’ (especially the

critical ones) failures to industries can range from short duration downtimes to

catastrophic and permanent stoppages, which often have very significant effects

on production, finance, safety and environment [12], [13]. Since rotating machines

form the backbone of most operations, it therefore becomes imperative to deduce

robust and reliable techniques that will accurately detect and diagnose their

incipient faults, so as to reduce the impacts of downtime to the barest minimum.

Over the years, a very popular means of prolonging the lead time to rotating

machines’ failures [14]–[17] is VCM, which is perhaps due to worrying statistics

indicating that up to 20-40% of casualties and unplanned outages could be directly

linked to vibration [18].

VCM is a branch of CM maintenance philosophy that employs vibration-based

techniques to ascertain the true conditions of machines and structures, so that

maintenance decisions (repair or replace) can be recommended based on

detected deviations from normal operational conditions. A correctly implemented

VCM program has the capability of significantly reducing maintenance costs,

through the elimination of sudden or abrupt failures. A typical VCM process is

often made up of the three basic stages shown in Figure 2.1 [19].

Literature Review

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Figure 2.1 Basic stages of a typical VCM process

2.1.1 Data collection

The initial stage of a typical VCM process for rotating machines is the

measurement and storage of vibration data. This stage of VCM usually entails the

installation of several instruments, which may slightly vary for different rotating

machines depending on complexity and fault types. However, most VCM systems

will usually require transducers, signal conditioners, analogue-to-digital converters

and means of storing the measured vibration data for further processing. A

transducer or sensor can be defined as an instrument that is capable of

transforming variations in physical quantities into an electrical signal. The vibration

signals measured from rotating machines by the transducers are usually analogue

signals which will need to be digitized for them to be admissible to the eventual

storage systems (usually a personal computer system). This digitization is

achieved through the aid of an analogue-to-digital converter (ADC). Sometimes,

Literature Review

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the range of the signals measured by the transducer may exceed or fall short of

the requirements of the ADC. Therefore, the incorporation of a signal conditioning

unit is always desired. Signal conditioning units perform various functions,

including the provision of required power to the transducers as well as the

amplification or attenuation of the measured signal, so as to ensure adequate

compatibility between measured signal range and the requirements of the ADC.

Figure 2.2 is a schematic representation of PC-based data collection and storage

stage of a typical rotating machine’s VCM system showing transducers

(accelerometers) A1-A4 installed at bearings B1-B4, flexible (FC) and rigid (RC)

couplings, signal conditioner, ADC and personal computer (PC).

Figure 2.2 Vibration data collection process for a typical rotating machine [20]

Literature Review

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In accordance with the theory of vibration, all vibrating components possess three

classes of closely related parameters (i.e. acceleration, velocity and displacement)

as shown by Equation (2.1). This therefore implies that the availability of any of

these parameters can adequately generate the other two parameters through

differentiation or integration [21].

(2.1)

In Equation (2.1), , and respectively denote the inertia, damping

and stiffness forces, while their sum is equivalent to the external force ( ). It is

therefore visible from the relationship that the inertia force is associated with

acceleration ( , while the damping and stiffness forces are respectively

associated with velocity ( ) and displacement ( ).

There are various types of transducers for measuring the vibration responses of

rotating machines in practice, including proximity probes for measuring the relative

displacement of a rotating shaft with respect to a fixed bearing pedestal,

seismometer for velocity measurements and accelerometers for acceleration

measurements. However, the setting up of a vibration data collection system

should be guided by certain precautions, which are not limited to but including [23]:

Knowledge of the technical specifications of the rotating machine on which

measurements are to be conducted.

Knowledge of the working principle and technical specifications of the

selected transducers (e.g. sensitivity, frequency range of measurement,

resonance frequency, etc.), so as to aid optimised selection.

Knowledge of the implications of different transducer mounting techniques

(e.g. stud, adhesive, wax and hand-held mounting techniques) on the

repeatability of measurements.

Knowledge of how the measured vibration data will be stored into the PC.

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2.1.2 Data processing

The vibration data measured and stored using the concepts described in Section

2.1.1 require processing, so as to extract the features that can be used to describe

the different operational conditions of the studied rotating machine. Measured

vibration signals are usually time domain signals which are complex in nature,

containing several frequency components with correspondingly different

amplitudes, due to the variety of responses generated by different components

(e.g. rotor, bearings, gears, blades, etc.) that form the machine train and possible

faults (e.g. misalignment, unbalance, crack, bend, rub, etc.). An earlier study by

Jardine et al. [19] classified rotating machinery data as waveform data, which can

be analysed using all or any of these three basic classes of techniques, namely;

time domain, frequency domain or time-frequency domain analyses techniques.

2.1.2.1 Time domain analysis

A time domain signal can be simply described as a plot of vibration amplitude

(displacement, velocity, acceleration, etc.) against time. During time domain

analysis, statistical features (e.g. peak, peak-to-peak, root-mean-square, crest

factor, kurtosis, etc.) that describe the time waveform are extracted in the time

domain. A very common application of time domain analysis in the industry is for

the overall comparison of the wave patterns of two “as installed” machines, so as

to establish their states of operational health with respect to each other, prior to

detailed analysis for detecting the exact sources of faults.

Time domain analysis has existed for a substantial period of time, with analysis in

earlier times involving the use of oscilloscopes and manual computation of the

different frequency components. A very popular and valuable kind of time-domain

analysis is the synchronous time averaging (STA) technique [22]–[24]. STA is very

useful in the localisation of vibration sources when there are several shafts running

at different speeds (e.g. in a multi-shaft drive assembly such as that shown in

Figure 1.1) in a machine train, as it directly measures vibrations that are

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associated with the running speed of the machine’s component of interest. This

therefore makes STA useful for eliminating vibrations that are not related (non-

synchronous) to the fundamental running speed of the reference shaft (such as

bearings faults, noise, etc.) through averaging, while retaining rotor related (such

as unbalance, rub, misalignment, looseness, etc.) vibrations.

Studies by Dalpiaz et al. [25] compared the effectiveness and sensitivities of

vibration signals processing techniques such as cepstrum and STA for the

detection of gear faults. The study [25] indicated that cepstrum analysis only

provided detailed information about the spectrum evolution, but was unable to

detect the gear faults from a single vibration measurement, due to the presence of

high energy activities (gear meshing frequencies) in both healthy and faulty gears.

On the other hand, STA provided absolute diagnostic information by effectively

identifying the location of the faulty gear.

2.1.2.2 Frequency domain analysis

Analysis in the frequency domain primarily entails the conversion of the complex

time domain vibration signal into the frequency domain, through the well-known

fast Fourier transformation (FFT) process. A significant merit of working in the

frequency domain over the time domain is its ability to easily isolate frequency

components of interest, which is further explained in Appendix A. One of the most

successful and widely used forms of frequency domain analysis is the spectrum

analysis, which involves either viewing the entire range of the machine spectrum

or focussing on a particular set of interesting frequency components [26]–[28].

2.1.2.3 Time-frequency analysis

The investigation of time-frequency analysis commenced due to the perceived

inabilities of the conventional spectrum analysis to effectively handle non-

stationary waveforms, which is quite possible with rotating machines. The

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conventional time-frequency analysis applies time-frequency distributions (which

represent the energy or power of the waveform signal in a dual dimensional

function of time as well as frequency) for more effective and revealing diagnosis of

rotating machinery faults. Some of the most popular time-frequency analysis

techniques are the short-time Fourier transform (STFT) or spectrogram [29]–[31].

STFT is based on the principle of dividing the entire waveform signal into various

segments with short-time windows, and subsequently performing a Fourier

transform on each segment.

2.1.3 Faults diagnosis

Faults diagnosis in VCM of rotating machines can also be referred to as the

interpretation of the measured vibration data. This stage of the VCM process

mainly involves the analysis of the various features (representing different

machine conditions) that have been extracted through any of the principles

described in Section 2.1.2, so as to ascertain the exact sources of the rotating

machine’s excessive vibration. Figure 2.3 shows a typical spectrum-based faults

diagnosis fault tree for some common rotating machine faults. As earlier

mentioned in Section 2.1.2, every component in a rotating machine train can be

described by its individual characteristic defect feature. Hence, the accurate

detection of these defect features provides significant guides towards the root

causes of abnormal rotating machines’ vibration.

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Figure 2.3 Typical spectrum-based VCM fault tree for a rotating machine

2.2 Standard Approaches to Vibration-based Fault Detection

Although a brief mention of the applications of some popular classes of VCM

techniques was made as part of Section 2.1.2 (Data processing), however, the

research and industrial maturity of VCM techniques such as amplitude spectrum

analysis for fault diagnosis makes it imperative to further highlight relevant

literature especially with respect to its sensitivity to different faults. This is then

followed by an overview of other standard VCM techniques such as rotor orbit

analysis, full spectrum analysis and order tracking.

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2.2.1 Spectrum analysis

Amongst the currently employed VCM techniques in practice, spectrum analysis

(based on the fast Fourier transformation (FFT)) is undoubtedly the most quotidian

due to its ease of computation and versatility. Once the FFT and eventual power

spectrum density (magnitude squared operation that leads to the loss of phase

information) operation is performed, the typical amplitude spectrum results to a

plot of amplitude at individual frequency components of the measured vibration

signal. Features (e.g. 1x, 2x, 3x, etc.) from several amplitude spectra representing

different machine operating conditions are then extracted and compared during

faults diagnosis. In this section, an overview of the spectrum-based characteristics

of some of the most commonly encountered rotating machine faults in practice will

be provided, so as to augment understanding. Additional theoretical explanation of

amplitude spectrum is provided in Appendix A.

2.2.1.1 Unbalance fault

Unbalance fault has been classified as one of the most common causes of

vibration in rotating machines [32]. Parkinson [33] and Foiles et al. [34]

respectively provided detailed and comprehensive reviews of some of the

conventional techniques commonly applied for correcting unbalance in rotors.

Machinery vibrations due to unbalance fault is usually characterised by a dominant

peak at the fundamental rotational frequency (1x RPM), which usually changes in

proportion to the square of the rotational speed and in the radial direction. Figure

2.4 provides a typical amplitude spectrum of a rotating machine with unbalance

fault. The total elimination of unbalance fault in rotating machines is almost

impracticable, due to the difficulties associated with achieving perfection in the

manufacture of components as well as their installation. Based on this premise, a

significant number of researches have been centred on estimating unbalance and

its correction.

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showing dominant 1x RPM peak as a result of unbalance fault.

2.2.1.2 Shaft bow

The amplitude spectrum produced as a result of a bent or bowed shaft will usually

be characterised by the presence of 1x and 2x RPM components, which will

generally be transmitted in both radial and axial directions [35]. The location of the

bend will determine the dominance of the 1x RPM amplitude (if at the centre of the

shaft) or 2x RPM (if bend is located near the ends of the shaft). A detailed review

by Mehrjou et al. [36] on CM techniques for detecting rotor faults in squirrel-caged

induction machines pointed out that a bowed rotor complicates alignment and

could as well lead to other problems, depending on the location.

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rotor bow.

2.2.1.3 Shaft misalignment

Another very common cause of vibration in almost all classes of rotating machines

is misalignment. Shaft misalignment in rotating machines refers to a state whereby

components that have been designed to be coaxial are not actually coaxial, owing

to assembly defects or deformation of certain machine sub-units [37].

Misalignment in rotating machines may either appear as angular or parallel. The

occurrence of angular misalignment is as a result of the formation of an angle by

the centre lines of the two coupled shafts. Vibration spectra produced by rotating

machines with angular misalignment will be characterised by pronounced peaks at

1x RPM, while the presence of 2x and 3x RPM components is highly possible [38].

Angular misalignments in rotating machines usually generate high axial vibrations.

In the case of parallel misalignment, the centrelines of the coupled shafts are

parallel to each other, but with a certain degree of offset and therefore do not

coincide at any point. Such misalignments produce dominant 2x RPM components

in the radial direction, due to the two hits that occur per rotational cycle. Owing to

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the fact that parallel misalignment rarely occurs in isolation, the appearance of 1x

RPM component is also very common.


showing dominant 1x RPM and 2x RPM peaks due to misalignment.

2.2.1.4 Mechanical looseness

Mechanical looseness can either occur in the form of internal looseness between

the machine and its base mounting, internal looseness of the machine

components or structural looseness. Internal looseness occurs due to lack of

proper fit between the components of a machine (bearing-to-bearing housing,

shaft-to-bearing, coupling-to-shaft, etc.), which consequently leads to the

excitation of numerous harmonics of the machine running speed. These

harmonics are usually generated due to combined effects of exciting forces from

the rotor and the non-linear response from the loose components [35]. Looseness

between machine and base mounting is commonly the resultant of a crack in the

base structure or bearing pedestal, which may generate high 2x RPM component

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and some harmonics. Structural looseness on the other hand occurs when there is

a weakness in the foundation or looseness in the supporting structure.

The presence of mechanical looseness in a machine train is often characterised

by chaotic response, which have been observed to sometimes excite multiples of

x or

x RPM [39]. Other studies on mechanical looseness in rotating machines

such as those related to bearing caps or supports have also been seen to have

large numbers of harmonics and sub-harmonics, which were dependent on the

analysis direction and point [40]. The vibration signatures produced by a rotating

machine with mechanical looseness have also indicated that the vibration

amplitude at the higher order frequency region will usually be greater than half of

the vibration amplitude caused by the rotational speed, which will persist after

machine balancing operations [41].



bearing looseness.

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2.2.1.5 Shaft crack

Another fault common to rotating machines is shaft crack. Although the primary

aim of studying shaft crack is for the purpose of fault detection and diagnosis,

however, the behaviour and responses that result from this fault also makes it an

interesting subject area. A cracked shaft will usually lose stiffness in a direction

perpendicular to the crack location. One of the most fundamental signs of the

emergence of a crack is the appearance of 1x RPM and 2x RPM components

(which is usually the outcome of the asymmetry in the shaft’s stiffness). The 2x

RPM component will usually be dominant when the operating speed is about half

the critical speed, which should disappear with a change in the rotational speed of

the machine [35]. Besides the second harmonic of the rotational speed (2x RPM)

and the sub-harmonics of the critical speed, additional higher order harmonics of

the rotational speed (i.e. 3x RPM, 4x RPM, etc.) may be observed due to the non-

linear effects associated with the crack breathing action (opening and closing) [42],

[43]. Research studies aimed at understanding the signatures of cracked rotors

have existed for decades, with some of the very early studies using the different

moments of inertia of rotors to detect the presence of cracks, once higher and sub-

harmonics are initially observed in the spectra [44]. Figure 2.8 shows the typical

amplitude spectrum for a rotating machine with a transverse crack on its rotor.

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showing the appearance of several harmonics of machine speed due to rotor

crack.

2.2.1.6 Shaft rub

The response generated by a rotating shaft experiencing a rub action is very

similar to that of a loose machine, especially with its chaotic nature. Shaft rub

could be partial, (which occurs when the shaft only makes contact at some certain

points during its rotational cycle) or whole (where there is a constant and

continuous rub throughout the entire rotational cycle). Shaft rub is characterized by

the generation of a number of frequencies, excitation of one or more natural

frequencies and may also produce a band of white noise in the high frequency

region of the spectrum [35]. In addition, a rub action may also be characterised by

the presence of sub-harmonics, which will be integer fractions of the machine

rotational speed

. It is important to note that the appearance of

sub-harmonics in the spectrum of a machine experiencing shaft rub could be

highly dependent on the position of the shaft natural frequencies [35]. Although the

duration of a shaft rub action may be short, its severity could still significantly

depend on which component in the machine train the shaft rubs. Shaft rubs

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against seals, glands or coupling guards may be less severe. However, shaft rubs

against machine components such as bearings or turbine blades rubbing on

casing could have devastating consequences irrespective of the duration. Figure

2.9 shows a typical example of the spectral response that could be generated as a

result of shaft rub action.


showing the appearance of sub-harmonics of machine speed due to rotor rub.

2.2.2 Rotor orbit analysis

Another well-established VCM technique for rotating machines is the rotor orbit

analysis. Rotor orbits generally represent the enlarged pathway of the exact

motion of a rotor’s centreline [45]. Rotor orbits are recreated from the vibration

signals measured by 2 vibration sensors (usually proximity probes) installed in the

vertical and horizontal directions of the rotor. Since it is often believed that

changes in rotor motions at certain times are always triggered by variations in the

rotor dynamic stiffness or changes in the forces exerted on it, rotor orbits can

sometimes provide meaningful information with regards to the rotor behaviour [45].

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Figure 2.10 shows how a rotor orbit can be constructed from measured vertical

and horizontal shaft displacements. The tachometer signal may also be used to

define the start and finish points of the orbit, so as to track phase changes.

Figure 2.10 Rotor orbit plot of a typical rotating machine

Several researchers have attempted to develop specific fault diagnosis patterns

for various rotor-related faults using orbit plots. For instance, Darpe et al. [46] and

Sinou [47] independently conducted experiments to investigate transverse crack

through the appearance of an inner loop orbit which varied in size when the

machine speed is approximately half of the first natural frequency, owing to the

presence of a dominant second harmonic of the machine speed. Although both

studies [46], [47] focussed on the detection of rotor crack, the experiments by

Darpe et al. [46] were done on an experimental rig with self-aligning ball bearings

with the aim of confirming earlier findings on the analysis of a Jeffcott rotor with

transverse breathing crack and passing through subcritical resonances. Also

based on a compendious experimental investigation of rotor cracks, Sinou [47]

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used rotors with slots (representing rotors with cracks) that are supported by bush

bearings. These investigations therefore led to the conclusions that rotor cracks

could be diagnosed based on variations in the orientation of the inner looped orbit

once it passes through sub-critical resonances [46].

The results of another experimental study conducted by Bai et al. [48] also

promulgated a rotor orbit with an inner loop for a small rig supported by ball

bearings. In this study [48] however, the inner loop was not due to a crack but

rather due to the occurrence of sub-harmonic resonance once the rig (under

unbalance load) speed was approximately twice its critical speed. In an attempt to

accurately establish specific diagnosis features for different machine operating

conditions based on rotor orbits, Muszynska and Goldman [49] simultaneously

investigated the dynamics of an unbalanced rotor supported by rolling element

bearings on several experimental rigs, including a rig with a loose bearing

pedestal and another with rotor-stator rub actions. Observations from the studies

stipulated that when partial rotor-stator rubbing occurred at high speeds, the orbits

display reverse precession loops as a consequence of the rub-generated

tangential force opposing the direction of rotation. Other research efforts aimed at

improving fault diagnosis using rotor orbit analysis include the detection of impact

rub phenomenon [50], cracked shaft [51], investigation of the causes of fractional

harmonic components in journal bearings as well as variations in oil temperature

and pressure [52], shaft misalignment [53], [54], backward whirl due to excessive

friction generated by rubbing components [49], etc.

2.2.3 Full spectrum analysis

The conventional spectrum analysis is based on vibration data acquired from only

one measurement direction (i.e. either vertical or horizontal), which therefore

makes it impossible for it to establish the relative phase correlation that exists

between vertical and horizontal spectral components [53]. But just as rotor orbit,

the full spectrum also offers information about the correlation that exists between

vibration data sets simultaneously measured in the vertical and horizontal

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directions (using vibration sensors). The initial steps of full spectrum analysis are

very similar to those applied for the conventional spectrum analysis, whereby the

time domain data from the vibration sensors are respectively broken down into

frequency components. A full spectrum is then created from the amplitudes of the

forward and backward whirl components of the filtered orbits. In concise terms, the

full spectrum can be regarded as the spectrum of an orbit. The vertical axis of the

full spectrum represents the peak-to-peak amplitude of the forward/backward

components, while the horizontal axis represents the ‘±’ frequency components.

The “+” represents forward components and are usually plotted on the right-hand-

side (RHS), while the “−” represents backward components and are

correspondingly plotted on the left-hand-side (LHS). More detailed and

comprehensive information, including the mathematical approach for generating

full spectra were presented in an earlier study conducted by Goldman and

Muszynska [55].

Industrial applications of full spectrum is not limited to but include the investigation

of axial run-out of shafts due to mechanical or electrical deformities [55]. Based on

the ambiguity often associated with the differentiation of certain rotor-related faults

such as shaft crack and shaft misalignment, some researchers have explored the

possibility of enhancing fault diagnosis quality by using full spectrum analysis. For

instance, using and experimental rig with 2 coupled rotors (each rotor carrying a

balance disc), Patel and Darpe [53] disclosed that although the vibration of rotors

due to parallel and/or angular misalignment is forward whirling (due to marginally

larger “+” harmonic components than “−” harmonic components), the presence of

backward whirl components at sub-critical speeds could provide a valuable means

of distinguishing misalignment and crack. The study [53] further emphasized that

the whirl nature of 2x and 3x components at 1/2 and 1/3 the critical speeds

respectively provide swift means differentiating shaft crack and shaft misalignment

faults. At 1/2 the critical speed, both +2x (forward) and -2x (backward) whirl

components are significant for shaft misalignment, unlike shaft crack that

possesses only significant +2x (forward) and very negligible -2x (backward) whirl

components. Similarly, at 1/3rd the critical speed, shaft crack exhibits prominent

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+2x and +3x whirl components [56], with correspondingly negligible -2x and -3x

components, while shaft misalignment fault showed very comparable +2x, -2x, 3x

and -3x components.

In another experimental study, Fengqi and Meng [57] examined the features of full

spectra for various kinds and severities of rub in rotating machines, where it was

concluded that stable 1x amplitude along with lower amplitudes of its harmonics

will be observable with relatively mild rub actions. On the other hand, the

amplitude of 1x decreases as the magnitude of rub increases, which will also

trigger the generation of more higher harmonic components. Additionally,

Goldmann and Muszynzka [55] provided a detailed summary of the observable

features from full spectrum when diagnosing commonly encountered rotating

machine faults such as unbalance, rotor crack, partial rub, full rub, etc.

2.2.4 Order tracking

The behaviours of rotating machines during transient operations often provide very

vital information that aid the detection or verification of impending faults that may

lead to very costly downtimes. During order tracking, 1x and other higher

harmonics of the machine speed need to be extracted from the measured vibration

data [58], [59], so as to establish amplitude-to-phase relationship of the extracted

harmonics (e.g. 1x, 2x, etc.) with the change in machine speed (which is

sometimes plotted as the Bode plot).

In a study conducted by Wang et al. [60] to accurately monitor the propagation of a

transverse crack on a shaft with variable speed, it was proclaimed that though

small in amplitude, transient vibrations due to cracks often modulate and distort

the prominent harmonic vibration orders which makes the phenomenon extremely

difficult to extract based on time waveform reconstructed order tracking alone.

Therefore, through the individual application as well as combinations of various

signal processing techniques (e.g. Vold-Kalman filter order tracking (VKF-OT),

Gabor order tracking (GOT), Fourier analysis, time-frequency analysis, computed

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order tracking (COT), etc.) on a set of simulated data representing a machine with

cracked rotor, Wang et al. [60] concluded that an integration of COT [61], VKF-OT

or GOT techniques offer the best possibilities for detecting both the prominent

harmonic and the small transient vibrations.

In another study, Abdul-Aziz et al. [62] experimentally monitored the behaviour of

a growing crack through spin tests conducted on a rotating rig, with the primary

aim of simulating the mission profile of a space aircraft engine. Crack detection in

this study [62] entailed comparing the bode plots of 2 scenarios (healthy toothed

disc and a toothed disc with a small artificially induced notch) on the same

experimental rig. In the bode plot for the experimental setup with a cracked disk, a

sharp rise in the amplitude response after settling past the 1st critical speed was

clearly observed and this behaviour was attributed to the crack. The response for

the healthy disk however remained smooth after crossing the 1st critical speed.

The findings from this study further affirms the observations from earlier studies

[63], [64], whereby a sharp rise in amplitude upon surpassing the 1st critical speed

was also reported.

2.3 Overview of Standard Vibration Based Fault Detection

Approaches

Over the years, a lot has been achieved in VCM of rotating machines through the

application of standard VCM techniques such as simple amplitude spectrum.

These achievements are immensely owed to a variety of factors such as the

sensitivity of the technique (i.e. amplitude spectrum) to a wide range of machine

faults (e.g. shaft bow, shaft misalignment, shaft crack, loose bearings, gear wear,

unbalance, bent shaft, gear crack, etc.), relative computational simplicity as well as

its applicability to different kinds of rotating machines. However, despite the

maturity level of the generally used amplitude spectrum (based on power spectrum

density), fault diagnosis based on this technique is tedious and often requires a

significant level of engineering judgement from an experienced analyst. Although

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the computation of amplitude spectra from measured vibration data is relatively

simple, however its lack of phase information often leads to over reliance on the

amplitudes at individual frequencies during fault diagnosis. In practice, the

amplitude/frequency relationship for different machine faults could appear similar.

For instance, the amplitude spectra due to shaft misalignment, loose bearing and

cracked shaft respectively shown in Figures 2.4-2.7 all contain several harmonics

of the machine speed.

Besides the loss of phase information, the limitations of diagnosis based on the

simple amplitude spectrum alone is further compounded by the fact that popular

vibration standards [10] recommend that vibration measurements should be

conducted at all orthogonal (xyz) axes of the bearing pedestals of rotating

machines. Consequently, several vibration sensors are often required at each

bearing pedestal, which leads to the generation of large volumes of data. The

method then becomes computationally intensive and complex for even the most

experienced analysts, especially when dealing with large rotating machines that

are supported by numerous bearings. Perhaps, a combination of these limitations

especially the lack of phase is the reason why spectrum analysis is usually

conducted in conjunction with other techniques such as orbit and phase analyses,

so as to enhance the confidence levels of the results.

The efficacy of monitoring the dynamic behaviour of rotating machines under

different operating conditions is well-known. However, the ambiguity associated

with rotor orbits representing clearly different machine operating conditions

sometimes introduces appreciable levels of inconsistency to the fault diagnosis

process. Thus, overcoming such inconsistencies would entail the introduction and

eventual analysis of additional parameters such as phase, using techniques such

as order tracking and full spectrum analysis. Effectively integrating all of these

techniques when analysing each machine condition will not only require

substantial expertise, but could also lead to expensive delays and plant

downtimes. As a consequence of the subjectivity and over dependence on human

engineering judgement associated with standard VCM techniques, VCM related

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researches have significantly diversified towards the application of model-based

fault detection techniques, artificial intelligence and pattern classification

techniques, higher order signal processing techniques, etc.

2.4 Emerging Approaches to Vibration Based Fault Detection

Recent advancements in computational and information technologies have offered

researchers ample opportunities to accurately detect and classify rotating machine

faults, using a variety of approaches. In this section, some of the emerging VCM

fault detection approaches will be highlighted.

2.4.1 Model-based approaches

Model-based fault diagnosis of rotating machines fundamentally entails the

development of an explicit mathematical model of the studied machine. Upon the

creation of a representative model, residual generation techniques (e.g. parameter

estimation) are then used to extract signals (also known as residuals) that will aid

fault detection and identification. The emergence of super-computers has provided

so much flexibility to model-based fault detection activities, with models ranging

from simplified 2D models to more complicated 3D models (Figure 2.11).

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Figure 2.11 3D model of a typical rotating machine.

In an attempt to obtain more precise and reliable understanding of the progression

of machine faults (e.g. crack propagation) based on previously deduced

information, considerable research has been done on model-based fault

identification. For instance, earlier studies by Sekhar [65] applied a model-based

identification technique to detect the presence of a breathing crack on a shaft that

is supported by 2 flexible bearings and carrying 2 discs. The crack location and

depth were identifiable even at fewer degrees of freedom (4 and 8). However, as

degrees of freedom (DOF) reduced, the accuracy of the estimated crack depth

also reduced due to the impossibility of accurately estimating full vibration data

from fewer data points. Using the same model and capitalising on the prospects of

the initial findings, Sekhar [66] extended the study to the detection of 2 transverse

breathing cracks. An FFT of estimated equivalent loads (which were dominant at

the nodes of the cracked elements) showed the appearance of 2x and 3x

harmonic components, which is an indication of crack.

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Despite shaft misalignment being one of the most commonly encountered rotor-

related faults in practice, an absolute understanding of the characteristic features

of this fault is yet to be established. This is sometimes due to the similarities

between the features exhibited by shaft misalignment fault and other rotor-related

faults such as crack. A quest for better understanding of the effects of

misalignment on the couplings has driven researchers including Sekhar and

Prabhu [37] to apply higher order finite element model to ascertain the presence

and location of misalignment in two coupled shafts. In this approach,

considerations were given to several parameters (shear force, slope, deflection,

bending moment, etc.) at each node. The study [37] deduced that both parallel

and angular misalignments of the connected shafts cause bending of the

coupling’s flexible diaphragms, and that the vibration response obtained contained

1x and 2x components. Research contributions from Patel and Darpe [54] also

indicated that the stiffness coefficients of rotors coupled with angular misalignment

vary with each cycle of rotation, and could exhibit up to the first 6 harmonics (i.e.

1x, 2x, 3x, …., 6x) of the rotational speed. Pennacchi et al. [67] elaborated on the

non-linearity generated as a result of coupling misalignment [67] in rotors with

journal bearings, while Jalan and Mohanty [68] differentiated between two

common rotating machine faults (i.e. misalignment and unbalance) as well as

detecting their locations, using residual generation model-based technique.

Besides the detection of shaft misalignment and crack faults, model-based

approaches have been extensively used to detect and quantify other rotor-related

faults. To mention a few, Sudhakar and Sekhar [69] highlighted that the

modification of equivalent loads and vibration minimization methods with a

theoretical fault model were less prone to errors and more effective in the

detection of unbalance when compared to the initial equivalent loads minimization

method. Other researchers have also estimated unbalance in rotating machines by

applying measured vibration data during a unit transient (a single run-down) of the

machine, while incorporating the rotor and bearing models for the estimation of the

multi-plane unbalance [32], [70]. This method proved fast and presented the

potential of overcoming some of the practical difficulties associated with the

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construction of a reliable finite element (FE) model that will adequately account for

the dynamics of the foundation [71].

A significant number of critical process machines (e.g. the rotary kilns in cement

manufacturing plants) that operate under extreme temperatures and loads require

near perfect temperature profiles (especially when restarting after a long

stoppage). This high level of perfection is sometimes unachievable due to

unforeseen failures of some auxiliary equipment (e.g. gearbox lubrication pump or

cooling water pump). This therefore leads to uneven heat/load distributions in the

shaft, which sometimes leads to shaft bow. Studies aimed at effectively detecting

and differentiating shaft bow include a model-based study of the dynamic

behaviour of a gear-rotor system with visco-elastic supports and a bowed shaft. It

was shown that the magnitude and phase of the bow exhibit significant effects on

the first critical speed [72]. Since the occurrence of multiple faults in typical

industrial rotating machines is quite common, efforts aimed at differentiating single

and multiple faults in rotating machines triggered earlier investigations into the

resultant responses generated by a bowed shaft with the presence of a transverse

crack [73]. In this study, a simulation of the responses from both faults (i.e. shaft

bow and crack) was conducted. Observations from the study [73] indicated that

slight shaft bows may not significantly affect the non-linear responses due to shaft

cracks, but could disguise the orbital response sensitivity of the cracked shaft at

half the critical speed. Pennacchi and Vania [74] also applied statistical methods

for studying the accuracy of faults identification of the bowed shaft of a power unit

generator during coast down. The study [74] concluded that the model-based

technique developed for the identification and differentiation of the faults was quite

reliable, based on insignificant differences observed (particularly at the points at

which the bow generated the highest vibration amplitudes) when compared to the

experimental technique.

Mechanical looseness is another common rotating machine fault that could have

devastating effects if undetected at its inchoate stage. The effects of mechanical

looseness sometimes extend beyond the machine with the loose components. For

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instance, looseness in machine foundation could lead to the transmission of

vibration to adjacent rotating machines. Some researchers have studied looseness

combined with impact rub by applying binary approaches such as non-linear finite

element method and contact theory on dual-disc rotor-bearing systems [75], [76],

where it was gleaned that the amplitude of vibration in the low frequency region

(due to looseness) is usually suppressed by the impact rub of the rotor and stator.

It was also concluded that impact rub induced as a result of bearing pedestal

looseness is directional.

However, despite the commendable research advances made in VCM of rotating

machines through the application of model-based techniques, the questions that

still linger around the ability to develop theoretical models that will accurately

represent the actual dynamics of rotating machines with extremely complex

configurations [19] has somewhat confined a significant aspect of its applications

to research.

2.4.2 Artificial intelligence and faults classification

Most of the matured rotating machines’ VCM techniques currently employed in the

industries still rely solely on human experiences for interpretation of diagnosis

features. This total reliance on human experience sometimes leads to significant

levels of subjectivity and errors. In order to minimise this reliance on personal

judgements, some researchers have explored the possibility of applying

techniques that can mimic the operations of the human brain. Such techniques are

generally referred to as artificial intelligence (AI) techniques. In the literature, some

of the most popular AI techniques for rotating machine faults diagnosis are artificial

neural networks (ANN), support vector machine (SVM), fuzzy logic, etc. AI

techniques such as ANN are based on computational models that imitate the

structure of the human brain [19]. A typical ANN model comprises of several

simple processing elements that are joined via a complicated layer structure that

allows the model to evaluate complicated tasks which are often characterised by

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multiple inputs and outputs. Figure 2.12 shows a typical ANN-based model with

multiple inputs (IP) and several target outputs (TM).

Figure 2.12 Typical ANN-based model

Noteworthy researchers have explored the possibility of completely automating

VCM of rotating machines using AI techniques such as ANN [77]–[84], so as to

create a smart approach that can effectively evade the elements of human

dependence associated with currently used techniques [85]. Among others, ANN

has been used to detect gear faults [80]–[82], rotor loading conditions [79] and

rolling element bearing faults [84]. While the research-based performance of AI

techniques such as ANN have continuously improved in comparison to

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conventional techniques, the deployment of ANN to the field is still restricted by

the lack of clearly stated guidelines for acquiring the training data as well as the

exact approach needed to train the model. This is perhaps why most of the studies

applying ANN for rotating machine faults diagnosis are still limited to the use of

experimental data for model training.

Another AI-based VCM technique for rotating machine faults diagnosis that is

growing in popularity is SVM. The real time analysis capability of SVM as well as

its supplemented decision boundary [86], [87] particularly makes it very attractive

for VCM of rotating machines. In an attempt to diagnose common rotating

machinery faults including crack, Jiang et al. [88] used SVM for classifying time

domain vibration features obtained via a multiple-sensor/feature-level fusion

approach. The authors [88] hinged the rationale behind this approach on the fact

that the sensitivity of single sensor-based diagnosis approaches may be low to

incipient faults, especially when dealing with complex machinery [89]. It is also

believed that the integration of several types of CM sensors may enhance the

accuracy with which quantities can be examined [89]. Based on these notions,

Jiang et al. [88] simulated various faults on a laboratory scale rig and the results

obtained were quite promising. However, the confidence levels of the study [88]

findings are still limited by the lack of clearly stated standards for selecting the

fundamental process for SVM (i.e. the Kernel function) [90].

In an attempt to simplify rotating machine fault diagnosis and at the same time

evade the aforementioned convolutions associated with popular AI-based

techniques including ANN and SVM, some researchers have examined the

possibilities of performing rotating machine faults diagnosis using classification

techniques such as principal components analysis (PCA). PCA is a multivariate

statistical analysis technique that is capable of reducing the dimensionality of data

sets. Original data sets such as measured vibration signal from a typical rotating

machine is often characterised by a large number of interrelated variables. PCA

transforms these interrelated variables onto a new subspace with significantly

lower dimensionality [91]. Thus the new subspace called PCs [91], [92], represent

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a set of uncorrelated valuables that retained the maximum variations available in

the original data set.

To attest to the opportunities that exist with the application of PCA-based

approaches for rotating machine faults classification, Malhi and Gao [93] showed

how the effectiveness of bearing faults classification can be significantly enhanced

through the application of PCA-based methods. In the study [93], several artificial

defects which varied in severities were seeded on the inner and outer rings of 5

different rolling element bearings. Initially, 13 machine condition indicators (i.e. 5

time domain features, 4 frequency domain features and 4 wavelet domain

features) were considered as input features of the faults classification algorithm.

However, through the application of PCA for dimensionality reduction, only 3 input

features namely RMS (time domain), power in defect frequency range (frequency

domain) and wavelet & Fourier ball pass frequency outer amplitude (wavelet

domain) were selected as input features for the PCA-based faults classification

algorithm. The study showed that based on the examination of the directionality of

all the initially considered machine condition indicators, the 3 selected features

exhibited the most significant variance due to changing defects conditions.

Furthermore, the results of the study indicated that the 3 features selected via

PCA significantly improved the accuracy of bearing faults classification when

compared to classification obtained from using features that were not selected by

PCA. Using the same principle of dimensionality reduction, other studies have

similarly detected and classified rolling element bearing [94], [95] and gear [91],

[96] faults. However, despite the knowledge about the potential of PCA-based

methods, the literature is still starved of studies that have applied PCA-based

methods for the detection and classification of rotor-related faults.

2.4.3 Higher order signal processing tools

The emergence of faults in rotating machines is always associated with the

appearance of several harmonics (i.e. 1x, 2x, 3x, 4x, etc.) of the machine speed.

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Understanding the relationship that exists between these harmonics is very vital

for detecting and differentiating incipient machine faults before they lead to

catastrophic failures. Unfortunately, the very common and popular VCM

techniques that dominate the field at present are unable to provide insights about

such harmonic relationships. Therefore, taking advantage of the continuously

improving technological advancements that has erupted within the past few

decades; researchers have sorted for ways to enhance the understanding of

rotating machine faults. A prominent step towards this endeavour is the

introduction of higher order signal processing techniques for detecting and

differentiating rotating machine faults. In order to foster a better understanding of

higher order signal processing techniques, the concise theoretical background

provided in Appendix A can be very useful. In practice, the 2 most popular higher

order signal processing techniques are the higher order spectra (HOS) and its

normalised form, which is also referred to as higher order coherences (HOC).

HOS is further divided into 2 main classes, namely the bispectrum [97] and

trispectrum [98]. The bispectrum and trispectrum are respectively the double and

triple Fourier transformations of the third and fourth order moments of a time

domain signal. The normalisation of HOS generates the HOC (i.e. bicoherence

and tricoherence), where bicoherence and tricoherence respectively represent the

normalised forms of bispectrum and trispectrum [98]. Since HOC is fundamentally

a normalisation of HOS, it is believed that fault diagnostic features generated by

both tools will not differ except that the amplitudes of the HOC will be bounded

between 0 and 1.

In order to demonstrate the relevance of higher order signal processing tools in

CM of rotating machines, Hassan et al. [99] showed how bicoherence can be used

to detect and monitor the progression of tail rotor gearbox failure due to lack of

lubrication. During the experimental study, the scenario of a leaking gearbox was

artificially created by wrecking the output seals, which eventually led to gear tooth

failure. Measured vibration data were then analysed using the power spectrum

density (PSD) and bicoherence techniques at different stages (i.e. 3 days, 2 days

and 1 day before total gearbox failure) of the gear fault. Results obtained from the

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PSD analysis were very similar for the different stages of the gear fault. On the

contrary, the study showed that the bicoherence amplitudes showed steady

progressions from 3 days before failure down to the point of failure. The

observations from this study further affirm the inadequacy of solely using PSD for

CM. Based on the bicoherence trends, the study also established that the tail

gearbox can safely run for additional 480 hours with continuous tail gearbox

lubrication oil leakage, which is very useful for maintenance planning. Jang et al.

[100] also used bicoherence to detect and distinguish balanced and unbalanced

stator current conditions of a 3-phase induction motor, which was adjudged to be

due to the magneto motive force (MMF) equalling the second harmonic (2x) of the

line frequency (i.e. 60Hz). The study [100] also showed how bicoherence can be

used to explain that quadratic interaction involves the product of 2 frequency

components.

According to another study conducted by Bouillaut and Sidahmed [101], it is

possible to better interpret gear vibrations that occur as a result of the rotational

frequency modulating the gear meshing frequency which leads to the appearance

of sidebands that will be spaced at the rotational frequency around the harmonics

of the meshing frequency. The study compared the abilities of VCM methods such

as PSD and HOCs to detect several operating conditions (healthy, spalling, crack,

etc.) of CH64 helicopter gearbox unit. The HOCs adequately detected the coupling

relationships that existed between the different frequency components of the

vibration signals measured for each case. However, the PSD was unable to

accurately distinguish between some of the cases as it only compares the

amplitudes at a particular frequency for each of the cases (owing to its lack of

phase information). Li et al. [102] also used bicoherence to detect and differentiate

5 operating conditions (healthy and 4 artificially seeded faults of varying severities

using the electric discharge machining method) of a taper roller bearing. As

observed from other studies, the PSD appeared similar for healthy and fault

conditions while the bicoherence provided distinct features for different conditions.

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Significant amounts of research [99]–[105] have clearly demonstrated the benefits

of fault diagnosis with higher order techniques over the commonly used PSD.

However, these studies have been grossly biased towards the application of the

normalised forms of HOS, also known as the HOC. Such bias led to the theoretical

and experimental exploration of HOS for detecting 2 rotating machine faults (i.e.

crack and misalignment) [106], where distinct bispectrum and trispectrum features

were observed for both faults [106]. However, the experiments were conducted on

a very simple rig supported by just 2 bearings. In practice, most industrial rotating

machines possess far more complex configurations and several bearings which

again triggered the use of bispectrum for detecting 3 faults (i.e. misalignment,

crack and rub) on a relatively rigid experimental rig with 4 bearings at 2 machine

speeds [107]. The diagnosis results obtained from the study were again

encouraging. However, it was observed that the detection of rub with bispectrum

alone was inconsistent at both machine speeds. In fact, the rub case exhibited

similar features to the healthy case.

Based on the mixture of the applications of HOC and HOS, it is still unclear from

the available literature whether both classes of higher order signal processing

tools are exactly same with respect to their fault diagnosis capabilities or whether

one of the classes outperforms the other.

2.4.4 Data Fusion

In practice, routine CM activities often involve the continuous measurement of

various operational parameters (e.g. vibration, temperature, airflow, speed,

pressure, energy consumption, sound, wear debris, etc.) at predefined intervals,

also referred to as the condition monitoring interval. The measured CM

parameters are then separately analysed and trended overtime, so as to detect

the emergence of incipient machine faults. For instance, Yang et al. [108]

established the relationship between temperature profiles and fatigue damage of a

reactor pressure vessel. The study [108] proposed a model for quantifying the

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stress-strain and fatigue failure from the observed temperatures, which can prove

very useful for the CM of rotating machines operating under extreme temperature

such as the cement plant rotary kilns. Similarly, Avdelidis and Almond [109]

conducted a study on the application of temperature profiles (thermal imaging) for

determining and monitoring the integrity of aircraft structure anchor points, using

conventional aluminium alloys and carbon fibre reinforced plastic skins.

Another useful parameter for rotating machine CM is the wear particle distribution

obtained from lubricating oils. Lubricating oils perform various vital functions in

rotating machines including the prevention of metal-to-metal contact between

critical machine components, cooling agents for hot surfaces, transport systems

for additives that enhance resistance of metal surfaces to wear, as well as the

movement of wear particles and contaminants away from the contact surfaces of

vital machine components. Through a careful analysis of the types, sizes, shapes,

and composition of wear particles, insights about the health of rotating machines

can be obtained [110]. Based on this premise, the study conducted by Peng and

Kirk [111] showed that boundary features such as particle size distribution and

shape were adequate for identifying cutting, spherical and rubbing wear particles,

but contained insufficient information for detecting laminar, fatigue chunk and

extreme sliding wear particles.

Other researchers [112]–[115] have explored the use of power characteristics for

monitoring changes in the operating conditions of critical rotating machines.

Hameed et al. [112] provided a comprehensive review of health monitoring

techniques for wind turbines, where it was shown that accurate information on the

overall condition of the rotor (a very important component of the wind energy

converter) can be obtained by trending the relation between wind speed and active

power output of the wind energy converter (WEC). The study [112] also showed

that the use of higher order signal processing tools (bispectrum and bicoherence)

for detecting the presence or absence of phase coupling between the frequency

components of the electrical power signal can be used to classify the WEC as

faulty or healthy.

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Despite the significant advances achieved through the separate applications of the

CM parameters, accurate analysis of all parameters would require the services of

a well-experienced and highly versatile CM analyst. Also, the complexity of

separately processing and analysing individual CM parameters is enormous.

However, with the current emphasis on sensor reduction and management of big

data [11], providing a holistic view of an entire rotating machine through

combinations of several sets of a particular CM parameter (e.g. vibration

measurements from several bearings) or combinations of different CM parameters

(e.g. vibration and temperature measurements from several bearings) will

significantly simplify CM. Such approaches are often referred to as data fusion,

data integration or data combination.

Though rapidly gaining attention in CM, the general concept of data/parameter

fusion cannot be described as completely new since it dates back to the existence

of human senses (i.e. taste, touch, sight, hearing and smell) [116]. Humans have

always combined several senses in order to enhance their survival rates. For

instance, it would require a combination of vision, touch, taste and possible smell

to adequately judge the quality of an edible fruit. Also, the combination of sights

and sounds helps an animal detect the exact location of its prey or predator.

Similarly, data fusion in applied sciences is built around the premise that enhanced

and simplified descriptions of the monitored system can be achieved through a

combination of different sensors and/or parameters [89]. Historically, data fusion

techniques were mainly developed for military activities such as automated target

recognition, battlefield surveillance and remote sensing [116]. However, ongoing

cross-functional knowledge transfer through research has significantly promoted

the application of the concept in other fields including CM of rotating machines.

Data fusion in CM of rotating machines can be performed at sensor level (also

referred to as multi-sensor data fusion) or at parameter level (also referred to as

feature or parameter fusion)

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2.4.4.1 Sensor level data fusion

Sensor level data fusion refers to the merging of measured data from several

condition monitoring (CM) sensors (e.g. vibration, sound, temperature, pressure,

etc.) installed on an equipment, so as to obtain precise and comprehensive fault

diagnosis features that could eventually simplify and/or enhance the overall CM

process [117]–[121]. In the context of rotating machine CM, multi-sensor data

fusion can be approached in 2 main ways. The former is the fusion of data

acquired by similar sensors (e.g. the fusion of vibration signals measured by 4

similar accelerometers installed on the bearings of a rotating machine), while the

latter entails the fusion of data acquired by different sensors measuring different

CM parameters. Figure 2.13 shows a schematic representation of steps involved

in a typical sensor level data fusion process, while Figure 2.14 shows an

integrated CM system for a typical industrial centrifugal fan, where 5 different CM

parameters (vibration, sound, airflow, wear particles and temperature) are fused

together to develop a unique condition indicator (CI). The CI can then be trended

over time and eventually used to define the appropriate planned maintenance

regions (PMR) for the monitored rotating machine. It is vital to note that data fusion

at sensor level is usually done prior to the extraction of the parameters or features

that will be used for actual fault diagnosis.

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Figure 2.13 Data fusion at sensor level

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Figure 2.14 Multi-sensor data fusion [122]–[126]

2.4.4.2 Parameter level data fusion

In contrary to the data fusion that occurs at sensor level, parameter level data

fusion requires that the fault diagnosis features (e.g. RMS, crest factor, 1x

amplitude, etc.) embedded in the signals measured by individual CM sensors are

separately extracted prior to fusion. Figure 2.15 shows a schematic representation

of the steps involved in a typical parameter/feature level data fusion process

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Figure 2.15 Data fusion at parameter level

In light of the potential opportunities available for simplifying VCM of rotating

machines through data fusion, Sinha and Elbhbah [127] proposed a technique that

fuses measured vibration data in the frequency domain so as to generate a single

composite spectrum (CS) that effectively represents the dynamics of the entire

machine. Based on the vibration data acquired from a laboratory scale rotating

machine with relatively rigid bearing supports, the proposed CS technique

provided clearly distinct and consistent features for 4 rotating machine conditions

(healthy, shaft misalignment, shaft crack and shaft rub) at 2 machine speeds

(34Hz and 50Hz). In contrary to the data intensiveness and rigour associated with

common approach to rotating machine fault diagnosis whereby separate amplitude

spectra are individually computed at each measurement location, the CS method

only generates a single composite spectrum irrespective of the number of

measurement locations therefore minimising fault diagnosis time, and this is highly

desired for enhancing machine uptime.

Although the CS frequency domain data fusion technique simplifies fault

diagnosis, however, the robustness of the technique is limited by two factors.

Firstly, the computed CS for each of the equal segments in the measured vibration

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signal loses phase information at intermediate measurement locations, owing to

the cross power spectrum density approach adopted whereby the Fourier

transformation (FT) at a particular bearing location is multiplied by the complex

conjugate of the FT at a successive measurement location. This therefore limits

the available phase information only to the first and last measurement locations.

Secondly, faults diagnosis based on CS is limited to comparisons of amplitudes at

individual frequencies for different machine conditions, owing to the complete loss

of phase information associated with the power spectrum density (PSD) approach

used to compute the final averaged CS. In order to address the latter limitation of

the CS being limited to just amplitudes at individual frequencies, Elbhbah and

Sinha [128] then developed the composite bispectrum (CB) data fusion method. It

is worth noting that exactly same experimentally simulated cases and rig were

used for developing the CS and CB data fusion methods. However, besides fusing

measured vibration data from several measurement locations, each computed CB

component is a representation of the interaction that exists between 2 frequency

components and a third that is equivalent to their sum. Hence the CB data fusion

is expected to provide better diagnosis, since it is not limited to amplitudes at

individual frequencies but the interaction that exist between several frequency

components.

In principle, the CB data fusion method provides significant advantages over CS

data fusion as well as other commonly applied VCM methods. However, the

following gaps still limit the confidence level of the method. Firstly, the computation

of CB components relies solely on the CS obtained from each of the equal FT

segments. This infallibly means that the CB components are also associated with

limited phase information, which may reduce the accuracy of fault diagnosis.

Secondly, the concept of CB is based on the theory of bispectrum computation.

While the capability of the bispectrum to establish the relationship between the

frequency components of a signal (i.e. relates 2 frequency components of a

measured signal to a third frequency component that equals the sum of the initial

2.) is known, earlier studies by Elbhbah and Sinha [107], [129] have also shown

the inability of bispectrum alone to distinguish certain rotating machine conditions

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(e.g. healthy and shaft rub at 50Hz machine speed). Thirdly, all the studies

conducted on the application of CS and CB data fusion methods were conducted

for only a rotating machine with rigid bearing supports and at separate machine

speeds.

However, it is known that rotating machines operate under all sorts of changing

conditions, with speed constituting a significant part of these changes. Some

researchers [130] have developed VCM techniques for detecting unbalance and

misalignment faults, based on the processing of vibration data measured during

acceleration and deceleration stages of a machine’s operation. Fault diagnosis

was then conducted through a comparison of the patterns obtained from various

features generated in time waveform and waterfall diagrams to an existing

database of known engine faults. Similarly, Modgil et al. [131] proposed an

advanced vibration diagnostic system which acquired data for engine test cells

from idle through to maximum power operations. The proposed VCM approach

(based on transient operations) could be very useful for monitoring aircraft

engines, particularly during landing and takeoff stages where the operations are

transient. However, the waterfall diagrams adopted entails the combination of data

obtained from the amplitude spectra at different machine speeds with diagnosis

being based at a particular speed, which undermines the usefulness of the

technique under continuously changing speed operations. Also, fault diagnosis

with these methods [130], [131] was based on FE models, which reignites the

widely asked question about the ability to accurately develop a FE model that

represents the actual rotating machine dynamics [19].

Significant levels of development have been attained with VCM techniques that

focus on transient operations. However, it is doubtful that the basic data

processing techniques would be robust enough to handle continuous operations

with variable speeds. Based on this premise, the development of a VCM technique

which is insensitive to changing speeds is highly justified. In addition to changing

speeds, there exist practical scenarios where identical rotating machines possess

slightly different dynamic behaviours owing to variations in the flexibilities of their

foundations. For instance, it is common for a plant or group of plants to purchase a

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number of the same rotating machine (e.g. multiple speeds roots blowers of

cement manufacturing plants) from an original equipment manufacturer (OEM).

Though the configuration of these machines is same, however, their dynamic

behaviours may slightly vary due to differences in the flexibilities of their

foundations. Figure 2.16 shows the picture of a typical multiple speeds roots

blower with various foundation options (e.g. steel, concrete, springs, etc.).

Figure 2.16 A typical multiple speeds cement plant roots blower with various

foundation options [132]–[136].

Currently, the detection of faults under such scenarios (i.e. identical multiple

speeds machines with different foundations) would involve separate analysis of

measured vibration data for each machine (e.g. roots blower 1 with concrete

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foundation, roots blower 2 with steel foundation, etc.) at different speeds and plant

locations. Therefore, if a typical cement manufacturing organisation owns 2

separate cement plants and each of the plants transports fine materials (e.g. raw

meal, cement, fine coal, etc.) through the aid of 3 multiple speeds roots blowers.

Depending on the practical requirements for each installation location (e.g. soil,

adjoining structures and vibration isolation requirements), the foundation

flexibilities for the blowers will vary and thus their dynamic characteristics. Table

2.1 shows that as many as 15 different sets of measured vibration data could be

available for analysis from each of the 3 blowers with different foundations and

operating at 5 speeds (i.e. 30 data sets for both cement plants).

Table 2.1 Roots blower scenarios for 2 cement plants

Operating Speeds (rpm)

Cement Plant 1 Cement Plant 2

RB1Concrete RB2Steel RB3Springs RB1Concrete RB2Steel RB3Springs

600 1 2 3 1 2 3

1200 4 5 6 4 5 6

1800 7 8 9 7 8 9

2400 10 11 12 10 11 12

3000 13 14 15 13 14 15

Based on the practical scenarios described in Table 2.1, it is obvious that

continuously monitoring several multiple speeds identical rotating machines will be

highly complicated especially using conventional VCM techniques including

amplitude spectrum, rotor orbits analysis, bode plots, waterfall analysis, etc.

Although relatively recent data fusion methods such as CS and CB offer significant

simplicity over the conventional techniques, however, the process of separately

fusing measured vibration data for a single machine at individual speeds could

also be associated with considerable levels of complexity. Hence, there exists the

need to develop a hybrid (i.e. combination of sensor level and feature level data

fusion approaches) data fusion technique that can effectively combine measured

vibration data from several VCM sensors at various speeds for different rotating

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machines. Figure 2.17 shows a unified data fusion approach, where data from

several CM sensors are fused together and features extracted for different

machine speeds. The features extracted at multiple speeds for multiple machine

foundations are again fused together to generate a unified fault diagnosis

technique that could be used for different speeds and foundation flexibilities.

Figure 2.17 A unified data fusion approach

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2.5 Summary

The significance of the achievements recorded in VCM of rotating machines using

standard techniques such as amplitude spectrum is irrefutable. Most of these

achievements are largely owed to its simplicity and sensitivity to most commonly

encountered rotating machine faults. Despite its usefulness, diagnosis based on

amplitude spectrum analysis alone sometimes leads to inconclusive results,

largely due to its utter reliance on the amplitudes at individual frequencies. As

such, other standard VCM techniques such as orbit analysis, order tracking and

full spectrum are often applied in conjunction with amplitude spectrum so as to

raise the credence level of the technique. It is rational to admit that such

combinations of several standard VCM techniques have also yielded tangible

results in some instances. However, standard techniques such as rotor orbits have

also been observed to generate indeterminate results. Besides the impediments

associated with individual standard VCM techniques, a combination of several

techniques is also associated with appreciable levels of complexity and expertise.

In an attempt to evade some of the limitations associated with standard VCM

techniques (particularly the over-reliance on human experience), some

researchers have ventured into techniques such as ANN and SVM. Although

useful and encouraging research results have been achieved with ANN and SVM

with respect to automatic faults classification, their deployment to the industry are

still impeded by the lack of clearly stipulated procedure for acquiring the training

data for ANN as well as a lack of clearly defined standard for selecting the SVM

Kernel function. Approaches involving the construction of FE models that attempt

to simulate the dynamic responses generated by typical rotating machines due to

changing operating conditions have also been attempted by several researchers.

While FE methods possess the ability to provide intricate understanding of

machine behaviour due to faults, it is sometimes impracticable to construct FE

models that are absolute replicas of complex industrial rotating machines.

In order to adequately respond to the industrial need for developing a simplified

but reliable fault diagnosis approach that will equally address the growing research

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need for management of large data and pattern classification, data fusion methods

appear to be the most auspicious especially under different speeds and

foundations. Based on the currently existing literature, fault diagnosis of rotating

machines has been restricted to a solitary machine. This therefore implies that a

significant research gap still exists with respect to the development of a robust

fault diagnosis approach that would accommodate the sharing of data between

several identical rotating machines. Such an approach would eliminate the need

for keeping separate data history for each of the identical rotating machines

available in a plant.

Experiments

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3 Chapter 3 EXPERIMENTS

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In order to foster a substantial acceptability of any newly proposed technique, an

experimental validation is often required, and this is commonly achieved through

the aid of an experimental test rig. A representative test rig may be described as

that which has been adequately set-up to correctly simulate the investigated faults

in the research. This chapter however presents details of various components that

make-up the test rig and the experimental simulation of the studied rotating

machine conditions. Prior to the experimental simulation of the different machine

conditions, the dynamic characteristics of the different experimental rigs were

determined, so as to adequately understand their dynamic behaviours.

Additionally, the chapter highlights the types, quantities and mounting positions of

instruments (transducers, data acquisition systems, signal conditioners, speed

controller, etc.) used for the collection and storage of the different experimental

data.

3.1 Experimental Rig and Components

In addition to the introductory description of a representative test rig, it should also

possess the capability of generating representative as well as repeatable

experimental data. Since the rig is an assembly of different components

(mechanical and electrical), a good understanding of the characteristics of these

components is required, so as to optimise their outputs. Such characteristics are

not limited to, but may include; operating ranges, material properties, stable

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ranges, frequency of calibration, operating environment, operational (input/output)

settings, etc. As these components will be used to generate data for VCM, it is

very vital that they are in perfectly healthy conditions at the commencement of the

experiment, so as to set-up reliable baseline parameters upon which all future

readings will be compared.

Furthermore, the setting up of the test rig and its associated components should

be correctly done. In accordance with the safety requirements of the University of

Manchester Dynamics Laboratory, a detailed risk assessment of all the tasks

associated with the experiments was conducted. Hence, this section will provide

details of how the test rig was set-up and the settings used for data collection.

Figure 3.1 shows pictorial representations of the major components that make-up

the experimental set-up.

Figure 3.1 Typical experimental set-up

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From Figure 3.1, it can be seen that rig rotation is achieved through the aid of an

induction motor that is flexibly coupled to the shaft (which is supported by 4 anti-

friction ball bearings). The variation of rig rotational speed is remotely done

through the aid of a PC-based motor speed controller. Vibration measurements

are then collected via sensors such as accelerometers (one diagonally mounted

on each bearing), proximity probes (2 mounted on bearings 1 and 3 pedestals in

the vertical and horizontal directions) and measurement microphones (mounted on

the rig protective cover near bearings 1 and 3 respectively). Signal conditioning

units are used to power each of the sensors as well as condition (amplify or

attenuate) the sensor outputs, so that it adequately matches the requirements of

the analogue-to-digital converter (ADC) that transforms the measured analogue

signals into digital forms that can be recorded onto a PC, using the customised

PC-based data acquisition software. The technical characteristics of the

experimental rig components will then be highlighted in the subsequent parts of

this section, while Section 3.2 describes the different instrumentation.

3.1.1 Electric motor and speed controller

The electric motor that drives the experimental rig is a 3-phase induction motor

and speed variation on the motor was achieved through the aid of a speed

controller. Figures 3.2(a)-(b) respectively shows pictures of the electric motor and

speed controller, while Tables 3.1-3.2 respectively provide their technical

specifications.

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Figure 3.2 Picture of electric motor and speed controller

Table 3.1 Technical specifications of the electric motor

S/No. Criteria Description

1 Manufacturer Crompton Greaves Ltd, India

2 Model GF 7965

3 Part No. IM 456

4 Serial No. KLG 18298

5 Power 0.75 kW

6 Voltage range 380v-415V

7 Phase 3

8 Frequency 50 Hz

9 Speed 2800 RPM

10 Current 1.85 A

11 Enclosure TEFC

12 Mounting Base foot + flange

Table 3.2 Technical specifications of the speed controller


1 Manufacturer Newton Tesla

2 Input voltage 200-240 Volts AC

3 Input frequency 50/60 Hz

4 Output voltage 0-200 Volts AC

5 Output frequency 5-60 Hz

6 Power rating 0.75 kW

7 Output current 4.1 A

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3.1.2 Anti-friction ball bearings

Vibration data under healthy machine condition and several rotor-related faults

were collected from experimental rigs with various foundation flexibilities, owing to

the fact that similarly configured industrial rotating machines sometimes exhibit

different foundations in practice. The initial sets of vibration data were collected

from an experimental rig with relatively rigid foundation, where the rotor assembly

was supported by 4 Plummer block anti-friction ball bearings (Figure 3.3(a)). Since

a significant number of practical rotating machines are flexibly mounted, further

vibration measurements were conducted on flexible foundations. This was

however achieved by replacing the initial Plummer block anti-friction ball bearings

with flange-mounted anti-friction ball bearings (Figure 3.3(b)).

Figure 3.3 Anti-friction ball bearings (a) Plummer block (b) Flange-mounted

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Table 3.3 Technical specifications of anti-friction ball bearings

S/No Criteria Bearing Type

Plummer Block Flange Mounted

1 Manufacturer SKF

2 Model No. SY20TF/RA SEY20/NP20 FY20TF/RCJY20/SF20

3 Number of rolling elements 8

4 Diameter of rolling elements (mm) 7.938

5 Bearing width (mm) 31

6 External diameter (mm) 47

7 Internal diameter (mm) 20

8 Bearing pitch circle diameter (mm) 33.5

3.1.3 Couplings

The experimental rigs consist of 3 separate shafts (i.e. 1m, 0.5m and motor

shafts), which were connected by two different types of couplings (i.e. flexible and

rigid). The electric motor shaft was flexibly (Figure 3.4(a)) coupled to the 1m shaft

on one hand, while the 0.5m and 1m shafts were rigidly (Figure 3.4(b)) coupled

together on the other hand.

Figure 3.4 Couplings (a) Flexible (b) Rigid

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3.1.4 Threaded bars

Vibration measurements for the flexibly supported experimental rig were

conducted under 2 distinct foundation flexibilities, so as to experimentally simulate

the practical case of identically configured rotating machines installed at different

plant locations. Therefore, the flexibilities of the foundations were adjusted using

the 2 sets of mild steel threaded bars shown in Figure 3.5. Initially, both sets of

threaded bars were 10mm in diameter (Type: TB-58BZP-M10). However, the

geometries of the threaded bars used for the second flexibly supported

experimental rig (Figure 3.5(b)) were slightly modified, where aL = cL = 40 mm

(length) x 10 mm (diameter) and bL = 50 mm (length) x 6 mm (diameter).

Figure 3.5 Threaded bars for flexible foundations

3.2 Instrumentation

The measurement of vibration response from all experimental rigs under different

experimentally simulated conditions (faults and speeds) was achieved through the

installation of several transducers (e.g. accelerometers, proximity probes,

instrumented hammer and microphones), signal conditioning units and data

acquisition systems. In this section, some of the properties and specifications of

the instruments used for this research will be briefly discussed.

aL

bL

cL

a b

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3.2.1 Accelerometers

Accelerometers are contact transducers that are capable of measuring dynamic

acceleration of vibrating systems. During the current research, 4 accelerometers

(1 on each bearing, mounted at 45° to the shaft’s axis of rotation) were used to

collect vibration data from all the experimental rigs. Figure 3.6 and Table 3.4

respective provide the picture and technical specifications of the accelerometers.

Figure 3.6 Accelerometers with their brass mounting studs

Table 3.4 Technical specifications of accelerometers


1 Model No. 352C33

2 ECN No. 28610

3 Sensitivity (±10%) 100mV/g

4 Frequency range (±5%) 0.5 to 10000 Hz

5 Resonant frequency ≥50 KHz

6 Temperature range -65 to +200 oF

7 Settling time (within 10% of bias) <10 seconds

8 Electrical connector 10-32 coaxial jack

10 Excitation voltage 18 to 32 VDC

11 Mounting torque 10 to 20 in-lb

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3.2.2 Proximity probes

Proximity probes are displacement transducers used to measure the gap or

relative displacement of a metal object in motion (e.g. the shaft of a rotating

machine) from the probe. In practice, proximity probes are commonly used for

protecting critical rotating machines (e.g. the rotary kilns of cement process plants)

by interrupting power supply to the machine once a preset shaft displacement

level is approached [137]. During the current study, the relative displacement of

the shaft under different experimentally simulated machine conditions were

measured using 4 MTN/ECPD+24V types of proximity probes (with a pair installed

at bearings 1 and 4 respectively in the vertical and horizontal directions as shown

in Figure 3.7(a)). Each proximity probe is powered by an EP080 driver (Figure

3.7(b)).

Figure 3.7 (a) MTN/ECPD+24V Proximity probes (b) EP080 drivers

3.2.3 Measurement microphones

Since changes in rotating machine sound pressure levels are also valuable

indications of changes in operating conditions, 2 high sensitivity condenser

measurement microphones (Figure 3.8(a)) were also installed on the experimental

rigs with flexible foundations (1 microphone installed at bearing 1 and the other at

mid-way between bearings 2 and 3) for sound pressure level measurements. Both

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measurement microphones were mounted on the experimental rig cover at a

distance of approximately 50 mm from bearing 1 and the rigid coupling

respectively. Each condenser microphone is powered by a type 2801 single-

channel power supply (Figure 3.8b), and the voltage output from the condenser

microphone is passed to the data acquisition card, through a sound amplifier

(Figure 3.8c).

Figure 3.8 (a) Condenser microphone (b) Single channel power supply (c) sound

amplifier

Table 3.5 Technical specifications of condenser microphone and power supply


1 Manufacturer Bruel & Kjaer

2 Power supply input voltage range 110-240 V AC

3 Power supply output voltage Max. 28 V RMS

4 Power supply frequency range 2 Hz - 200 kHz

5 Microphone Resonance frequency Approx. 25 kHz

6 Sensitivity 12.5 mV/Pascal

3.2.4 Instrumented hammer

An impact hammer was used for identifying the natural frequencies and mode

shapes of the experimental rigs. In practice, the identification of the natural

frequencies of rotating machines or structures through impact hammer test usually

entails striking the test structure or machine with an instrumented hammer and

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then acquiring the response with a transducer (e.g. accelerometer). The impulse

from the hammer contains an almost steady force, over a broad frequency range,

which is why it is able to excite all resonant frequencies within that range [138].

The selection of hammer size is often guided by the structure or machine to be

excited. For instance, large rotating machines (e.g. large turbo generator sets,

cement rotary kilns, induced draft fans, etc.) or structures (e.g. bridges) may

require instrumented sledge hammers, while small to moderate experimental rigs

may require mini-hammers [138]. The hammer senses the applied force through

the aid of an integrated ICP quartz element (mounted on the striking head), which

transfers the impact force to the analogue-to-digital converter (ADC), after

adequate signal conditioning. Additionally, the frequency range to be excited can

be varied by replacing the hammer tip (i.e. harder hammer tips excite higher

frequency ranges than softer hammer tips) [21]. Figure 3.9 and Table 3.6

respectively show the picture and technical specifications of the instrumented

hammer used during this research.

Figure 3.9 ICP-PCB 086C03 instrumented hammer

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Table 3.6 Technical specifications of ICP-PCB 086C03 instrumented hammer


Performance

1 Sensitivity (±15%) 10 mV/N

2 Measurement range ±224 N pk

3 Resonant frequency ≥22 kHz

4 Non-linearity ≤1%

Electrical

1 Excitation voltage 20-30 VDC

2 Constant current excitation 2 to 20 mA

4 Output bias voltage 8 to 14 VDC

Physical

1 Sensing element Quartz

2 Sealing Epoxy

3 Hammer mass 0.16 kg

4 Head diameter 1.57 cm

5 Tip diameter 0.63 cm

6 Hammer length 21.6 cm

7 Electrical connection position Bottom handle

8 Extender mass weight 75 g

9 Electrical connector BNC jack

3.2.5 Signal conditioning units

Transducers such as accelerometers and impact hammers require electrical

power supply. Additionally, the magnitudes of the output signals from these

transducers are often very small, and associated with different forms of

contamination, which therefore necessitates the need for some form of

amplification or filtration prior to digitization [139]. This preparation of the output

signals from the transducers is often referred to as signal conditioning. In this

research, PCB 482C signal conditioning units (picture and technical specifications

are respectively shown in Figure 3.10 and Table 3.7) were used for the realisation

of these purposes.

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Figure 3.10 PCB 482C signal conditioning unit

Table 3.7 Technical specifications of ICP-PCB 086C03 instrumented hammer


Performance

1 Channels 4

2 Input sensor type ICP, voltage, charge

3 Voltage gain X0.1 to x200

4 Voltage gain increment 0.1

5 Charge conversion (selectable) 0.1, 1.0, 10.0 mV/pC

6 Frequency range (gain <100) 0.05 to 100 kHz

7 Frequency range (gain 100) 0.05 to 75 kHz

Electrical

1 Sensor excitation +24 VDC

2 Excitation current 0 to 20 mA

3 Computer control RS-232

4 LED fault monitor Open/short/overload

5 Power required +9 to -18 VDC

Physical

1 Input power connector 6-socket mini DIN

2 Sensor input connectors BNC

3 Signal output connectors BNC

4 Size (H x W x D) 8.1 x 20 x 15 cm

5 Temperature range +32 to +120 0F or 0 to +50 0C

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3.2.6 Analogue-to-digital converter (ADC)

Outputs generated by the different VCM transducers (i.e. accelerometers,

proximity probes and microphones) used for collecting the vibration data during

the current research are often in analogue forms. For these analogue signals to be

compatible with the PC onto which they will be stored for further data processing,

an analogue-to-digital converter (ADC) is required. ADCs convert continuous time

signals into discrete forms [140]–[143], which enables data storage onto computer

systems for eventual signal processing and rotating machine faults diagnosis. The

NI 6229, 16-bit, 16-channel ADC (picture and technical specifications are

respectively shown in Figure 3.11 and Table 3.8) was used during this research.

Figure 3.11 NI 6229/16-bit/16-channel ADC

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Table 3.8 Technical specifications of NI 6229/16-bit/16-channel ADC


Analogue Input

1 Number of channels 16 differential or 32 single ended

2 ADC resolution 16 bits

3 Sampling rate 250 kS/s single channel; 250 kS/s multi-channel (aggregate)

4 Input range ±10 V, ±5 V; ±1 V, ±0.2 V

5 Input FIFO size 4,095 samples

Analogue Output

1 Number of channels 4

2 DAC resolution 16 bits

3

Maximum update rate

1 channel-833 kS/s, 2 channels-740 kS/s/channel, 3 channels-666 kS/s/channel and 4 channels-625 kS/s/channel

4 Output FIFO size 8,191 samples shared amongst channels used

Digital I/O/PFI

1 Number of channels 48 total; 32 (PO.<0...31>), 16 (PFI<0…7>/P1, PFI<8…15>/P2)

3.2.7 Data acquisition software

The measured vibration data from the various VCM transducers (after analogue-

to-digital conversion) were then stored on to a Dell Optiplex 990 (with Intel(R)

Core(TM) i7-2600 CPU @ 3.40GHz; 4.00 GB RAM and 64-bit operating system)

PC, through the aid of the customized LABVIEW-based (version 2.0) data

acquisition software (designed by Austin consultants for the University of

Manchester) shown in Figure 3.1. Although this software is quite simplified and

user friendly, however, care must be taken while entering the various fields (for

instance transducer channels, sampling frequency, voltage ranges and file

names). Table 3.9 provides a summary of the software settings used for acquiring

the research data.

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Table 3.9 LABVIEW-based (version 2.0) data acquisition software settings

ADC Channel

Transducer Type

Transducer Location

Voltage Range

Sampling Frequency

Dev1/ ai 0

Accelerometer

Bearing 1

-2 to +2

10kS/s (flexible supports)

&

5kS/s (for rigid support)

Dev1/ ai 1 Bearing 2



Dev1/ ai 4

Proximity

probes

Bearing 1 (vertical)

-10 to +10

Dev1/ ai 5 Bearing 1 (horizontal)

Dev1/ ai 6 Bearing 4 (vertical)

Dev1/ ai 7 Bearing 4 (horizontal)

Dev1/ ai 16 Microphones

Bearing 1 -2 to +2

Dev1/ ai 17 Bearings 2 & 3

3.3 Experimental Rig Foundations

In the current research, vibration data (under different faults and rotating machine

speeds) were collected from an experimental rig with 3 distinct foundations (i.e.

rigid support, flexible support 1 and flexible support 2), so as to experimentally

simulate the practical scenario of a particular rotating machine (e.g. pump)

acquired from an original equipment manufacturer (OEM) by different users in

different plant locations. Such differences in locations and/or users often result to

variations in the flexibility of the machines’ foundations and hence their dynamic

characteristics. Therefore, this section provides the details of the 3 experimental

rigs, with particular emphasis on their foundations.

3.3.1 Rigid support (RS)

In the RS experimental rig (Figures 3.12-3.13), two mild steel shafts of similar

diameters (20mm) and respective lengths of 1000mm and 500mm were connected

together through the aid of the rigid coupling shown in Figure 3.4(b). The 1000mm

shaft was then coupled to the electric motor shaft using the helical “W” series

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metric single piece flexible coupling shown in Figure 3.4(a). Three mild steel

balance discs of similar dimensions (100mm (outer diameter), 20mm (inner

diameter) and 15mm (thickness)) were mounted on the shafts (i.e. two balance

discs on the 1000mm shaft, between bearings 1 and 2; and the third balance disc

on the 500mm shaft, between bearings 3 and 4). Each of the balance discs

contains 12 radial holes of 6mm diameter each, and spaced at 30 degrees apart.

The shafts were then supported by 4 Plummer block anti-friction ball bearings,

which are tightly fastened to a lathe bed, through the aid of mild steel base plates.

The entire experimental rig assembly is placed on neoprene rubber pads (for

isolating vibration from adjacent machines). A total of 4 accelerometers (1 per

bearing pedestal in the horizontal direction) were installed on the experimental rig

for vibration data collection.

Figure 3.12 Picture of RS experimental rig

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Figure 3.13 Schematic of RS experimental rig with dimensions

It is very crucial to highlight that the original design and construction of the RS

experimental rig shown in Figures 3.12-3.13 formed part of an earlier research

conducted by Elbhbah and Sinha [107] at the Dynamics Laboratory of the

University of Manchester.

3.3.2 Flexible supports

In addition to the vibration data collected from the RS experimental rig, two flexibly

supported (i.e. FS1 and FS2) experimental rigs were also considered. It must be

noted that the majority of the components (i.e. electric motor, 1000mm shaft, 500m

shaft, base plates, lathe bed, neoprene dampers, balance discs, etc.) that make up

the RS, FS1 and FS2 experimental rigs are identical and similarly sized. However,

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RS supports are relatively rigid while FS1 and FS2 supports are flexibly mounted

(Figure 3.14-3.15).

Figure 3.14 Picture of FS experimental rig

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Figure 3.15 Schematic of FS experimental rig

In Figure 3.15, the components labelled a-m respectively represent accelerometer,

rigid coupling, shaft, balance disc, bearing flange, threaded bar, flange-mounted

anti-friction ball bearing, flexible coupling, tachometer, electric motor, electric

motor base mount, lathe bed and neoprene rubber pad. Additionally, Figure 3.16

shows that the flexibilities of FS1 and FS2 vary slightly, owing to the different

geometries of the threaded bars (Figure 3.5) that connect their bearings to the

pedestals.

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Figure 3.16 Picture of flexible supports (a) FS1 (b) FS2

3.4 Dynamic Characterisation

In order to better understand the dynamic behaviours of the different experimental

rigs, their natural frequencies (by appearance) and mode shapes were

experimentally identified using the impact response method of modal analysis.

Experimental modal analysis is a widely known design testing and qualification

technique in various disciplines [144]. The knowledge of the modal properties of a

system greatly paves way for design improvements and useful life enhancement

[145], [146]. In order to ensure a structured and guided approach to modal testing,

the UK Dynamic Testing Agency (DTA) further recommended a four-stage

approach, namely [144], [147]; preparation (i.e. clear definition of experimental

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objectives and identification of relevant resources), exploration (i.e. the definition

of data acquisition parameters such as number of averages, acquisition duration,

frequency resolution, sampling frequency, etc., which may involve some initial trial

runs), measuring (i.e. actual collection of experimental data) and analysis.

According to earlier studies by Elbhbah and Sinha [127], the first few natural

frequencies (by appearance) of the RS experimental rig were experimentally

identified using the impact response method as 68Hz, 144Hz and 352.5Hz. Similar

approaches were again adopted for the determination of the natural frequencies of

FS1 and FS2 experimental rigs, where responses were measured in both vertical

and horizontal planes, owing to the flexibilities of the rigs (i.e. FS1 and FS2) in

both planes. During the experiments, FS1 and FS2 were respectively excited by

the ICP-PCB instrumented hammer shown in Figure 3.9 and the vibration

responses were measured using an ICP accelerometer similar to that shown in

Figure 3.6. Hence, Figure 3.17 shows a picture of the experimental setup for

determining the natural frequencies of FS1 and FS2 experimental rigs.

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Figure 3.17 Modal test setup for determining FS1 and FS2 natural frequencies

The first few natural frequencies (by appearance) for FS1 and FS2 in both vertical

and horizontal directions (based on response measurements at bearing 2) were

identified using the peak picking method. Figures 3.18-3.21 and Table 3.10

respectively show plots of the frequency response functions (FRF) and a summary

of the natural frequencies.

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direction (a) FRF amplitude, (b) FRF phase



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Table 3.10 Experimentally identified natural frequencies for FS1 and FS2

Experimental Rig Natural Frequencies (Hz)

1st

2nd

3rd

4th

FS1 50.66 56.76 59.2 127.6

FS2 47 55.54 57.98 127

In order to experimentally determine the mode shapes, an experimental approach

similar to that applied for natural frequencies’ determination was adopted, except

for the fact that 9 ICP accelerometers (distributed across the length of the

experimental rigs) were used to measure the responses. Figures 3.22-3.23

respectively show a picture of the experimental setup and the schematic

representation of the exact locations (in millimetres) of the 9 ICP accelerometers

used for measuring the responses, while Figure 3.24 shows samples of the first

few mode shapes (by appearance) for FS1. In Figure 3.23, B1-B4, FC and RC

respectively denote bearings 1-4, flexible and rigid couplings. Locations 1-9 (L1-

L9) in Figure 3.24 represent the locations at which the responses were measured,

which also correspond to the distances shown in Figure 3.23.

Figure 3.22 Modal test setup for determining FS1 and FS2 mode shapes

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Figure 3.23 Locations of ICP accelerometers for mode shapes’ determination

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Figure 3.24 FS1experimentally determined mode shapes (a) 50.66Hz, dominant in vertical direction (b) 56.76Hz, dominant in

horizontal direction

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3.5 Experimentally Simulated Faults

On all the experimental rigs (i.e. RS, FS1 and FS2), several cases were simulated,

which represented different operating conditions of typical rotating machines in

practise. Hence, this section provides detailed descriptions of the experimental

simulation of the different cases on all the experimental rigs.

3.5.1 Rigid support (RS)

Although, details of the experimental simulation of the 4 cases (healthy,

misalignment, cracked shaft and shaft rub) studied on the RS rig have been

provided in an earlier study conducted by Elbhbah and Sinha [107], however,

similar information will be repeated here, so as to further enhance clarity.

3.5.1.1 Case 1: Healthy

The healthy case was intended to simulate a near perfect machine, through the

alignment of all the coupled shafts. However, the impossibilities of practically

manufacturing error-free components still imposed some residual unbalances on

the healthy case. Additionally, a perfect alignment between the coupled shafts was

unrealistic (as is often the case in practise), thereby inducing some residual

misalignment between the coupled shafts (especially at the rigid coupling).

Therefore, the healthy case still contained some degree of residual unbalance and

residual misalignment.

3.5.1.2 Case 2: Misalignment

A 2mm misalignment was induced in both vertical and horizontal directions of

bearing 1 (i.e. near the flexible coupling shown in Figure 3.12). The misalignment

in the vertical direction was induced by placing a 2mm thick mild steel shim

underneath bearing 1 base mount, while horizontal misalignment was achieved by

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moving the bearing 2mm (using a calibrated dial indicator for distance

measurement) from its axis in the horizontal direction, through the aid of the

pedestal slots.

3.5.1.3 Case 3: Cracked shaft

A crack of 0.25mm (width) by 4mm (depth) was created on the 1000mm (length)

shaft, using the spark erosion electric discharge machining (EDM) technique [107].

EDM has continuously gained popularity amongst machining processes. Its

application of heat energy for material reduction from electrically conductive

components has particularly made it (EDM) very relevant to various industries,

including; medical, aerospace, automobile and general manufacturing [148].

Another merit of EDM lies in the fact that the electrode does not make direct

contact with the work piece, thereby eliminating mechanical stresses and

vibrations during the machining process [148]. With the recent advancements in

technology, EDM electrodes go as low as 0.1mm, which makes them very suitable

for the precise manufacture of intricate shapes and components [149]. During the

EDM process, the mechanism that erodes materials from the work piece converts

electrical energy to heat energy, through a variety of high frequency

(approximately between 20-30 kHz) electrical discharges between the electrode

and the work piece, which is soaked in a dielectric fluid [150], [151]. The amount of

heat energy produced, leads to the creation of a plasma channel between the

anode and cathode (at temperatures as high as 8000-20000 degrees Celsius)

[152], which leads to the melting of materials at the surface of the electric poles

[148]. Upon cutting-off the direct current supply, the plasma layer breaks down,

thereby leading to a drastic reduction in temperature, which consequently leads to

the removal of molten materials (in the form of microscopic debris) from the

surfaces of the poles [148]. In order to therefore simulate an incipient rotor crack,

which will be quantifiable (i.e. width and depth), EDM process was applied, as

shown on Figure 3.25.

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Figure 3.25 Cracked shaft

3.5.1.4 Case 4: Shaft rub

The shaft rub case was simulated through the use of a Perspex sheet, with a

centrally located hole of 21mm diameter. The 1000mm (length) x 20mm (diameter)

shaft was then passed through the hole in the Perspex sheet, near bearing 1.

Figure 3.26 Shaft rub

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3.5.2 Flexible supports (FS1 and FS2)

In the flexibly supported rigs (FS1 and FS2), a total of ten (10) cases were

experimentally simulated, so as to cover a reasonably wide range of practical

operating conditions of typical industrial rotating machines. Although there are two

different flexible support set-ups (FS1 and FS2), however, all cases have been

simulated in exactly the same manner, so as to allow direct comparisons between

FS1 and FS2. Since it often impossible to achieve a perfect alignment in the

reference case, all the experimentally simulated cases contained additional

residual misalignment (which is often the case in practice). Vibration data were

then collected at 3 distinct machine speeds; 1200 RPM (20 Hz), 1800 RPM (30

Hz) and 2400 RPM (40 Hz) for each case under FS1 and FS2 supports, so as to

extensively understand the dynamics of the machines under different operating

conditions. Since full details of the specific experiments will be provided in the

subsequent chapters (including figures), only a summarised list of the

experimentally simulated cases and their abbreviations are provided in Table 3.11.

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Table 3.11 Experimentally simulated cases, abbreviations, severities and locations

Case Description Abbreviation Severity and Location

1 Healthy with residual

misalignment HRM

Some residual misalignment, possibly

at couplings

2 Unbalance UNB

M5 x 25mm grub screw of 2.6g mass

was inserted in one of the 12

equidistant holes on the balance disk

positioned at 190mm from bearing 2.

3 Bent shaft BS 3.4mm run-out was created at the

centre of the 1000mm shaft.

4 Shaft crack SC

4mm (depth) x 0.25mm (width) crack

on 1000mm shaft at 160mm from

bearing 1

5 Loose bearing LB Loosening some of the bearing 3

threaded bar nuts

6

Shaft misalignment

SM1 0.4mm mild steel shim beneath LHS of

bearing 1 foundation

7 SM2 0.4mm mild steel shim beneath LHS

and RHS of bearing 1 foundation

8 SM3 0.8mm mild steel shim beneath LHS of

bearing 1 foundation

9 SM4 0.8mm mild steel shim beneath LHS

and RHS of bearing 1 foundation

10 Shaft rub SR

Partial rub using 2 Perspex blades

(TDC and BDC of 1000mm shaft),

275mm from bearing 1

3.6 Summary

This chapter provided details of the different experimental rigs (RS, FS1 and FS2),

as well as the various components (mechanical and electrical) that constitute

them. Details of the transducers and instrumentation that aided vibration data

collection and storage were also provided. The chapter also highlighted the

experimental determination of the dynamic characteristics (natural frequencies and

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mode shapes) of the rigs as well as the experimental simulation of different cases

that represented practical operating conditions of industrial rotating machines.

Hence, the subsequent chapters of this thesis will focus on the research findings

and their corresponding explanations.

Experimental Observations of Rotor Orbit Analysis in Rotating Machines

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4 Chapter 4 EXPERIMENTAL OBSERVATIONS

OF ROTOR ORBIT ANALYSIS IN ROTATING MACHINES

----------------------------------------------------------------------------------------------

Reformatted version of the following paper:

Paper title: Experimental observations of rotor orbit analysis in rotating

machines

Authors: A. Yunusa-Kaltungo, A.D. Nembhard and J.K. Sinha

Published in: Proceedings of 9th IFToMM International Conference on Rotor

Dynamics (IFToMM ICORD 2014), Milan/Italy, September 22-25 2014

Series title: Mechanisms and Machine Science

Volume: 21

DOI: 10.1007/978-3-319-06590-8

Publisher: Springer International Publishing

Abstract

A better understanding of the characteristic features of different faults associated

with rotating machines is very vital, so that appropriate and timely maintenance

interventions can be recommended prior to the occurrence of catastrophic failures.


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Rotor orbit analysis of machine vibration data collected using proximity probes has

been observed to be useful for faults diagnosis in rotating machines. Although this

analysis is extensively applied for rotating machine faults diagnosis in several

industries, however, very limited experimental results are still available in

literatures. In the current study, rotor orbit analysis has been conducted on an

experimental rig of 1500mm rotor length, supported by 4 flexibly mounted anti-

friction ball bearings. A number of faults have also been experimentally simulated

on the rig for the purpose of this study. Hence, the paper presents the experiments

conducted, the rotor orbit analysis and observations, which may further enhance

the understanding of rotating machines’ behaviours under different faults.

Keywords: Condition monitoring, faults diagnosis, rotating machines, flexible

foundation, rotor orbits

4.1 Introduction

A highly desired attribute of any vibration-based fault diagnosis (VFD) technique is

its ability to develop unique, reliable and consistent features that express the

changes in operating conditions of a rotating machine due to the emergence of

faults. One of such VFD techniques that have been considerably applied over the

years for detecting and estimating malfunctions in rotating machines is the rotor

orbit analysis of vibration data, measured using proximity probes. Measuring

vibration signals for rotor orbit analysis as already detailed in earlier studies [55],

[153]–[155], involves installing two orthogonal proximity probes, where the

measured vibration signal by each of the probes is indicative of the rotor peak-to-

peak displacement in that particular direction. The rotor orbit plot is then

constructed by combining the measured vibration displacements from the two

orthogonal proximity probes. Rotor orbit analysis has been applied for the

diagnosis of different rotating machine conditions, such as; analysis of impact rub

phenomenon [50]; rotor misalignment [53], [54]; detecting the causes of the

appearance of sub-harmonic components in journal bearings, including oil


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temperature and pressure variations [52]; influence of rotor cracks [51]; etc. While

these studies [50]–[55], [153]–[155] have shown the usefulness of rotor orbit

analysis for diagnosing rotating machine faults, very limited experimental results

on the technique are still currently available in literatures, which consequently

restrict the detailed understanding of the technique with different rotating machine

faults. Hence, the current study conducts rotor orbit analysis on vibration

displacements measured by proximity probes from two identical rotating rigs with

different foundation flexibilities, so as to further enhance the understanding of

rotating machines’ behaviours under different faults.

4.2 Experimental Rigs

The experiments were conducted on two identical rotating machines with slightly

different foundation flexibilities (i.e. FS1 and FS2), which aims to simulate a

practical case of installing the same rotating machine at two different locations.

Figure 4.1 shows the first experimental rig (i.e. FS1), containing two mild steel

shafts of 1000mm and 500mm lengths respectively. Both shafts are of similar

diameters (i.e. 20mm) and are rigidly coupled together, while the 1000mm shaft is

flexibly coupled to a 0.75 kW electric motor. Three mild steel balance discs with

125mm outside diameter, 15mm thickness and 20mm inside diameter were

respectively mounted on the 1000mm and 500mm shafts. Two of the balance

discs were mounted on the 1000mm shaft at distances of 300mm from the flexible

coupling and 190mm from bearing 2 respectively, while the third balance disc was

mounted on the 500mm shaft at 210mm from both bearings 3 and 4. The

experimental rig is however supported by 4 flange-mounted anti-friction ball

bearings. The second experimental rig (i.e. FS2) is an exact replica of FS1 with

respect to configuration, components and capacity. However, both FS1 and FS2

are slightly unique in the stiffness of their foundations (Figure 4.2), due to the fact

that FS1 and FS2 bearings were respectively mounted using 10mm and 6mm

thick threaded bars (Figure 4.2).


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Figure 4.1 Experimental rig with flexible bearing foundation

Figure 4.2 Flexible anti-friction ball bearings foundations (a) FS1 (b) FS2

4.3 Vibration Experiments

A total of 9 experimentally simulated cases on both rigs (FS1 and FS2) at 2400

RPM machine speed were used in the current study, and the vibration

displacements were collected using 2 orthogonally mounted (near bearing 1)

proximity probes for further signal processing. It is salient to note that the machine


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speed is below the first critical speeds (Hz) for FS1 and FS2 foundations

respectively. In order to better understand the dynamic behaviours of both rigs,

impact-response experimental modal analysis technique was used to identify the

first few natural frequencies (by appearance) of FS1 rig as; 50.66Hz, 56.76Hz,

59.2Hz and 127.6Hz. As in the case of FS1, the first few natural frequencies (by

appearance) of FS2 rig were similarly identified as; 47Hz, 55.54Hz, 57.98Hz and

127Hz.

4.3.1 Case 1: Healthy with residual misalignment (HRM)

A healthy case adjudged to be containing some residual misalignment was

considered as the reference case, since it was practically difficult to achieve a

perfectly aligned rig.

4.3.2 Case 2: Unbalance (UNB)

The unbalance case was experimentally simulated by inserting an M5 x 25mm

grub screw of 2.6g mass in one of the 12 equal divisions on the balance disc near

bearing 2 (i.e. 190mm from bearing 2).

Figure 4.3 Unbalance case


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4.3.3 Case 3: Shaft crack (SC)

A 4mm deep crack with width of 0.25mm was created on the 1000mm shaft, at a

location of 160mm from bearing 1, through the aid of the wire electric discharge

machining (EDM) process. As it was unlikely for the crack to breathe, a 0.23mm

mild steel shim was then inserted in the crack to ensure breathing action.

Figure 4.4 Loose bearing case

4.3.4 Cases 5-8: Shaft misalignment (SM)

Four different severities of shaft misalignment (i.e. SM1, SM2, SM3 and SM4)

were experimentally simulated by inserting mild steel shims of different

thicknesses beneath bearing 1 foundation, which are shown in Table 4.1 and

Figure 4.5.


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Table 4.1 Shaft misalignment severities and locations

Case Misalignment Abbreviation Severity and Location

5 Scenario 1 SM1 0.4mm mild steel shim beneath LHS of bearing 1 foundation

6 Scenario 2 SM2 0.4mm mild steel shim beneath LHS and RHS of bearing 1 foundation

7 Scenario 3 SM3 0.8mm mild steel shim beneath LHS of bearing 1 foundation

8 Scenario 4 SM4 0.4mm mild steel shim beneath LHS and RHS of bearing 1 foundation

Figure 4.5 Shaft misalignment cases (a) SM1 (b) SM2

4.3.5 Case 9: Shaft rub (SR)

Finally, the shaft rub case was simulated by installing 2 Perspex blades (i.e. one at

the top and the other at the bottom) at 275mm from bearing 1, which was aimed at

experimentally simulating a practical case of rotating blades (e.g. turbine or fan

blades) rubbing against the casing at some locations.


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Figure 4.6 Shaft rub case

4.4 Results and Observations

The vibration data measured by 2 proximity probes for all the experimentally

simulated cases on the rig with 2 different foundation flexibilities (i.e. FS1 and

FS2) at 2400RPM machine speed, have been used to construct the typical rotor

orbit plots shown in Figures 4.7-4.8. The LB cases clearly yielded the highest shaft

displacement in both FS1 (Figure 4.7(d)) and FS2 (Figure 4.8(d)), which is quite

evident in the rotor orbit size. However, with the exception of SR cases (Figure

4.7(i) and Figure 4.8(i)) on both FS1 (Figure 4.7) and FS2 (Figure 4.8), the rotor

orbits for all the experimentally simulated cases are very identical in shape and

size. This observation however deviates from suggestions from earlier studies

[53], [54]. For instance, the rotor orbits due misalignment have been earlier

described as containing inner loops, which may sometimes constitute a shape

similar to the “figure-8” [53], depending on severity. Hence, based on the specific

cases experimentally simulated in the current study, it has been observed that the

application of rotor orbits for absolute faults diagnosis in rotating machines may be


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difficult and limited under certain machine operating conditions (e.g. support

flexibility, type and location of fault).


SM2 (g) SM3 (h) SM4 (i) SR


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SM2 (g) SM3 (h) SM4 (i) SR

4.5 Spectrum Analyses

Figures 4.9-4.10 show the typical amplitude spectra for just 4 cases (HRM, SC,

SM4 and SR) on both FS1 (Figure 4.9) and FS2 (Figure 4.10) at 2400RPM, which

have been computed using a 95% overlap; frequency resolution ( ) = 0.6104Hz;

sampling frequency (fs ) = 10000Hz and number of data points (N) = 16384. The

amplitude spectra clearly show some depictions through the changes in harmonic

patterns for each of the experimentally simulated cases on both FS1 and FS2 rigs.


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Figure 4.9 Typical amplitude spectra for FS1 at 2400RPM (a) HRM (b) SC (c) SM4

(d) SR


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Figure 4.10 Typical amplitude spectra for FS2 at 2400RPM (a) HRM (b) SC (c)

SM4 (d) SR

4.6 Summary

Experimental observations on orbit plots have been presented for a number of

faults on a rotating machine with 2 different foundations. Under both installation

conditions, the machine speed was below the first critical speed. Therefore, the

dynamics of the machines for both installations are expected to be identical, which

has also been observed here. However, based on the cases experimentally

simulated in the current study, there is no significant change in the orbit features

for the different experimentally simulated faults for both installation conditions,

except for the shaft rub case (SR). However, changes in the harmonic patterns for

different faults are clearly visible in the amplitude spectra. Hence, the consistency


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of the present observations and the general understanding of rotor orbit analysis

could be significantly enhanced through a series of planned future investigations of

more cases at different locations and severities.

A Comparison of Signal Processing Tools: Higher Order Spectra Versus Higher Order Coherences

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5 Chapter 5 A COMPARISON OF SIGNAL PROCESSING TOOLS: HIGHER ORDER

SPECTRA VERSUS HIGHER ORDER COHERENCES

----------------------------------------------------------------------------------------------

Reformatted version of the following papers:

Paper 1 title: A comparison of signal processing tools: Higher order spectra

versus higher order coherences

Authors: A. Yunusa-Kaltungo and J.K. Sinha

Published in: Journal of Vibration Engineering & Technologies, Volume 3, Issue 4,

August 2015, Pages 461-472

Paper 2 title: Faults diagnosis in rotating machines using higher order

spectra


Published in: Proceedings of ASME Turbo Expo 2014: Turbine Conference and

Exposition, Dusseldorf/Germany, June 16-20 2014

Series title: Structures and Dynamics

Volume: 7A


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DOI: 10.1115/GT2014-25090

Publisher: American Society of Mechanical Engineers

Abstract

A class of signal processing tools, higher order spectra (HOS) and their

normalised amplitudes higher order coherences (HOC) have been receiving

attentions in numerous applications, including health monitoring (HM) techniques

for structures and machines. It is however difficult to decide which of the tools

(HOS or HOC) gives the best diagnostic features. In this paper, HOS and HOCs

have been compared using numerically simulated signals with and without noise.

The cross-power spectral density (CSD) between two signals and its ordinary

coherence are also compared. The results and observations on the different

spectra and their coherences are discussed here. It is observed that the use of

HOS may be more advantageous over HOC analysis.

Keywords: Cross-power spectrum, bispectrum, trispectrum, ordinary coherence,

bicoherence, tricoherence

5.1 Introduction

The cross-power spectral density (CSD) between two signals and its normalised

amplitude between 0 and 1 known as ordinary coherence are well-known signal

processing tools, used to find the relation between the two signals at each

frequency component within both signals [146], [156]. Similarly, the existence of a

relationship between the different frequency components within a signal is also

possible. Over the past few decades [98], [103], [157]–[160], the detection of such

relation between the frequency components within a signal using higher order

signal processing tools (higher order spectra and higher order coherences) has

gained tremendous attention. The two most popular higher order statistical


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techniques are the higher order spectra (HOS) and the higher order coherences

(HOC). HOS, mainly bispectrum [97], [98], [103], [107], [129], [146], [158]–[164]

and trispectrum [98], [159] are respectively the double and triple Fourier

transforms of the third and fourth order moments of a time domain signal. The

normalisation of the amplitudes of HOS produces the HOC, where bicoherence

represents normalised bispectrum and tricoherence similarly represents

normalised trispectrum [98], [159]. It is therefore believed that this normalisation

should not alter the characteristics of the spectrum pattern except that the

amplitudes have been limited to a range of between 0 and 1. However the

amplitude normalisation process adopted for the HOS is based on the concept of

the cross-power spectral density (CSD) between two signals and its ordinary

coherence [146], [156]. Hence it is unlikely that the HOC may appear like the HOS

with just normalised amplitude between 0 and 1.

HOS and HOC have been extensively used in a number of applications, including

structural health monitoring, fault detection and characterisation in medicine, rotor-

dynamics, electronics, aerospace, etc. In rotor-dynamics, machinery faults such as

misalignment, crack and shaft rub have been detected using bispectrum [107],

[129], [161]. In a similar study, both bispectrum and trispectrum were used to

identify crack and misalignment in the shaft of a rotating machine [106], [165],

while bispectrum has also been specifically used to detect faults associated with

induction motors [166]. Medical applications of higher order statistical tools include

the use of bispectrum components of the heart rate variability for the detection of

congestive heart failure [167], the classification of different electrocardiogram

(ECG) signals using a combination of bispectrum components and principal

components analysis [168], [169], detection and analysis of epileptic conditions

[170]–[172], etc. In aerospace, bicoherence has been used to separately detect

unbalance, misalignment and a combination of both faults in AH-64 helicopter

drive train assembly [173] and the gearbox of the American NAVY CH-46

helicopter [101]. HOS has similarly been used for studying the non-linear effects of

vibration signals in helicopter drive trains [173]. Structural applications include the

use of HOC for fatigue crack detection in a cantilever beam [174] as well as


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determining the early contact between two components [175]–[177]. Other

applications of HOS and HOC include rolling element bearings condition

monitoring using bicoherence [100], [102], [164], [178], [179]; hidden mines

detection in coastal systems [180]; analysis of the cutting process in

manufacturing systems [181]; study of material properties [182]; the analysis of

speech and sound in audio processing [183]–[185]; and for the assessment of the

performance of measurement instruments [186].

Some of the above applications have made use of HOS, while others have used

HOC. However, it still remains unclear whether HOS or HOC provide the best

diagnostic features, or whether the two classes of signal processing tools (HOS

and HOC) offer similar features. In this paper therefore, a number of numerically

simulated signals with different amplitudes, frequency components and phases

have been used for the computation of HOS and HOC, with and without noise to

bring out their usefulness and impact on the data analysis and diagnosis. The

cross-power spectral density (CSD) between two signals and its ordinary

coherence are also compared. The results and observations suggest that the HOS

has clear advantages over the HOC which are illustrated in the paper.

5.2 Computational Approaches for Spectra and Coherences

The averaged power spectrum density (PSD) of a time domain signal is

computed as;

=

(5.1)

where =

N is the number of data points for

DFT analysis; is the sampling frequency; is the frequency resolution; is the


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number of segments of size N; and are respectively the discrete

Fourier transform (DFT) and its complex conjugate at frequency for the rth

segment of the time domain signal that is characterised by a time length of t,

with a reasonable amount of overlap.

Similarly, the CSD between two time domain signals and was computed

as;

(5.2)

The HOS however provide the relation that exists between frequencies within a

time domain signal , since they involve both amplitudes and phases [98],

[157]–[159]. In simpler terms, the bispectrum (which is the double Fourier

transform of the third order moment of a time domain signal, ) basically

involves the combination of two frequencies, and (with both having

amplitudes and phases) with a third frequency which is the summation of the

first two, and computed as [98], [157]–[159], [163];

(5.3)

Similarly, the trispectrum (which is the triple Fourier transform of the fourth order

moment of a time domain signal ) involves the combination of three

frequencies, , and (all having amplitudes and phases) with a fourth

frequency which is the summation of the first three, and computed as

[98], [157]–[159], [163];


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(5.4)

Furthermore, the normalization of the HOS between amplitude scales of 0 and 1

produces the HOC (where little or no coherence tends to 0 and high coherence

tends to 1). In other words, the normalization of the bispectrum results to

bicoherence, while that of the trispectrum similarly results to tricoherence. The

HOC have been computed as [98], [157]–[159], [163];

Bicoherence, b2 (fl, fm) =

(5.5)

Tricoherence, t2 (fl, fm, fn) =

(5.6)

The coherence between two time domain signals and is a measure of the

linear correlation between them, at a given frequency , where a coherence

nearer to unity signifies that the time domain signals and are linearly

correlated [156], [186]. On the other hand, a reduction in coherence from unity

between the two time domain signals and , may either signify the

presence of noise or a nonlinear relationship [156]. Therefore, the ordinary

coherence between the time domain signals and is computed as [156];

(5.7)


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where represents the CSD between the time domain signals and ,

while and are their respective PSD at frequency , as shown by Equations

(5.1)-(5.2).

5.3 Simulated Example

In the simulated example, a typical rotating machine with a rotating speed of 3000

RPM (50Hz) has been considered. Vibration response of rotating machines

usually generates responses at rotating speed, which is referred to as the

fundamental frequency (50Hz), and also known as 1x. Due to the emergence of

different faulty conditions [128], rotating machines produce higher harmonics i.e.

100Hz (2x), 150Hz (3x), 200Hz (4x), ….., etc. Hence, the time domain signal

in Equation (5.8), is used to describe a rotating machine with different health

conditions.

(5.8)

where , , , ...., represent the vibration amplitudes at the various

frequency harmonics ( , , ,..., ) and their respective

phases.

A total of 4 cases were simulated (as shown in Table 5.1), and Figure 5.1 shows

the amplitude spectra of the 4 simulated cases computed as per Equation (5.1),

using number of data points (N) of 4096, sampling frequency ( ) of 3000Hz,

frequency resolution ( ) of 0.7324Hz and an overlap of 80% for the averaging.

In case 1, the vibration amplitudes are general low, with 1x amplitude being

slightly higher than those at the higher harmonics (2x, 3x, 4x, …, etc.), which is a


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representation of a typical healthy case. In the other 3 cases, the vibration

amplitudes have changed (i.e. higher than observed in case 1), which indicates 3

different fault conditions.

Table 5.1 Simulated amplitudes and phases

Simulation Vibration amplitude (g) Frequency (Hz) Phase (degrees)

Case 1

a1 0.15 f1 50 -60

a2 0.06 f2 100 95

a3 0.02 f3 150 160

a4 0.008 f4 200 120

a5 0.001 f5 250 37

a6 0.0006 f6 300 -52

Case 2

a1 1 f1 50 25

a2 0.8 f2 100 35

a3 0.64 f3 150 45

a4 0.48 f4 200 75

a5 0.32 f5 250 105

a6 0.06 f6 300 130

Case 3

a1 0.7 f1 50 48

a2 0.4 f2 100 92

a3 0.33 f3 150 145

a4 0.18 f4 200 90

a5 0.08 f5 250 175

a6 0.04 f6 300 45

Case 4

a1 0.4 f1 50 -130

a2 0.8 f2 100 -55

a3 0.2 f3 150 75

a4 0.6 f4 200 175

a5 0.3 f5 250 125

a6 0.02 f6 300 60


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Figure 5.1 Typical amplitude spectra (a) Case 1 (healthy) and (b)-(d) Case 2-

Case 4 (different faulty conditions)

5.4 CSD and Ordinary Coherence Analysis

For all 4 simulated cases, the CSD and ordinary coherence have been computed,

using Equations (5.2) and (5.7), and Figures 5.2-5.3 show the CSD and ordinary

coherence plots. In Figures 5.2(a)-5.2(d), all the CSD plots displayed different

features, (showing different magnitudes at the various harmonics of the

fundamental frequency) which clearly show the responsiveness of the CSD to

amplitude and phase changes between the different signals. Amplitudes of

different CSD components shown in Figure 5.2 are also summarized in Table 5.2

for easy comparison. Furthermore, their ordinary coherence plots are shown in

Figure 5.3, with all the magnitudes at the different harmonics of the fundamental


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frequency tending towards unity as expected, irrespective of the amplitude and

phase changes. This simply indicates and further confirms the well known fact that

the ordinary coherence generally provides the relation between 2 signals at a

frequency, and hence frequently used in several applications including modal tests

[146].

Figure 5.2 Typical CSD plots (a) Signals 1&2, (b) Signals 1&4, (c) Signals 2&4,

and (d) Signals 3&4

(a) (b)

(c) (d)


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Figure 5.3 Typical ordinary coherence plots (a) Signals 1&2, (b) Signals 1&4, (c)

Signals 2&4, and (d) Signals 3&4

Table 5.2 Magnitudes of CSD components

Frequency, Hz

CSD, Sxy

1 and 2 1 and 4 2 and 4 3 and 4

50 0.3501 0.7003 0.2802 0.2005

100 0.12 0.3202 0.3198 0.2401

150 0.08237 0.2105 0.06592 0.05002

200 0.01798 0.08671 0.1081 0.6003

250 0.003929 0.02552 0.02386 0.01486

300 0.0004179 0.002422 0.0008087 0

5.5 Bispectrum and Bicoherence Analysis

The bispectrum and bicoherence have also been computed for all 4 simulated

cases, using Equations (5.3) and (5.5), for which the typical amplitude-bispectra

and the bicoherence plots are shown on Figures 5.4-5.5. In Figure 5.4, B11


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represents the relationship between 1x (twice) and 2x components; B12 = B21

represents the relationship between 1x, 2x and 3x components; B22 represents the

relationship between 2x (twice) and 4x components; etc. Similarly, in Figure 5.5,

b211 represents the relationship between 1x (twice) and 2x components; b2

12 = b221

represents the relationship between 1x, 2x and 3x components; b233 represents the

relationship between 3x (twice) and 6x components; etc. It can be seen that all the

amplitude-bispectra plots in Figures 5.4(a)-5.4(d) displayed different

characteristics, with Figure 5.4(a) showing no visible peaks at any location,

representing a healthy condition, while Figures 5.4(b)-5.4(d) show various

bispectrum components with different magnitudes, which clearly represents

different fault conditions. On the contrary, the bicoherence plots in Figures 5.5(a)-

5.5(d) showed identical patterns, with numerous bicoherence components for all

the simulated cases.

Figure 5.4 Typical amplitude-bispectra plots (a) Case 1 (healthy) and (b)-(d) Case

2-Case 4 (different fault conditions)


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Figure 5.5 Typical bicoherence plots (a) Case 1 (healthy) and (b)-(d) Case 2-Case

4 (different fault conditions)

5.6 Trispectrum and Tricoherence Analysis

Similarly, the trispectrum and tricoherence were computed for all the simulated

cases using Equations (5.4) and (5.6), for which the typical amplitude-trispectra

patterns for 2 of the 4 cases are shown in Figure 5.6. T111 represents the

relationship between 1x (thrice) and 3x components; T112=T121=T211 represents the

relationship between 1x (twice), 2x and 4x components; etc. Similarly, in Figure

5.7, t2111 represents relationship between 1x (thrice) and 3x components; t2112 =

t2121 = t2211 represents relationship between 1x (twice), 2x and 4x components; etc.

The amplitude-trispectra plots shown in Figures 5.6(a)-5.6(b) possessed very

different features, with Figure 5.6(a) showing only the T111 trispectrum component

or sphere (where sphere diameter represents amplitudes of vibration and spheres

presence at certain locations indicating the intersection of 3 frequencies in l, m and

b233

b211

b212

(a)

b233

b211

b212

(b)

b233

b211

b212

(c)

b233

b211

b212

(d)


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n axes), which is a representation of a typically healthy machine. Figure 5.6(b)

however displayed additional components (T112= T121= T211) to the T111 component,

which is an outcome of the changes in the amplitudes and phases (representing a

typical faulty condition). The tricoherence plots in Figure 5.7 however show very

identical features for both healthy and faulty conditions, as shown in Figures

5.7(a)-5.7(b) respectively.

Figures 5.4-5.7 have clearly showed that irrespective of amplitude or phase

changes, HOC (bicoherence and tricoherence) will always tend towards 1. On the

other hand, HOS (bispectrum and trispectrum) adequately respond to amplitude

and phase changes. This observation was consistent for all the 4 simulated cases.

Figure 5.6 Typical amplitude-trispectra plots (a) Case 1 (healthy) and (b) Case 2

(faulty)


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Figure 5.7 Typical tricoherence plots (a) Case 1 (healthy) and (b) Case 2 (faulty)

5.7 Signals with Noise

Now, different levels of noise are also added to the signals in Table 5.1, so as to

further understand the behaviors of HOS and HOC. The 3 noise levels considered

are at 10 dB, 20 dB and 30 dB (with 10 dB being the noisiest). The magnitudes of

the HOS components as well as the plot patterns remained unchanged at all noise

levels. On the contrary, as the noise levels increased towards 10 dB, the

magnitudes of the HOC components (e.g. b233 and b2

23 significantly reduced from

1 at zero noise to 0.304 and 0.454 respectively) began to decrease, which shows

the dependency of HOC on noise levels, and this is further illustrated by Table 5.3.


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Table 5.3 Magnitudes of bispectrum and bicoherence components

SNR (dB) Case Bispectrum Components Bicoherence Components

B11 B12 B13 B22 B23 B33 b211 b

212 b

213 b

222 b

223 b

233

10

1 0.001 0 0 0 0 0 0.999 0.998 0.981 0.981 0.454 0.304

2 0.805 0.513 0.313 0.305 0.166 0.025 1 1 1 1 0.999 0.973

3 0.196 0.092 0.04 0.028 0.011 0.004 1 1 0.999 0.999 0.996 0.977

4 0.129 0.063 0.048 0.386 0.047 0.001 0.999 0.998 0.999 1 0.998 0.924

20

1 0.001 0 0 0 0 0 1 1 1 0.998 0.921 0.824

2 0.799 0.512 0.308 0.306 0.165 0.025 1 1 1 1 1 0.996

3 0.195 0.092 0.042 0.029 0.011 0.005 1 1 1 1 1 0.997

4 0.128 0.064 0.048 0.385 0.048 0.001 1 1 1 1 0.921 0.997

30

1 0.001 0 0 0 0 0 1 1 1 1 0.989 0.981

2 0.8 0.512 0.308 0.308 0.164 0.025 1 1 1 1 1 1

3 0.196 0.092 0.042 0.029 0.011 0.004 1 1 1 1 1 1

4 0.128 0.064 0.048 0.385 0.048 0.001 1 1 1 1 1 0.999

zero noise

1 0.001 0 0 0 0 0 1 1 1 1 1 1

2 0.8 0.512 0.307 0.307 0.164 0.025 1 1 1 1 1 1

3 0.196 0.092 0.042 0.029 0.011 0.004 1 1 1 1 1 1

4 0.128 0.064 0.048 0.384 0.048 0.001 1 1 1 1 1 1


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5.8 Summary

A total of 4 signal cases have been simulated, with each case having differing

amplitudes and phases, but same frequency components so that the comparison

between spectra and coherences can be made. Initially, the CSD and their

ordinary coherences were analyzed, and it was observed that the ordinary

coherence provides linearity relation at each frequency between 2 signals,

irrespective of the amplitude and phase at each frequency in the signals. A similar

behavior was also observed when HOS and HOCs were compared. This simply

indicates that HOCs are not amplitude normalization of HOS. Hence HOCs cannot

be used to represent a real system, due to their lack of sensitivity to amplitude and

phase changes, as well as their dependence on noise levels. On the other hand,

HOS components responded adequately to changes in amplitude and phases,

which is a highly desirable characteristic for many applications and diagnosis, so

as to distinguish the different states of signals. It can therefore be concluded that

HOS provide better representation of features at each combination of frequency

components in a signal than HOCs, which make HOS more useful for different

applications including health monitoring and diagnosis technique for structures and

rotating machines.

Combined Bispectrum and Trispectrum for Faults Diagnosis in Rotating Machines

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6 Chapter 6 COMBINED BISPECTRUM AND TRISPECTRUM FOR FAULTS DIAGNOSIS

IN ROTATING MACHINES ----------------------------------------------------------------------------------------------


Paper 1 title: Combined bispectrum and trispectrum for faults diagnosis in

rotating machines


Published in: Proceedings of the Institution of Mechanical Engineers, Part O:

Journal of Risk and Reliability, Volume 228, Issue 4, February 2014, Pages 419-

428

Paper 2 title: HOS analysis of measured vibration data on rotating machines

with different simulated faults

Authors: A. Yunusa-Kaltungo, J.K. Sinha and K. Elbhbah

Published in: Proceedings of 3rd International Conference on Condition Monitoring

of Machinery in Non-Stationary Operations (CMMNO 2013), Ferrara/Italy, May 8-

10 2013

Series title: Lecture Notes in Mechanical Engineering

DOI: 10.1007/978-3-642-39348-8


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Publisher: Springer-Verlag Berlin Heidelberg

Abstract

Over the years, condition monitoring (CM) of rotating machines has been

extensively applied for enhancing equipment reliability and maintenance cost

effectiveness, through the early detection and reliable diagnosis of incipient

machine faults. Earlier studies suggest that bispectrum analysis is a good tool for

detecting and distinguishing rotor related faults in rotating machines, with a

significantly reduced number of vibration sensors. Now, the trispectrum analysis is

also applied to the measured vibration data, so as to explore the usefulness of this

analysis in the diagnosis. It is observed that the trispectrum further improves the

reliability of rotating machine faults diagnosis. This paper presents the results and

observations related to the bispectrum and trispectrum analysis for fault(s)

diagnosis, through an experimental rig with different faults simulation.

Keywords: Machine reliability, rotating machines, condition monitoring, higher

order spectrum, bispectrum, trispectrum

6.1 Introduction

Rotating machines form the heart of most industrial activities, which makes the

reliability of this class of machines imperative to any organisation. In the past,

some failures associated with rotating machines have had devastating effects on

personnel, environment, finance, etc [187]. Hence, the development of a reliable

and cost effective fault diagnosis approach that will enhance the planning and

scheduling of maintenance activities, through the provision of reasonable lead

times to failure is always desirable. Vibration-based condition monitoring (VCM) is

a well-known technique for the diagnosis of faults related to rotating machines [8],

through the installation of various numbers of vibration transducers at individual

bearing pedestals of the monitored machine. The present efforts are aimed at


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minimising the transducer requirements for VCM, through the use of higher order

spectra (HOS), namely bispectrum and trispectrum [98], [103], [157]–[160]. This is

because HOS have the capability to combine different frequency components in a

signal (as opposed to the conventional spectrum analysis that only provides

insights of the amplitudes of individual frequency components [188]), and hence

the relationships that exist amongst the different harmonics and sub-harmonics of

the machine’s rotational speed in the vibration responses from the machine can be

used for the diagnosis of rotor related fault(s). Earlier studies have explored the

possibilities of fault diagnosis by mainly applying the bispectrum [107], [129], while

very limited research study related to the trispectrum [189] was done. It has been

observed that the bispectrum analysis [107], [129] provides a much better feature

for the diagnosis of different faults simulated on an experimental rig, when

compared to the spectrum analysis alone, without the phase and orbit analysis.

Earlier studies by McCormick and Nandi [190], as well as Li et al. [191] have

significantly identified the potentials of using HOS for the diagnosis of machine

faults. However, the former study [190] was solely based on fault diagnosis of

rolling element bearings, while the latter study [191] on the other hand focused on

the detection of incipient gear faults using a combination of bispectrum and

artificial neural networks (ANN). Sinha [106] also applied HOS for detection of

crack and misalignment on a rotating machine with a rotor supported by just two

bearings. However, a significant number of rotating machines are more complex in

structure, with several bearings and couplings. In the present study, a combination

of the newly introduced trispectrum analysis and the earlier bispectrum analysis

[107], [129] are jointly applied to the measured vibration acceleration data for 4

different experimentally simulated cases (healthy, shaft misalignment, cracked

shaft and shaft rub) on an experimental rig supported by 4 anti-friction ball

bearings, so as to enhance the reliability of the diagnosis feature for each fault.

The observations from the earlier studies [107], [129] based on bispectrum

analysis clearly suggested that bispectrum analysis performs extremely well in

detecting and differentiating between all the simulated cases at certain speeds.

However, the incorporation of trispectrum analysis in the current study further

enhances the possibilities of developing a more robust set of condition monitoring


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indicators (CMI) that will be applicable to various operating conditions of a

machine. Furthermore, a comparison of HOS with the conventional and widely

applied spectrum analysis, which is based on power spectrum density (PSD) for

measured vibration data is also presented here, so as to clearly show the

advantages of HOS analysis. Experiments were carried out at 2 different rotating

speeds – 2400RPM (34Hz) and 3000RPM (50Hz), and the results observed from

both bispectrum and trispectrum analyses at these two speeds are also discussed.

6.2 PSD and HOS Computations

The PSD of a time domain signal can be computed as;

=

(6.1)

where =

N denotes the number of data points

for discrete Fourier transform (DFT) analysis; represents the sampling

frequency; is the frequency resolution; is the number of segments with size

N; and respectively denote the DFT and its complex conjugate at

frequency for the rth segment of the considered time domain signal ,

having a time length of t, with sufficient amount of overlap.

The HOS offers insight on the relationship existing amongst the frequency

components present in a time domain signal , as they entail amplitudes as well

as phases [98], [157]–[159]. In similar definitions, the bispectrum of a time domain

signal , represents a combination of two frequencies (each having amplitude

and phase), and with a third frequency which is equivalent to the sum

of the initial two, and was computed as [157]–[159];


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(6.2)

Similarly, the trispectrum of a time domain signal , involves the combination of

three frequencies (each having amplitude and phase) , and with a fourth

frequency that is equivalent to the sum of the initial three, and was

computed as [98], [159], [188];

(6.3)

In the current paper, the HOS (bispectrum and trispectrum) have been computed

by dividing the measured vibration data into a number of overlapping segments

( ). The DFT for each of the segments is then computed, and the products of the

spectral coefficients generate the HOS, which are eventually averaged across the

segments [98]. Each of the bispectrum components amplitude is a function of two

frequencies, usually plotted in the xyz orthogonal axes, with axes x and y

respectively representing frequencies, while the amplitude of the bispectrum is

plotted on the z axis. On the other hand, each trispectrum component is a function

of three frequencies, requiring a 4-dimensional plot. Therefore, the spherical plot

method earlier suggested by Collis et al. [98] is adopted here, where the

appearance of individual spheres at certain locations signifies the coupling that

exists between the frequencies at that location and the sizes of the spheres relate

to the amplitudes of the trispectrum components for individual cases.

6.3 Experimental Setup

The photographic and schematic representations of the experimental rig are

shown on Figures 6.1and 6.2 respectively, which is situated in the Dynamics

Laboratory of the University of Manchester. The rig principally consists of two


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rigidly coupled steel shafts of uniform diameters (20mm) but varying lengths

(1000mm and 500mm respectively), which were supported by 4 anti-friction ball

bearings mounted on relatively stiff pedestals (just as indicated by Figure 6.1). The

1000mm shaft is connected to the electric motor via a flexible coupling. The motor

speed is regulated through the aid of a PC-based speed controller (NEWTON

TESLA CL750 and FR Configurator SW3), so as to accommodate the selection of

preferred shaft speeds during the experiment. There are 3 balance steel discs of

dimensions 125mm (OD) x 15mm (thickness), with 2 of the discs fitted on the long

shaft (first disc is 300mm from the drive motor and the second is 190mm from the

second bearing) and the third on the shorter shaft (210mm from both bearings 3

and 4) as shown on Figure 6.1. Further details about the experimental setup are

available in Elbhbah and Sinha [107].

Figure 6.1 Photographic representation of the experimental rig


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Figure 6.2 Schematic representation of the experimental rig

6.4 Simulation of Faults

The following four cases (healthy, misalignment, cracked shaft and shaft rub) have

been simulated on the experimental rig (Figure 6.1), and vibration data were

collected at 2 different rotational speeds of 2040RPM (34Hz), which corresponds

to half of the first natural frequency of the rig and at 3000RPM (50Hz). For all 4

cases, only 4 accelerometers (1 at each bearing pedestal, in the horizontal

direction) were used for the collection of the vibration responses. All vibration data

were recorded on to a PC, through the aid of a 16-channel, 16-bits Data

Acquisition Card (NI 6229), for subsequent analysis using a MATLAB code.

Further details about the simulated faults are also available in Elbhbah and Sinha

[107].


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6.5 Data Analysis

The measured vibration data from the 4 bearings, at rotational speeds of

2040RPM (34Hz) and 3000RPM (50Hz) have been analysed using spectrum,

bispectrum and trispectrum, which were computed as per Equations (6.1)-(6.3), in

Section 6.2. The vibration data were analysed using an 80% overlap, frequency

resolution ( of 0.6104Hz at a sampling frequency (fs) of 5000Hz, and a number

of data points, N = 8192. The observations and results are hereby discussed

accordingly.

6.5.1 Spectrum analysis

As extensively analysed in earlier studies [128], the amplitude spectra at 34Hz for

bearing 1 (Figure 6.3), displayed significantly low peaks at 1x and its higher

harmonics for the healthy case (Figure 6.3(a)). The shaft misalignment case

(Figure 6.3(b)) contained similar harmonic components as the healthy case, but

with much higher amplitudes. The cracked shaft case presented additional 4x and

5x harmonic components to the 1x and 2x components in the earlier cases (i.e.

healthy and shaft misalignment), while shaft rub case (Figure 6.3(d)) showed sub-

harmonic components (0.5x and 1.5x). At 50Hz (Figure 6.4) however, the

amplitude spectra at bearing 1 still possessed 1x and 2x peaks with relatively low

amplitudes for the healthy case (Figure 6.4(a)). On the other hand, the features for

misalignment (Figure 6.4(b)), cracked shaft (Figure 6.4(c)) and rub (Figure 6.4(d))

cases have completely changed at 50Hz (mainly due to the fact that 34Hz is

exactly half of the first natural frequency of the machine, which governed the

excitation of 1x), with misalignment showing 1x, 2x, 4x and 6x peaks, while the

cracked shaft case displayed very prominent peaks at 1x and 2x only. The sub-

harmonic components in the rub case disappeared at 50Hz, leaving the presence

of only 1x and 2x peaks with very low amplitudes. Furthermore, a plot of the

normalised amplitudes (i.e. the normalisation of the amplitudes of the higher

harmonics, mainly 2x, 3x, 4x, with the amplitude of 1x) at both 34Hz and 50Hz for

bearing 1 is shown on Figure 6.5, where it can be clearly seen that virtually no


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separation exists amongst the different cases (significant overlap amongst all

cases). This however explains why it is difficult to adequately differentiate between

the various operational states of a machine, using spectrum analysis alone.

Figure 6.3 Typical amplitude spectra at 34Hz for bearing 1


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Figure 6.4 Typical amplitude spectra at 50Hz for bearing 1


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Figure 6.5 Typical normalised amplitude spectrum components at 34Hz ((a)-(b))

and at 50Hz ((c)-(d)) for all the simulated cases

6.5.2 Bispectrum analysis

The findings from the earlier studies [107], [129] already suggested that

bispectrum analysis provided better diagnosis for the different faults. This is

however briefly discussed here, so that the usefulness of trispectrum for a robust

fault(s) diagnosis can be brought out. The amplitude bispectra plots at the two

rotational speeds (34Hz and 50Hz) are shown in Figures 6.6-6.7 [107], [129]

respectively.


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(c) cracked shaft (d) shaft rub


(c) cracked shaft (d) shaft rub


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As explained in Section 6.2, the bispectrum indicates the relation between 2

frequencies, and with their sum ( ) in a time domain signal . Also, in

Figures 6.6-6.7, the different bispectrum components indicate the relationship

between the different frequencies in the measured vibration signal. For instance,

indicates the relation between one times (twice) and two times the rotational

frequency of the machine, where and in Equation (6.2) are equal to the

rotational frequency of the machine, and is two times the rotational

frequency of the machine. Similarly, , indicates the relation between one times,

two times and their sum (i.e. three times) the rotational frequency of the machine;

relates one times, three times and four times the rotational frequency of the

machine; while relates two times (twice) and four times the rotational

frequency of the machine in the measured vibration signal. The sub-harmonic

bispectrum component indicates the relation between fractions of the rotational

frequency of the machine (twice) and their sum (i.e. and are respectively

fractions of the rotational frequency of the machine, while equals their sum).

On the other hand, the sub-harmonic bispectrum component indicates the

relation between a fraction of the rotational frequency of the machine, one times

the rotational frequency and their sum. Using the current set-up as illustration, the

bispectrum component at 34Hz is respectively the product of the amplitudes

and phases of 1x twice (i.e. the combination of the amplitude and phase at

machine speed of 34Hz twice) and 2x (68Hz). Also, component is respectively

the product of the amplitudes and phases of 1x (34Hz), 2x (68Hz) and 3x (102Hz),

etc. However, the bispectra responses for all simulated cases were quite

consistent at both speeds (34Hz and 50Hz) and at all bearings, except for the

shaft rub case (Figure 6.7(d)). Hence, a summary of the observations from the

experiment are explained here.

At both rotational speeds, the healthy case (Figures 6.6(a) & 6.7(a)) contained

generally small and negligible and (= bispectrum components. For

misalignment, all the bispectrum components slightly went higher in amplitudes,

when compared with the healthy case. In the crack case, all the bispectrum

components significantly went higher in amplitudes (with an order of as much as


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ten times, when compared to the misalignment case). The rub case at 34Hz

(Figure 6.6(d)) displayed an entirely different feature from the other 3 cases, owing

to the fact that most of the rotor’s unbalance energy have been converted to sub-

harmonic responses, which was responsible for the cluster of peaks around

and (= ). At 50Hz however, the rub case displayed a response that looked

identical to the healthy case, due to inadequate shaft deflection (which created a

“touch and go effect” as opposed to the substantial rub experienced at 34Hz)

[107], [129].

6.5.3 Trispectrum analysis

Figures 6.8-6.9 show the amplitude trispectra plots, where signifies the

relation between one times (thrice) and three times the rotational frequency

components; = = signifies the relation between one times (twice),

two times and four times the rotational frequency components; signifies the

relation between fractions of the rotational frequency (thrice) and their sum; =

= signifies the relation between fractions of the rotational frequency

(twice), one times and two times the rotational frequency. As explained for the

bispectrum analysis in Section 6.5.2, trispectrum component in the current

set-up at 34Hz machine speed represents a combination of the amplitudes and

phases of 1x (34Hz) twice, 2x (68Hz) and 4x (136Hz).


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Figure 6.8 Typical amplitude trispectra plots at 34Hz for bearings 1 (a-d) and 3 (e-

h); (a and e) healthy, (b and f) misalignment, (c and g) cracked shaft, (d and h)

shaft rub


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Figure 6.9 Typical amplitude trispectra at 50Hz (a) healthy (b) misalignment (c)

cracked shaft (d) shaft rub


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Table 6.1 Summary of the diagnostic features for bispectrum and trispectrum

Case(s) Bispectrum Trispectrum Remark(s)

Healthy Small B11 and negligible B12=B21 components

T111 only On all bearings and same at both rotational speeds

Misalignment Peaks at B11, B12=B21 and B22 (Higher than healthy)

Prominent peak at T111 but small T121=T211=T112 at Bearing 1 Consistent observations for

trispectrum, but bispectrum components are speed dependent.

Prominent peak at T222 and small T122=T212=T221 peak at remaining bearings

Cracked shaft Prominent peaks at B11 , B13=B31, B12=B21 and B22 and much higher amplitude compared to Misalignment

Small T111 Consistent observations at both rotational speeds Large T121=T112=T211

Shaft rub B11, Bss, B1s=Bs1, B12=B21, etc. T111, Tsss, T1ss=Ts1s=Tss1, etc.

Consistent observations for both bispectrum and trispectrum analyses except at 3000RPM for bispectrum analysis due to “touch and go” kind of rub.


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The healthy cases at both rotational speeds (34Hz and 50Hz) only possessed the

component (Figures 6.8(a), 6.8(e) and 6.9(a)), which was as a result of the

residual misalignment between bearings 2 and 3. The misalignment case

possessed components = = which were small and equal in size, and

a large component. At 34Hz [12], misalignment at bearing 3 showed small

= = and a large , which also corresponded to the observation at

50Hz. The crack case possessed a response that was somewhat a reverse of the

misalignment case in size, but similar in components (i.e. = were

large and the was small). Just as in the case of the bispectrum at 34Hz, the

rub case displayed several sub-harmonics ( ). These

observations also conformed to the findings of Sinha [106], except for the

misalignment response at bearing 3 (at 34Hz speed), which possessed

= = and components. This variation is due to the fact that the initial

experiment [106] involved the use of just 2 bearings and a single coupling, as

opposed to the present work that had four bearings and 2 couplings (one flexible

and one rigid). However, the appearance of the = = and

components (at 34Hz speed) is due to the fact that bearing 3 is located next to the

rigid coupling, while bearing 1 is located near the flexible coupling, and therefore

some of the energy generated by the misalignment at bearing 1 are absorbed by

the flexible coupling [192]. The current study showed a strong consistency in the

responses at all 4 bearings for all 4 cases and at both speeds, except for the

misalignment case which had responses at bearings 2, 3 and 4 being similar, but

different from the response at bearing 1 (which is due to the fact that the

misalignment is at bearing 1, which is also the flexible coupling location [192]).

Although earlier studies [107], [129] have shown the advantages of bispectrum

among the different cases (healthy, misalignment, cracked shaft and shaft rub),

however, the trispectrum gave an even better, clearer and very consistent

distinction amongst all the experimentally simulated cases and at both rotational

speeds. While the bispectrum analysis for rub case provided a plot that was very

similar to the healthy case (absence of sub-harmonic components) at 50Hz, due to

the partial rub action, the trispectrum was able to maintain its consistency at both


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rotational speeds (e.g. the presence of sub-harmonic components

at both 34Hz and 50Hz), which is explained more

illustratively in Section 6.5.4.

6.5.4 Diagnostic Features

The observations of both bispectrum and trispectrum analyses have been

summarised in Table 6.1, so as to bring out the indicative diagnostic features for

each of the experimentally simulated cases at both rotational speeds. In the

amplitude bispectra plots shown in Figure 6.6, the appearance of relatively small

B11 and B12 peaks for the healthy case at 34Hz is related to the combination of the

amplitudes and phases of the 1x (34Hz) and 2x (68Hz) frequency components

seen in the amplitude spectrum (Figure 6.3(a)), which is due to some residual

misalignment in the machine set-up. Similarly, the appearance of additional B22

component in the misalignment case (Figure 6.6(b)) is an indication of the coupling

that exists between 2x and 4x components in the amplitude spectrum (Figure

6.3(b)). Although the 4x component is not quite visible in the amplitude spectrum

(Figure 6.3(b)), due to the relative dominance of the 1x component (i.e. half the 1st

natural frequency). However, the relationship between the 2x and 4x components

is clearly highlighted in the amplitude bispectrum (Figure 6.6(b)), since it involves

both amplitude and phase information. In the cracked shaft case (Figure 6.6(c)),

the appearance of multiple bispectrum components (B11, B12, B13 and B22) again

relates to the presence and relationships between the 1x, 2x, 3x, 4x, etc.,

components in the amplitude spectrum (Figure 6.3(c)), while the Bss and B1s in the

rub case (Figure 6.6(d)) are respectively the combination of the sub-harmonic

components 0.5x (visible as the humps in Figure 6.3(d)) twice and the 1x

component. At 50Hz machine speed (Figure 6.7), although the bispectrum

components for the healthy, misalignment and cracked shaft cases are same,

however, the magnitudes of the B11 component has significantly reduced in

comparison to the 34Hz speed (mainly because 50Hz is far from any of the natural

frequencies and their multiples). In the shaft rub case at 50Hz (Figure 6.7(d)), the


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sub-harmonic components have disappeared, due to the inability of the shaft to

deflect enough to cause a continuous rub (i.e. “a touch and go” rub action was

observed).

As similarly explained for the amplitude bispectra, the healthy case at 34Hz for

bearing 1 (Figure 6.8(a)) is characterised by T111 trispectrum component, which

signifies the combination of amplitudes and phases of 1x (34Hz) thrice and 3x

(102Hz) frequency components. In the misalignment case (Figure 6.8(b)), the

massive T111 component as well as the T112=T121=T211 (which signifies the

relationship between twice 1x (34Hz), 2x (68Hz) and 4x (136Hz)) components are

governed by the combinations of the amplitudes and phases of 1x, 2x and 4x

frequency components. The lack of visibility of the 4x (136Hz) component in the

amplitude spectrum (Figure 6.3(b)) is also due to the dominance of the 1x

frequency component (half of the first natural frequency of the machine). Although

the cracked shaft case (Figure 6.8(c)) contains similar trispectrum components as

the misalignment case (Figure 6.8(b)), however, the significant changes observed

in the magnitudes of the components (a significant increase in T112=T121=T211

magnitude and a corresponding reduction in T111 magnitude) also conforms with

the presence of higher harmonic components (2x, 4x, 5x, etc.) in the amplitude

spectrum (Figure 6.3(c)). The rub case at 34Hz (Figure 6.8(d)) contains sub-

harmonic trispectrum components Tsss (representing a combination of the

amplitude and phase at 17Hz thrice and at 51Hz), Tss1=Ts1s=T1ss (combination of

amplitude and phase at 17Hz twice, 34Hz and 68Hz), as well as T111 component.

The sub-harmonic trispectrum components in the rub case can be confidently

related to the sub-harmonic humps visible in the amplitude spectrum on Figure

6.3(d). As the machine speed changed from 34Hz to 50Hz (i.e. away from the

natural frequency of the machine), the trispectrum components for each case

remained consistent for all the simulated cases, except that the T111 component

has been transformed to T222, which corresponds to the appearance of significant

2x, 4x and 6x components in the amplitude spectrum (Figure 6.4(b)). As discussed

in the preceding Sections (6.1, 6.2 & 6.5), the advantages of HOS lies in the fact

that they integrate different frequency components in a signal, which makes the


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development of unique features for different cases at different speeds possible

(which is unachievable through the use of spectrum analysis alone, as it only

involves the amplitudes at individual frequencies).

6.6 Summary

Bispectrum and trispectrum analyses have been applied to an experimental rig,

with different simulated faults at different machine speeds, so as to enhance the

reliability of fault diagnosis in rotating machines. Only 1 accelerometer per bearing

pedestal was used, with the aim of reducing the number of often used sensors to a

fewer number. The observations indicate that the faults identification and their

characterisation, using bispectrum and trispectrum analyses is possible. This is

due to the fact that both bispectrum and trispectrum give the combined relation

between the different harmonics of the machine speed in their vibration responses.

The appearance of different harmonics in vibration response is related to the

different faults in the machine, which is expected to be unique in terms of

amplitudes and phases at each harmonic component for every fault. While earlier

studies have shown the potentials of bispectrum analysis for machine operational

states distinction, the current work has however shown that bispectrum analysis

alone could be limited in its capability to differentiate between certain faulty and

healthy conditions (such as intermittent shaft rubs at certain machine speeds).

However, the trispectrum analysis was able to effectively and consistently capture

all the changes in the machine operational states. Hence, the present study shows

the possibilities of enhancing fault diagnosis and maintenance cost effectiveness,

through a combination of bispectrum and trispectrum analyses. However, more

experiments are planned in the future, so as to further establish the findings in the

present study.

Use of Composite HOS for Faults Diagnosis of Rotating Machines with Different Foundation Fle…

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7 Chapter 7 USE OF COMPOSITE HIGHER

ORDER SPECTRA FOR FAULTS DIAGNOSIS OF ROTATING MACHINES

WITH DIFFERENT FOUNDATION FLEXIBILITIES

----------------------------------------------------------------------------------------------


Paper 1 title: Use of composite higher order spectra for faults diagnosis of

rotating machines with different foundation flexibilities

Authors: A. Yunusa-Kaltungo, J.K. Sinha and A.D. Nembhard

Published in: Measurement 70 (2015) 47-61

Paper 2 title: Coherent composite HOS analysis of rotating machines with

different support flexibilities


Published in: Proceedings of 10th International Conference on Vibration

Engineering Technology of Machinery (VETOMAC X 2014), Manchester/United

Kingdom, September 9-11 2014

Series title: Mechanisms and Machine Science

Series volume: 23


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DOI: 10.1007/978-3-319-09918-7

Publisher: Springer International Publishing

Abstract

It is commonly observed in practise that rotating machines installed at different

plant locations often exhibit different dynamic behaviours, due to variations in the

flexibilities of their supports, which often affects fault diagnosis. In the current

study, a similar scenario has been experimentally simulated on a rotating rig with

different foundation flexibilities. Also, different faults were experimentally simulated

at different machine speeds so as to develop a reliable diagnosis technique that

will be suitable for different machine foundations. Recently developed data fusion

methods for constructing composite spectrum (CS) and composite bispectrum

(CB) for a machine are again applied for faults diagnosis here. In addition, the

present study introduces the composite trispectrum (CT) as a new feature for

diagnosis. The paper hereby presents the computational concepts of all composite

spectra, rig details, data analysis and diagnosis.

Keywords

Rotating machines, flexible foundation, faults diagnosis, data fusion, composite

bispectrum, composite trispectrum

7.1 Introduction

The dynamic behaviours of ‘as installed’ rotating machines at different locations in

a plant and/or in different plants is observed to be significantly different in many

cases [193], [194]. This is mainly due to different flexibility of the foundation at

different places. For instance, two large turbo-generator sets may exhibit different

dynamic behaviours as a result of the differences in their foundations [195]. To

further enhance clarity, an abstract representation of machine and foundation is


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shown in Figure 7.1, where machines can be identical (for example pump and

motor units, identical turbines, etc.), but may have different foundations. It is also

important to state that the term rotating machine in Figure 7.1 solely refers to the

rotor-bearing-motor assembly (including other integral components such as

couplings, discs, etc.), that may have been acquired with such a machine from the

original equipment manufacturer (OEM), which can be identical for several rotating

machines. The foundation on the other hand refers to all machine installations

onsite, including structural connections (e.g. piping, bracing, etc.) that can have an

influence on the ‘as installed’ machine dynamics.

Since rotating machines are sometimes subjected to a wide range of operating

conditions, which often leads to the emergence of faults that require early and

effective diagnosis that will avoid compromising personnel and equipment safety

[187]. These factors make the fault diagnosis process complex. This however

explains why good prior understanding of the modal parameters and dynamic

behaviours of rotating machines play a very vital role in vibration-based fault

diagnosis. Perhaps, model-based diagnosis approach [32], [65], [66], [196]–[199]

may prove useful for such cases where foundation dynamics is generally taken

into account. However, some of the popular techniques highlighted in research

articles [19], [200]–[202] summarising various fault diagnostics and prognostics

techniques may or may not be directly applicable for reliable diagnosis when

dealing with rotating machines installed on different foundations.

Within the past few decades [159], appreciable research contributions on the

application of higher order signal processing techniques for fault diagnosis in

rotating machines have been made. This was based on the premise that fault

diagnosis using conventional and well-known linear spectral analysis techniques

such as power spectrum density (PSD) alone is unable to establish the

interactions that exist between frequency components of measured vibration

signals when faults occur, due to its lack of phase information [159]. However,

these studies have been dominated by the application of the normalised forms of

the higher order spectra (HOS), known as the higher order coherences (HOCs)

[99]–[105], [203]. Sinha [106] experimentally and theoretically explored the


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application of HOS (bispectrum and trispectrum) for fault detection on a very

simple rotating rig, supported by just two bearings. However, a significant number

of industrial rotating machines often posses a more complicated configuration, with

more bearings. This therefore triggered further investigation of HOS for the

diagnosis of more rotor-related faults on a relatively rigid rotating machine

supported by four bearings, at a single [189] and multiple machine speeds

respectively [204]. In the latter study [204] it was shown that bispectrum could not

adequately distinguish between certain machine conditions (intermittent rotor rubs

and healthy conditions) at certain machine speeds, which led to the combination of

bispectrum and trispectrum features for a more robust diagnosis. Despite the

significant contributions on HOS and HOCs, as well as considering the fact that a

significant number of industrial rotating machines are mounted on flexible

foundations, none of the earlier studies has been geared towards diagnosing faults

associated with ‘as installed’ identical rotating machines with different foundations.

Hence, the current paper aims to simulate an industrial scenario through an

experimental rig with different flexible foundations. The impacts of the different

foundations on the rig have also been confirmed by conducting modal tests to

obtain the modal parameters [205]. Different faults have been experimentally

simulated and the observed dynamic behaviours for each fault have been found to

be different for the different foundations, and hence the diagnosis features. In this

study, the recently developed data fusion technique for computing composite

spectra (CS) [128] and composite bispectra (CB) [127] for a machine is used on

the present experimental data. Furthermore, the concept of composite trispectrum

(CT) for a machine has also been introduced as an additional diagnosis feature, so

as to significantly enhance the ability of the proposed technique to discriminate

between different machine conditions, owing to the fact that the CT component

expresses the relationships between more frequency components in the measured

vibration data. The current research effort is based on the development of a

reliable and simplified fault diagnosis approach that will be applicable to rotating

machines with different foundation flexibilities. The developed method can utilise

the diagnosis features for identical rotating machines with different foundations.


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Several sets of measured vibration data from the rig with different foundations

under various experimentally simulated faults at different machine speeds are

analysed using all composite higher order spectra. Hence, the paper provides

details of signal processing, rigs, experiments and faults diagnosis using

composite higher order spectra.

Figure 7.1 Abstract representation of rotating machine and foundation

7.2 Composite Spectra Computations

Earlier studies by Elbhbah et al. [128] and Sinha et al. [127] have respectively

provided the concepts of CS and CB. The computational concepts are again

presented here.

Let’s consider a rotating machine with “b” number of bearings from which vibration

data were measured, and the measured vibration data were divided into “ns”

number of equal segments, then the CS for the entire rotating machine was

computed as [127], [128];

(7.1)


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where = (k-1) ; k = 1, 2, ...., N/2; = fs/N; N denotes the number of data

points for Fourier transformation (FT); and

respectively denote

the coherent composite FT and its complex conjugate for the rth segment of the

measured vibration data collected from “b” number of bearings at frequency, .

Hence, is thus computed as [128];

(7.2)

In Equation (7.2),

, ....,

respectively denote the coherence [127]

derived between vibration signals recorded at bearing locations 1-2, 2-3, …, (b-1)-

b. Also,

,

, ....,

respectively denote the

coherent cross-power spectrum between bearings 1-2, 2-3, …, (b-1)-b, which was

computed as [128];

(7.3)

The CS [128] computed as per Equation (7.1) contains no phase information,

which therefore limits its analysis to just amplitudes at individual harmonic

components. In practise however, rotating machines often produce several

harmonic components due to faults, and the inter-relations that exist between

these harmonic components are expected to be different for different faults.

Hence, the introduction of CB and CT, which express the relation between few

harmonic components, may become desirable.


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The CB [127] is thus computed as;

(7.4)

Based on the premise that the CT provides information about the inter-relation that

exists between more frequency components, an additional CT component is also

proposed on a similar concept as the CB [127], so as to further understand the

usefulness of data fusion in rotating machine fault diagnosis and resultant machine

vibration behaviour. It is also important to note that the bispectrum [103], [157],

[158], [190], [191] is a representation of the combination of 2 frequencies (each

containing amplitude and phase information), and with a third frequency

which is equivalent to the sum of the initial 2 for a signal. Similarly, the

trispectrum [98], [106], [159], [189], [204] is a representation of the combination of

3 frequencies (each containing amplitude and phase information), , and

with a fourth frequency which is equivalent to the sum of the initial 3

for a signal. Hence, the CT for “b” number of signals can be computed as;

(5)

7.3 Experimental Rig with Different Foundations

The experimental rig with different foundations (FS1 and FS2), i.e. slightly different

support flexibilities have been simulated for this study. In FS1 (Figures 7.2-7.3),

two mild steel shafts (1000mm and 500mm lengths respectively) of 20mm

diameters are rigidly coupled together, while the 1000mm shaft is coupled to an

electric motor through the aid of a flexible coupling. Two mild steel balance discs


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of dimensions 125mm (outside diameter) x 20mm (internal diameter) x 15mm

(thickness) were mounted on the 1000mm shaft at distances of 300mm from the

flexible coupling and 190mm from bearing 2 respectively. A third similarly

dimensioned balance disc was also mounted on the 500mm shaft at an equal

distance of 210mm from both bearings 3 and 4. The entire assembly is however

supported by 4 flange-mounted anti-friction ball bearings.


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Figure 7.2 Photograph of the experimental rig


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Figure 7.3 Schematic of the experimental rig

FS2 is similarly configured as FS1 in terms of machine size, capacity, components

and the respective location of each component. However, both experimental rigs

slightly differ in their support flexibilities (Figure 7.4), owing to the fact that the


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bearings on each rig were mounted with threaded bars of different thicknesses.

FS1 bearings were mounted on 10mm threaded bars, while FS2 bearings were

mounted on 6mm threaded bars (Figure 7.4). In Figure 7.3, components (a)-(m)

respectively represent accelerometer (a), rigid coupling (b), shaft (c), balance disc

(d), bearing flange (e), threaded bar (f), flange mounted anti-friction ball bearing

(g), flexible coupling (h), tachometer (i), electric motor (j), electric motor base

mount (k), lathe bed (l) and neoprene rubber pad (m). Figure 7.3 also shows the

schematic representation of vibration data collection in which the data from

accelerometers are collected into the PC, through the conditioner unit and the

analogue-to-digital device. It is also important to note that the accelerometers were

stud mounted at 45° from both vertical and horizontal directions, so that the

accelerometers can measure the vibration from both directions. Accelerometer

installation is typically shown in Figure 7.4.

Figure 7.4 Different rig supports (a) FS1 (b) FS2


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7.3.1 Modal tests and data analysis

In order to better understand the dynamic characteristics of both experimental rigs,

experimental impulse response [21] method of modal analysis was conducted

using instrumented hammer and accelerometer. Hence, Table 7.1 shows the first

few natural frequencies (by appearance) identified for FS1 and FS2 respectively.


Experimental Set-up Natural Frequencies (Hz)

1st

2nd

3rd

4th

FS1 50.66 56.76 59.2 127.6

FS2 47 55.54 57.98 127

7.4 Experiments

A total of six cases were experimentally simulated on both rigs and at 3 machines

speeds (1200RPM, 1800RPM and 2400RPM). Since it is generally difficult to

achieve a perfect alignment on the rigs, a healthy case associated with some

residual misalignment (HRM) has been considered as a healthy (HRM) reference

case. In addition to the HRM case, 5 other cases, namely; bent shaft (BS), shaft

crack (SC), loose bearing (LB), shaft misalignment (SM) and shaft rub (SR) were

also simulated on both rigs and at all speeds. The BS case was simulated by

creating a 3.4mm centre line run-out on the 1000mm shaft, using a fly press. The

SC case (Figure 7.5(a)) was studied by creating a 4mm (depth) x 0.25mm (width)

breathing crack on the 1000mm shaft at a distance of 160mm from bearing 1,

using the wire electric discharge machining (EDM) process. The LB case (Figure

7.5(b)) was however simulated by loosening some of the threaded bar nuts on

bearing 3. A slight misalignment (using a 0.4mm mild steel shim) in the vertical

direction beneath bearing 1 support block was used to simulate the SM case

(Figure 7.5(c)). Finally, the SR case (Figure 7.5(d)) was simulated by placing 2

Perspex blades (at top and bottom dead centres respectively) at a distance of


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275mm from bearing 1. For the purpose of simplification and clarity, each of the

experimentally simulated cases, the fault locations on the rig and abbreviated

names have been summarised in Table 7.2. Several sets of vibration

measurements were then collected through the aid of 4 (i.e. 1 per bearing)

diagonal stud mounted accelerometers (Figure 7.4) for further signal processing. It

is important to note that for each case (e.g. HRM, FS1, 1800RPM), 20 sets of

measured vibration data were collected.

Figure 7.5 Experimentally simulated cases (a) SC (b) LB (c) SM (d) SR


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Table 7.2 Summary of cases, locations and abbreviations

S/No. Case(s) Fault Location Abbreviation

1 Healthy with some residual misalignment

Possible residual misalignment at couplings HRM

2 Bent shaft Centre of 1000mm shaft BS

3 Shaft crack 160mm from bearing 1 on the 1000mm shaft SC

4 Loose bearing Bearing 3 threaded bar nuts LB

5 Shaft misalignment Bearing 1 support block in vertical direction SM

6 Shaft rub 275mm from bearing 1 on the 1000mm shaft SR

7.5 Data Analysis

A computational code has been developed in MatLab for computing CS, CB and

CT as per Equations (7.1)-(7.5). The 20 sets of measured vibration data for each

of the simulated cases at each machine speed have been analysed using; 95%

overlap, frequency resolution ( ) = 0.6104 Hz, sampling frequency (fs) = 10000

Hz, number of data points (N) = 16384 and 148 number of averages. Figures 7.6,

7.7 and 7.10 show typical CS, CB and CT plots of the measured vibration data for

HRM and LB cases for the rig with FS1 and FS2 at 1200RPM.

7.6 CS Analysis and Observations

In Figure 7.6, the composite spectra (CS) for HRM and LB cases (Table 7.2) for

the rig with FS1 and FS2 at 1200RPM have been used to illustrate the ability of

CS to differentiate between various rotating machine conditions. On both FS1 and

FS2 foundations, the HRM case (Figures 7.6(a)-(b)) were characterised by

prominent 1x components and negligible 3x components (which is due to the

residual misalignment in the case). On the contrary, the LB cases (Figures 7.6(c)-

(d)) for the rig with both foundations (FS1 and FS2) were characterised by 1x

components of significantly larger amplitudes than in the HRM case, plus the

appearance of several higher harmonic components (3x, 4x, 5x, etc.) of notable


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amplitudes. This observation was however consistent for all the cases simulated

on the rig with both foundations and at all speeds.

Figure 7.6 Typical composite spectra at 1200RPM (a) HRM for FS1 (b) HRM for

FS2 (c) LB for FS1 (d) LB for FS2

7.7 CB Analysis and Observations

The composite bispectra (CB) in Figure 7.7 clearly show distinct features for the

HRM and LB cases for both foundations (FS1 and FS2) at 1200RPM, and these

observations were also fairly consistent for all cases at all speeds. The CB plots in

Figure 7.7 are plotted in x, y and z axes, where x and y axes relate to the

frequencies and z represents the amplitude related to the frequency components

in the x and y axes. The amplitude peaks (Table 7.3) are denoted by B11, B12, B13,

etc. For instance, B11 CB component represents the relation between 1x (twice)

and 2x frequency components, while B12=B21 represents the relation between 1x,

2x and 3x frequency components, and so on. Figures 7.7(a)-(b) respectively

denote the HRM case for both foundations, which only contain relatively small B11


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and B12 = B21 CB components, which is again due to the residual misalignment

associated with this case.

Although the LB case for both foundations (Figures 7.7(c)-(d)) also contained B11

and B12 = B21 CB components, their magnitudes were significantly larger than

observed in the HRM case. In addition, the LB case also contained prominent

B13=B31, B33 and B23=B32 CB components peaks. It is important to note that each

of the CB components in Figure 7.7 contains amplitude and phase information.

Also, individual CB components amplitudes and phase have been investigated for

FS1 and FS2 at all measured speeds. Figures 7.8-7.9 show that even the

individual CB components such as B11 (amplitude and phase) provides a

possibility of distinction for all cases.

Figure 7.7 Typical coherent composite bispectra (CB) at 1200RPM (a) HRM for

FS1 (b) HRM for FS2 (c) LB for FS1 (d) LB for FS2


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Table 7.3 CB components for HRM and LB cases (FS1 and FS2) at 1200RPM

CB Components FS1 at 1200 RPM FS2 at 1200 RPM

HRM LB HRM LB

B11 3.78E-03 7.42E-03 1.21E-03 4.67E-03

B12=B21 8.36E-04 2.18E-03 4.29E-04 2.51E-03

B13=B31 - - 7.63E-03 - - 1.07E-02

B23=B32 - - 1.13E-03 - - 9.07E-02

B33 - - 6.44E-04 - - 4.84E-03

Although each case in the CB plots shown in Figure 7.7 appears different with

respect to the amplitudes of each component (Table 7.3), however, diagnosis may

not be straightforward based on visual inspection. Hence it is good to compare

either different CB components or both amplitude and phase for a particular

component for each case. Amplitude and phase for a number of CB components

are analyzed to understand their usefulness in fault diagnosis. Figures 7.8-7.9

show typical amplitude and phase plots for B11 and B12 for all the 20 sets of data

collected for each case (i.e. a total of 120 sets of data at each machine speed for

each foundation), at all machine speeds with both foundations. It is obvious from

the figures that each of the cases appears in different regions (separated from

each other). Hence, a combination of the amplitude and phase of a single CB

component also offers appreciable fault diagnosis potentials.


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(f) FS2 (2400RPM)


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7.8 CT Analysis and Observations

The composite trispectra (CT) in Figure 7.10 clearly display different features for

the HRM and LB cases for both foundations. Unlike the CB, each CT component

(containing amplitude and phase information) is a function of 3 frequencies

(plotted in x, y and z axes), usually represented by spheres [98]. The appearance

of each sphere at a particular location generally represents the relation between

the frequencies at that particular location, while the sizes of the spheres represent

the amplitudes related to the frequency components in the x, y and z axes. The CT

components are generally denoted by T111, T112=T121=T211, T113=T131=T311, etc.

T111 signifies the relation between 1x (thrice) and 3x frequency components; while

T112=T121=T211 signifies the relation between 1x (twice), 2x and 4x frequency

components; and so on. The HRM cases for both foundations (Figures 7.10(a)-(b))

only contain T111 CT component probably due to some residual misalignment. The

LB cases for both FS1 and FS2 (Figures 7.10(c)-(d)) were characterized by T111

(which was significantly larger than in the HRM cases) and T113=T131=T311 CT

components.


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Figure 7.10 Typical coherent composite trispectra (CT) at 1200RPM (a) HRM for

FS1 (b) HRM for FS2 (c) LB for FS1 (d) LB for FS2

Table 7.4 CT components for HRM and LB cases (FS1 and FS2) at 1200RPM

Case(s) FS1 at 1200 RPM FS2 at 1200 RPM

T111 T113=T131=T311 T111 T113=T131=T311

HRM 2.44E-03 - - 4.47E-04 - -

LB 1.29E-02 6.67E-03 8.09E-03 3.01E-03


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Although, the CT plots for both FS1 and FS2 appear similar in components;

however, the components differ in amplitudes as can be clearly seen from Table

7.4. Similarly, a combination of several CT components’ amplitudes and phase for

the 20 sets of data collected for each case (i.e. a total of 120 sets of data at each

machine speed for each foundation) at all machine speeds with both foundations

was also investigated for further fault diagnosis. It can be observed from Figures

7.11-7.12 that the combination of amplitudes and phase of CT components such

as T111 and T112 offered good distinction between the different cases for all

foundation flexibilities and at all machine speeds considered.


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(f) FS2 (2400RPM)


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7.9 Combined Diagnostic Features

Although individual CB and CT components such as B11 and T111 provided

appreciable separation between the different cases, however, the combinations of

several CB and CT components amplitudes and phase has also been investigated

for further enhancement of the fault diagnosis. Many combinations provided very

good separations at all measured speeds for the different foundations. Typically,

just a combination of B11 and T111 CB and CT components amplitudes shown in

Figure 7.13 was observed to provide the required result for all cases at all speeds,

which significantly reduces the computational load that may be associated with the

use of higher harmonic components.


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Figure 7.13 Typical combined magnitudes of B11 CB and T111 CT components

(a) FS1 (1200RPM) (b) FS2 (1200RPM) (c) FS1 (1800RPM) (d) FS2 (1800RPM)

(e) FS1 (2400RPM) (f) FS2 (2400RPM)


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7.9.1 Sensitivity analysis

The sensitivity of the proposed technique to various scenarios (Table 7.5) of signal

processing parameters was also examined, so as to further ascertain the

robustness of the technique. Hence, using the typical plots of combined CB (B11)

and CT (T111) components’ magnitudes for FS2 foundation at 1200 RPM shown in

Figure 7.14 for illustration, it was observed that variations in signal processing

parameters had insignificant effects on the earlier separation of the different faults

shown in Figure 7.13. It is also important to note that the measured vibration data

are generally contaminated by noise, which is often the case with most real life

vibration data recorded from rotating machines. Hence, the proposed method

seems to be robust and reliable, even with measurement noise and changing

signal processing parameters.

Table 7.5 Different scenarios of signal processing parameters

Signal Processing Parameters

Scenarios

1 2 3 4

Number of data points (N) 8192 8192 16384 16384

Frequency Resolution (df), Hz 1.2207 1.2207 0.6104 0.6104

Number of averages 220 220 11 11

Segments Overlap 98% 98% 85% 85%

Window None Hanning None Hanning

Sampling Frequency (fs), Hz 10000


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Figure 7.14 Typical combined magnitudes of B11 CB and T111 CT components at

1200RPM for FS2 foundation (a) scenario 1 (b) scenario 2 (c) scenario (d)

scenario 4

7.9.2 Practical application

The proposed method clearly indicates the separation of other faults from the

healthy condition. Hence, the emergence of any faulty condition in a typical

rotating machine will definitely trigger the classification of such a machine as one

with fault. Also, once the historical data describing the operations of typical rotating

machines are available for reference, then onward classification of the machines


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when faults emerge becomes possible. However, it is important to note that the

task of accurately differentiating a faulty machine from a healthy one in itself is

vital for fault diagnosis, especially considering the complexities often associated

with the fault diagnosis process of rotating machines with multiple bearings, for

instance, steam turbo generator sets. Hence, the proposed method of data fusion

for computing a single CB and CT from all bearings data simplifies the fault

diagnosis process.

7.10 Summary

The paper introduces the concept of CT for fault diagnosis in combination with the

earlier CB. It is experimentally observed that the combination of a single CB and

CT component provides a much better separation and diagnosis for each fault.

The proposed method is tested on a rig with 2 different flexible foundations (FS1

and FS2). Hence, the potentials of the method to diagnose different faults

associated with ‘as installed’ rotating machines with different foundation flexibilities

and operating at different speeds was clearly highlighted, which is a very vital

consideration for a significant number of plants. It is planned to apply the proposed

method to different experimental rigs with different foundations and possibly on

industrial rotating machines with different foundations, so as to further enhance the

confidence level of the proposed diagnosis method. Also, further analysis on the

sensitivity of the proposed technique to different faults severities are scheduled for

future studies.

An Improved Data Fusion Technique for Faults Diagnosis of Rotating Machines

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8 Chapter 8 AN IMPROVED DATA FUSION

TECHNIQUE FOR FAULTS DIAGNOSIS OF ROTATING MACHINES

----------------------------------------------------------------------------------------------


Paper title: An improved data fusion technique for faults diagnosis of rotating

machines

Authors: A. Yunusa-Kaltungo, J.K. Sinha and K. Elbhbah

Published in: Measurement 58 (2014) 27-32

Abstract

The composite spectrum (CS) data fusion technique has been shown to simplify

rotating machine fault diagnosis by earlier studies. Fault diagnosis with the earlier

CS relied solely on the amplitudes of several harmonics of the machine speed,

owing to the loss of phase information leading to its computation. The proposed

improved CS applies the concept of cross power spectrum density for computing a

poly-Coherent Composite Spectrum (pCCS) of a machine, which retains amplitude

and phase information at all measurement locations. The present study compares

the proposed pCCS method with the earlier CS method for faults diagnosis in

rotating machines, using experimental data from a rotating rig. Results and

observations show that the proposed pCCS offered a much better representation

of the machine dynamics when compared to the earlier CS method and hence

better fault diagnosis.


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Key words Vibration-based condition monitoring, rotating machine, fault

diagnosis, data fusion, composite spectrum, poly-Coherent Composite Spectrum

8.1 Introduction

Measured vibration data at individual bearing pedestals of a rotating machine have

been successfully analysed with several vibration-based condition monitoring

(VCM) techniques such as; spectrum analysis [55], higher order spectra analysis

[98], [106], [159], [189], [190], [204], [206], wavelet analysis [207]–[213], artificial

intelligence-based diagnosis [214]–[219], model-based identification [197], etc.

However, large and complex rotating machines with multi-shafts are often

associated with numerous bearings, which imply that several vibration data

measured from each bearing location, will have to be separately analysed during

fault diagnosis. Therefore, the development of a VCM technique that will

significantly simplify the fault diagnosis process in rotating machines is highly

desirable. Earlier studies by Elbhbah and Sinha [128] proposed the use of reduced

sensors (i.e. a single accelerometer per bearing pedestal) for vibration

measurements in rotating machines. The study [128] also proposed the use of a

single composite spectrum (CS) for the representation of the entire machine

dynamics, which offered some useful fault diagnosis features in rotating machines.

In the earlier CS technique however [128], the concept of cross power spectral

density (CSD) [146] was used for fusing the vibration data measured at all bearing

pedestals, which did not utilize phase information from the measured vibration

data at the different measurement locations.

The current study however proposes the use of a poly-Coherent Composite

Spectrum (pCCS) of a machine, which is also based on the concept of CSD, but

has been extended to involve a number of signals. Hence, amplitude and phase

information are retained for all measured vibration data, which is further explained

in Sections 8.2 and 8.3. The computational approaches and observations from

both techniques are hereby discussed in this paper. Furthermore, the present

study compares the proposed pCCS method with the earlier CS method for fault


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diagnosis in rotating machines, using experimental data from a rotating rig.

Results and observations indicate that the proposed pCCS offered a much better

representation of the machine’s dynamics when compared to the earlier CS

method and hence better fault diagnosis.

8.2 Earlier Composite Spectrum

Assuming that vibration measurements were collected from “b” number of bearing

locations of a rotating machine, and the measured data have been divided into a

number of equal segments (ns), then the CS for the entire machine was computed

as [128];

(8.1)

where and

respectively denote the coherent composite Fourier

Transformation (FT) and its complex conjugate for the rth segment of the

measured time domain vibration data from “b” bearing locations at frequency, .

was thus computed as [128];

(8.2)

where

and

respectively denote the coherence [156] between

bearings1-2, 2-3, …, (b-1)-b (where b = 1, 2, ..., b). Also,

.....

respectively denote the coherent cross-power spectrum

between bearings 1-2, 2-3, …, (b-1)-b, which was computed as [128];


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(8.3)

It can be clearly seen from Equations (8.2)-(8.3) that all the phase information at

the intermediate measurement locations will be lost due to the CSD approach

adopted for the data fusion. For example, the multiplication of the FT of the rth

segment of the measured time domain vibration data at frequency at bearing 2

(i.e. ) in the second term (

) of Equation (8.2) by its complex

conjugate (i.e.

) in the first term (

) of the same equation

automatically produces a real number, thereby signifying a loss of phase

information between the two measurement locations (i.e. bearings 2 and 3) and so

on. Similarly, Equation (8.1) shows that the final CS has lost all of its phase

information, due to the multiplication of the coherent composite FT by its complex

conjugate.

8.3 Proposed poly-Coherent Composite Spectrum (pCCS)

It has been clearly shown in Section 8.2 that all phase information at the

intermediate vibration measurement locations is lost during the computation of CS

using the earlier method. Therefore, an improved CS that provides a better

representation of the entire machine dynamics is required. Hence, the improved

CS is defined as;

=

(8.4)


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where, ,

, ,

, ...., and

respectively denote

the FT of the rth segment at frequency of the time domain vibration data at

bearings 1, 2, 3, 4, ...., (b-1) and b. Similarly, ,

, , ....,

respectively

denote the coherence between bearings 1-2, 2-3, 3-4, …, (b-1)-b, while

is the poly-Coherent Composite Spectrum (pCCS) at frequency, . The

computation of the proposed pCCS shown in Equation (8.4) is also based on the

concept of CSD. However, it has been extended to a number of signals instead of

just 2 signals used in CSD, so that amplitude and phase information of signals are

retained for better representation of the machine dynamics.

8.4 Experiments and Observations

As conducted in the earlier study [128], 4 different conditions (healthy,

misalignment, crack and rub) were simulated at 2 separate speeds (2040RPM and

3000RPM) on an experimental rig (Figure 8.1). The healthy case contained some

residual unbalance and possibly little misalignment. A 2mm misalignment (in both

vertical and horizontal directions) was introduced near bearing 1 for the

misalignment case. In the crack case, a crack of 0.25mm (width) by 4mm (depth),

with a 0.22mm steel shim insert was used to simulate a shaft with a breathing

crack. A Perspex sheet with a 21mm hole was used to simulate shaft rub near

bearing 1. The rig consists of 2 rigidly coupled shafts (1000m and 500m lengths)

of similar diameter (20mm). The 1000mm shaft is flexibly connected to an electric

motor, while the entire shaft assembly is supported by 4 anti-friction ball bearings

as shown in Figure 8.1 [128].


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Figure 8.1 Photograph of experimental rig [128]

Vibration data were collected from all bearing pedestals for all the experimentally

simulated cases (healthy, misalignment, crack and rub) at both speeds (2040RPM

and 3000RPM). Hence, the averaged spectra for all cases have been computed

using a sampling frequency (fs ) = 5000Hz, number of data points (N) = 8192,

frequency resolution ( ) = 0.6104Hz, 80% overlap with Hanning window and 146

number of averages. Figures 8.2-8.3 respectively show typical pCCS and phase

plots for 2 cases (healthy and crack), at 2040RPM and 3000RPM. The healthy

cases at both machine speeds (Figures 8.2(a) & 8.3(a)) show no visible peaks,

while the crack cases (Figures 8.2(c) & 8.3(c)) are characterized by conspicuous

peaks at several harmonics (e.g. 1x, 2x, 4x, etc.). Similarly, the phase plots

(Figures 8.2(b), 8.2(d), 8.3(b) & 8.3(d)) are different for each of the experimentally

simulated cases at both machine speeds.


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crack


crack


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8.4.1 Diagnosis features

The pCCS amplitudes and phases of several vibration measurements for each of

the experimentally simulated cases at both machine speeds have been computed.

Figures 8.4-8.5 show a combination of the amplitude and phase of the first 2

harmonics (i.e. 1x and 2x) of the machine speed, where it can been seen that

there is a clear separation between each of the experimentally simulated cases, at

both 2040RPM and 3000RPM speeds.


2040RPM


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3000RPM

8.5 Diagnosis with Earlier Composite Spectrum Method

Although the earlier method of CS [128] provided some meaningful diagnosis

features, however, its lack of phase information leads to a strong reliance on the

amplitudes at the different harmonics during fault diagnosis. Hence, fault diagnosis

with the earlier data fusion method of the CS could entail the use of several

harmonic amplitudes as can be seen from Figures 8.6-8.7.


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Figure 8.6 Typical normalised CS amplitudes for all four cases at 2040RPM


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Figure 8.7 Typical normalised CS amplitudes for all four cases at 3000RPM

8.6 Summary

The poly-Coherent Composite Spectrum (pCCS) has now been defined, which is

an improved version of the earlier composite spectrum (CS) data fusion. In the

present pCCS, a combined information of amplitude and phase from all

measurement locations is achieved, which is expected to provide a more accurate

representation of the entire machine dynamics. The proposed method has also

been applied for fault diagnosis on an experimental rig, where it was observed that

the amplitude and phase information of pCCS at the operating speed or any

harmonic can provide a much better diagnosis, when compared to the earlier

method (which relied on several harmonics of the machine speed for fault


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diagnosis). Future fault diagnosis using pCCS is planned on different rotating

machines with more faults.

A Novel Faults Diagnosis Technique for Enhancing Maintenance and Reliability of Rotating…

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9 Chapter 9 A NOVEL FAULTS DIAGNOSIS

TECHNIQUE FOR ENHANCING MAINTENANCE AND RELIABILITY OF

ROTATING MACHINES ----------------------------------------------------------------------------------------------


Paper title: A novel faults diagnosis technique for enhancing maintenance

and reliability of rotating machines

Authors: A. Yunusa-Kaltungo, J.K. Sinha and A.D. Nembhard

Submitted to: Structural Health Monitoring Journal (in press)

Abstract

Equipment standardisation as a cost-effective means of rationalising maintenance

spares has significantly increased the existence of several identical (similar

components and configurations) ‘as installed’ machines in most industrial sites.

However, the dynamic behaviours of such identical machines usually differ due to

variations in their foundation flexibilities, which is perhaps why separate analysis is

often required for each machine during fault diagnosis. In practise, the fault

diagnosis process is even further complicated by the fact that analysis is often

conducted at individual measurement locations for the different speeds, since a

significant number of rotating machines operate at various speeds. Hence, through

the experimental simulation of a similar practical scenario of 2 identically

configured ‘as installed’ rotating machines with different foundation flexibilities, the


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present study proposes a simplified vibration-based fault diagnosis (FD) technique

that may be valuable for fault detection irrespective of foundation flexibilities or

operating speeds. On both experimental rigs with different foundation flexibilities,

several common rotor-related faults were independently simulated. Data

combination method was then used for computing composite higher order spectra

(composite bispectrum and composite trispectrum), after which principal

component analysis is used for fault separation and diagnosis of the grouped data.

Hence, the current paper highlights the usefulness of the proposed FD approach

for enhancing the reliability of identical ‘as installed’ rotating machines, irrespective

of the rotating speeds and foundation flexibilities.

Key words Reliability, condition based maintenance, data fusion, composite

spectra, principal component analysis, multiple speeds, multiple foundations

9.1 Introduction

Faults always occur in rotating machines due to the vast and severe conditions

under which they operate across several industries. The lack of early detection of

such faults often leads to depleted machine reliability, which could have

catastrophic consequences on the safety and profitability of any organisation

[187]. A maintenance activity (which has evolved over time) has always been

applied for the detection and elimination of these faults. Maintenance can be

described as the combination as well as synchronisation of all technical,

administrative and managerial tasks directed towards ensuring that a machine

adequately performs the functions for which it was acquired [220]–[222]. Initially,

maintenance interventions (mainly repair and replace) are only conducted to

restore already failed machines back to operating condition. This type of

maintenance strategy ultimately required huge investments in spares,

incorporation of high levels of redundancies in plant designs, and a significantly

large maintenance team. The capital intensiveness and high equipment failure

levels associated with breakdown maintenance (BM) triggered the shift towards a

periodic or planned preventive maintenance (PPM) philosophy that entailed the

repair of machines over a predefined time period, irrespective of machines’


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conditions. Although the planned preventive maintenance approach significantly

reduced plant interruptions, however, the cost associated with this practise was

also high. Based on this premise, maintenance experts have continuously sorted

after a more effective maintenance philosophy that will only be triggered by the

presence of symptomatic changes in a machine’s operating conditions due to

faults, such as condition-based maintenance (CBM).

In an adequately implemented and managed CBM system, the decision to repair

or replace a machine is often guided by the results obtained from the analysis of

measured machine operations data (e.g. vibration, temperature, sound, etc.). The

reviews by Jardine et al. [19], Lee et al. [90], Heng et al. [223] and Lee et al. [200]

offered extensive details and trends of commonly applied CBM diagnostic and

prognostic techniques for machines. In these reviews [19], [90], [200], [223], it was

also highlighted that vibration-based fault diagnosis (VFD) techniques [224]–[228]

are amongst the most popular, owing to the fact that different components in a

machine assembly often exhibit peculiar vibration characteristics due to faults.

Machinery vibration signals have been processed using time [25], [229], frequency

or time-frequency [29], [230] domain techniques. The frequency domain signal

analysis, based on Fourier transformation (FT) is one of the most conventionally

applied VFD signal processing techniques in practise, since it provides the

opportunity to easily identify frequency components of interest [19]. Some of the

frequency domain vibration signal processing techniques used for fault diagnosis

in rotating machines include power spectrum [55], higher order spectra [98], [106],

[159], [189], [190], [204], holospectrum [231], cepstrum [232], composite spectrum

[128], composite bispectrum [127], etc.

Despite the maturity of spectrum-based techniques, the quest for more profound

understanding of the dynamic characteristics of vibrating systems has led to the

application of model-based approaches [233] for rotating machines’ fault

diagnosis. These model-based approaches [233] usually involve the development

and application of explicit mathematical models for simulating the behaviour of an

‘as installed’ machine. The emergence of very powerful computers has

significantly reduced the complexity and time required to perform model-based


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fault diagnosis. Such technological advancements have also enhanced the ease

with which researchers can reliably analyse and predict future behaviours of

vibrating systems. Kerschen et al. [234] provided extensive reviews on model-

based analysis of vibrating systems. Other researchers have also applied model-

based approaches for analysing rotating machine faults such as unbalance and

misalignment [32], rotor crack [66], [198], [235], etc. Although model-based

analysis can offer more descriptive results if a precise model is built, however, it is

sometimes near impossible to achieve the required precision when dealing with

very complex structures [19].

In order to reduce dependence on human interference and experience, some

researchers have adopted artificial intelligence (AI) techniques such as artificial

neural networks (ANN) [77]–[84], support vector machine (SVM) [86], [87], [236]–

[238], and fuzzy logic [239]. ANN is basically a computational model that contains

simple processing elements that are linked via a complex layer structure, thereby

imitating the formation of the human brain [19]. A comprehensive review on more

than a decade-long applicability of artificial neural networks in the industry was

compiled by Meireless et al. [77]. Other studies have also shown the capabilities of

ANN in classifying rotating machine conditions [78], detection of rotor loading

conditions [79], gear faults identification [80]–[82], fan blade faults detection [83]

as well as diagnosis of rolling element bearing faults [84]. Although AI-based

techniques possess the potentials to automate VFD processes, however, studies

[19], [223] have also highlighted the difficulties associated with providing physical

interpretations of the trained model as well as the complexity of the training

process. SVM is another popularly used AI-based technique that has proven

capable of providing accurate decision results in some cases, mainly due to its

augmented decision boundary and real time analysis capability [86], [87]. Although

SVM has been used to detect faults related to rotors [236], bearings [237], gears

[80], pump valves [238], etc., however, studies [90] have also shown that there is

still a lack of standard technique for selecting its key process (i.e. Kernel process)

function. Other efforts aimed at further simplifying rotating machine fault diagnosis

using pattern recognition tools such as principal components analysis (PCA) has

also been explored by some researchers [93]. The application of PCA for fault


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diagnosis is particularly strengthened by its ability to compress large multi-

dimensional input data sets into lower dimensional but representative data sets

[90]. Nembhard et al. [240] recently applied PCA for detecting and classifying

rotor-related faults such as misalignment, crack and shaft rub. In this study [240],

the combination of measured vibration and temperature features was explored.

PCA has also been used for identifying faults related to rolling element bearings

[95], [241] and gears [91], [94], [96].

As valuable and significant as the contributions from these earlier studies are, they

have been predominantly used to diagnose faults associated with rotating

machines on single foundations and at single machine speeds. In practice

however, 2 or more identical (similar components and configurations) rotating

machines installed at different plant locations may exhibit different dynamic

characteristics, due to variations in their foundation flexibilities. These differences

in dynamic characteristics often require that separate analysis is conducted for

each machine at the different operating speeds, which may complicate the fault

diagnosis process. Hence, the development of a unified VFD technique that will be

capable of detecting and differentiating rotating machine faults, irrespective of

foundation flexibility and machine speed is highly desirable. In the present study,

the earlier [127], [128] and improved [242] composite higher order spectra (i.e.

composite bispectrum and composite trispectrum) data combination (in the

frequency domain) techniques have been respectively used to compute fault

diagnosis features for 2 identical flexibly supported rotating machines, operating

under different faults and speeds. Through the application of a PCA-based fault

diagnosis algorithm, a unified fault diagnosis technique capable of fault detection

and classification, irrespective of machine speed or foundation is proposed. The

proposed technique is expected to reduce the complexity and subjectivity

associated with fault diagnosis at individual machine speed and foundation, which

is often characterised by the appearance of several features. The study also

compares the results of the diagnosis features computed using the earlier and

improved composite higher order spectra approaches. Hence, detailed

descriptions of the composite spectra computations, experimental rigs, vibration


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experiments with different faults, signal processing and the results of the proposed

unified PCA-based fault diagnosis technique are presented here.

9.2 Composite Spectra Computations

The computational approaches for the composite spectra based on both the earlier

[127], [128] and the proposed improved [242] methods are also described here.

9.2.1 Earlier method

The earlier proposed method for computing the composite spectrum (CS) of a

rotating machine from which vibration measurements were collected from “b”

number of bearing locations is [128];

(9.1)

where and

are respectively the coherent composite Fourier

Transformation (FT) and its complex conjugate for the rth segment of the

measured vibration data from “b” bearing locations at frequency, . ns represents

the number of equal segments used for FT computation. Hence, is thus

computed as [128];

(9.2)


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In Equation (9.2),

, ...,


between bearings1-2, 2-3, …, (b-1)-b (where b = 1, 2, ..., b). Also,

.....

respectively denote the coherent cross-power

spectrum between bearings 1-2, 2-3, …, (b-1)-b, which was computed as [128];

(9.3)

where q = 1, 2, ..., (b-1).

It is evident from Equations (9.2)-(9.3) that in the earlier method of CS

computation, all the phase information at the intermediate measurement locations

will be lost. This is due to the cross power spectrum density (CSD) approach

adopted for the earlier data combination process.

The composite bispectrum (CB) is computed as [127], [243], [244];

(9.4)

Through the application of a similar computational concept as the CB [127], the

composite trispectrum (CT) [243], [244] can be computed as;

(9.5)

Where each bispectrum [157], [158], [191] component represents the combination

of 2 frequencies (with each possessing amplitude and phase information), and


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with a third frequency which equals the sum of the first 2 for a signal.

Also, each trispectrum [98], [106], [159], [189], [190], [204] component represents

the combination of 3 frequencies (with each possessing amplitude and phase

information), , and with a fourth frequency that equals the sum

of the first 3 for a signal. It is also vital to note that if the frequencies , and

are equivalent to the th, th and th harmonics of the vibration response at the

rotor RPM (1x), then the CB and CT components defined in Equations (9.4)-(9.5)

can also be referred to as and .

9.2.2 Improved method

The improved CS is also based on CSD, but has been extended to several signals

(instead of just 2 signals applied in the earlier method), called the poly-Coherent

Composite Spectrum (pCCS). Unlike the earlier method of data combination

described in Section 9.2.1, the improved computational approach (i.e. pCCS)

retains both amplitude and phase information. It is therefore anticipated that this

feature (amplitude and phase) retention capability of pCCS will lead to better

representation of the entire machine dynamics. Hence, the improved CS is defined

as [242];

(9.6)

where, ,

, ,

, ...., and

respectively denote

the FT of the rth segment at frequency of the vibration responses at bearings 1,

2, 3, 4, ...., (b-1) and b. Similarly, ,

, , ....,

respectively denote the

coherence [156] between bearings 1-2, 2-3, 3-4, …, (b-1)-b. is the poly-

Coherent Composite Spectrum (pCCS) at frequency, .


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The CB and CT have also been introduced based on the improved CS [242], and

are respectively defined as;

(9.7)

(9.8)

In Equations (9.7)-(9.8), is the poly Coherent Composite Fourier

Transformation (FT) for the rth segment of the measured vibration data from “b”

bearing locations at frequency, , which was computed as [242];

(9.9)

9.3 Proposed Fault Diagnosis Method

The large number of data usually generated from the computation of CB and CT

sometimes makes visual diagnosis very difficult and subjective. The analysis

becomes even more complicated when dealing with multiple identical (similar

components and configurations) rotating machines with slightly different dynamic

characteristics (due to variations in their foundation flexibilities) and operating at

different speeds. This perhaps explains why some researchers have explored

other avenues for simplifying rotating machines FD, through the application of

pattern classification tools such as PCA. As previously highlighted in Section 9.1,

PCA [240] is a well-known statistical analysis technique, capable of significantly

reducing the dimensionality associated with originally measured data sets through

the definition of new variables, often referred to as the principal components


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(PCs). The first few of the computed PCs usually offer the maximum

representation of the variability that exists in the originally measured data [91].

Similarly, the current study proposes a simplified and unified PCA-based FD

technique, that will be capable of identifying changes in the operating conditions of

several identical ‘as installed’ rotating machines, irrespective of the variations in

their foundation flexibilities and/or operating speeds. Hence, the proposed PCA-

based FD technique could eliminate the need for conducting individual analysis

(which is often the case in practise) for several identical ‘as installed’ rotating

machines with different foundation flexibilities and speeds. Figure 9.1 provides a

flowchart that illustrates the different steps of the proposed FD technique. The

concept of PCA is briefly discussed in Section 9.3.1, while Section 9.3.2 provides

details of the computational approach for the proposed FD technique.


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Figure 9.1 Proposed faults diagnosis process flow chart

9.3.1 Concept of PCA

PCA is a multivariate statistical analysis technique that is capable of reducing

large interrelated data sets to smaller numbers of variables, without necessarily

compromising the variance that exists in the original data set. The fundamental

concept of PCA revolves around the projection of data sets onto a subspace of

lower dimensionality [91]. PCA explains the variance that exists within an original

data matrix that is characterised by n1 observations (e.g. number of vibration

measurements recorded from a typical rotating machine as part of continuous

condition monitoring activities) and n2 variables (e.g. CB and CT fault diagnosis

components) in terms of an entirely new set of variables, the PCs.


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The concept of PCA has existed for decades, with the initial proposal of the

technique dating back to 1933 by Hotelling [245], where it was used for analysing

problems related to the statistical dependency between variables in multivariate

statistical data obtained from examination scores [91], [245]. From then onwards,

the relevance and applications of PCA has significantly grown across various

disciplines including process monitoring, statistical analysis and faults diagnosis

[91], [245]–[248]. Kresta et al. [249] provides a comprehensive introduction as well

as a review of the applications of PCA in process systems engineering, while the

studies by Morison [250] and Jackson [245] respectively offered information on the

complete treatment of the PCA algorithm. Hence, for the purpose of this study, it

suffices to just highlight that PCA was performed and the original data set is

eventually expressed as a linear combination of orthogonal vectors along the

directions of the PCs.

Let’s consider that n1 number of independent samples (also referred to as

observations) of n2 random variables (also referred to as features) which can be

represented by an n1 x n2 matrix, F. The computation of the PCs of F reduces to

the solution of an eigenvalue-eigenvector problem [91], [92],

(9.10)

In Equation (9.10), is the covariance matrix of F. A is the orthogonal matrix

whose mth column is equivalent to the mth eigenvector of corresponding to the

mth largest eigenvalue of . is a diagonal matrix, whose mth diagonal element is

the mth largest eigenvalue of . In general, as many as n2 PCs can be computed.

However, it is expected that the vast majority of variation in F will be accounted for

by t PCs, where .

In the current study, PCA is applied for examining the relationship between

several experimentally simulated rotating machine conditions. The features used

are comprised of computed vibration-based condition monitoring indicators for


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rotating machines under different states of health. Diagnosis through the

application of many condition monitoring (CM) features can be complex and

tedious. Hence, for implementing a simplified diagnosis approach, reduction in

data dimensionality while retaining correlation among them becomes useful.

Therefore PCA is used to achieve this objective.

9.3.2 Computational approach of the proposed FD technique

Assuming that vibration data were collected from a rotating machine at various

speeds, then the PCA feature matrix F related to Equation (9.10) can be

mathematically expressed as;

(9.11)

F is a feature matrix including feature matrices at different speeds, ,

, ..., ,

where , ,....., are the different rotor speeds in RPM.

Let’s now consider a typical rotating machine, from which sets of vibration data

were separately collected under a number of different operating conditions, say “r”

and at a particular rotor speed, . Then the feature matrix can be similarly

defined as;

(9.12)


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where ,

,....., are matrices for each of the experimentally simulated

cases, , , ..., at rotor speed .

If “p” number of vibration data sets were collected from a rotating machine under a

particular machine operating condition (case), , and at a particular rotor speed

. Then, the feature matrix is computed as;

(9.13)

where X1, X2, X3, ...., Xq are individual features for “p” number of observations

under a particular machine operating condition (case) and at a rotor speed .

To further enhance clarity of the PCA feature matrix shown in Equation (9.13),

consider that , , and respectively represent CB and CT

components that have been computed using Equations (9.7)-(9.8) for a particular

machine operating condition ( ), for “p” number of measured data sets at rotor

speed . Hence, the PCA feature matrix can be similarly written as;

(9.14)

Now, let’s further assume that fault diagnosis is to be conducted on a particular

rotating machine with “B” number of flexible support (FS) at rotor speeds , then

Equation (9.12) can be modified thus;


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(9.15)

Hence, if the vibration data were then collected at several machine speeds ( , ,

..., ) for the same rotating machine with “B” flexible foundation (FS), then;

(9.16)

Finally, if several identical rotating machines with different flexible foundations ,

, ..., exists, and vibration measurements were conducted on each of them at

rotor speeds , ,....., . Then the multiple speeds and multiple foundations

PCA feature matrix can be written as;

(9.17)

Once matrix F in Equation (9.11) is constructed, then PCA is carried out as

described in Section 9.3.1.

9.4 Experimental Example

It is often noticed in practice that the dynamic characteristics of “as installed”

identical rotating machines in different locations may slightly vary, owing to

differences in the flexibilities of their foundations. Hence, the current study


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attempts to experimentally simulate a similar example, through the aid of 2 rotating

rigs with identical components and configurations (Figure 9.2), but differ in

foundations (FS1 and FS2). FS1 bearings are mounted with 10mm thick bright

mild steel threaded bars, while FS2 bearings are mounted using 6mm thick bright

mild steel threaded bars (Figure 9.3). A full description of the experimental rig and

faults simulation is provided in Section 9.4.1.

Figure 9.2 Experimental rig


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Figure 9.3 Different rig supports (a) FS1 (b) FS2

9.4.1 Rig and faults simulation

Since both experimental rigs (FS1 and FS2) [244] are identical, only FS1 is

illustrated here (Figure 9.2). In FS1, two 20mm diameter mild steel shafts of

lengths 1000mm and 500mm respectively are rigidly coupled together, while the

1000mm shaft is flexibly coupled to an electric motor. 3 mild steel balance discs of

dimensions 125mm (external diameter) x 20mm (internal diameter) x 15mm

(thickness) were evenly mounted across the entire length of the rig. 2 balance

discs were mounted on the long shaft at 300mm from the flexible coupling and

190mm from bearing 2 respectively. The third balance disc was then mounted on

the short shaft at an equal distance of 210mm from both bearings 3 and 4. The

complete assembly (rotor, balance discs, couplings, etc.) is supported by 4 flange-

mounted anti-friction ball bearings.

A total of 6 cases were experimentally simulated on both FS1 and FS2, at 3

machine speeds (1200RPM, 1800RPM and 2400RPM). The reference case is a


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healthy case that is associated with some residual misalignment (HRM), as it was

very difficult to obtain a perfectly aligned rig. In addition to the HRM case, bent

shaft (BS), shaft crack (SC), loose bearing (LB), shaft misalignment (SM) and

shaft rub (SR) cases were also simulated on both rigs at all the considered

machine speeds. The BS case was simulated by using a fly press to create an

axial run-out of 3.4mm at the centre of the 1000mm shaft. To study the SC case

(Figure 9.4(a)), a crack of 4mm (depth) and 0.25mm (width) was created on the

1000mm shaft using the wire electric discharge machining (EDM) process. As it

was very unlikely for the created crack to breath, a 0.23mm mild steel shim was

inserted in the crack to cause breathing. The LB case (Figure 9.4(b)) was

simulated by loosening the threaded bar fixation nuts on bearing 3. A slight

misalignment of 0.4mm in the vertical direction near bearing 1 was used to

simulate the SM case (Figure 9.4(c)). For the SR case (Figure 9.4(d)), 2 Perspex

blades (i.e. 1 at the top and the other at the bottom of the 1000mm shaft

respectively) were mounted at a distance of 275mm from bearing 1.

On both FS1 and FS2 rigs, vibration data were measured under 36 scenarios (i.e.

18 scenarios of 6 cases at 3 speeds each for FS1 and FS2 respectively), where

each scenario corresponds to specific rig/case/speed combinations (e.g.

FS1/HRM/1200RPM). In order to enhance understanding, details of all the

considered scenarios are provided in Table 9.2. Furthermore, 20 sets of measured

vibration data (a total of 120 sets of measured vibration data per experimental rig)

were collected through the aid of 4 diagonally mounted PCB accelerometers (1 at

each bearing location) for further processing through a computational code

developed in MATLAB.


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Figure 9.4 Experimentally simulated cases (a) SC (b) LB (c) SM (d) SR

9.4.2 Experimental modal analysis

Experimental modal analysis is a widely accepted technique for design

improvements and useful life enhancement of ‘as installed’ rotating machines and

structures [145], [146]. The knowledge of the modal properties of a machine

significantly enhances the understanding of the dynamic behaviour of that

machine. Similarly, the first few natural frequencies (by appearance) of both FS1

and FS2 rigs have been experimentally identified using the impact-response

method. During the experiment, both FS1 and FS2 were excited at 2 locations with

an instrumented hammer (PCB) in both vertical and horizontal directions. The first

excitation location was at 209mm from both balance discs 1 and 2 (i.e. exactly

midpoint of the 1000mm shaft), while the second excitation location was at 44mm


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from bearing 3 and disc 3 (Figure 9.5). During the excitation of FS1 and FS2, the

dynamic responses were measured with a PCB accelerometer installed on bearing

2. Table 9.1 provides a summary of the identified natural frequencies, while

Figures 9.6-9.7 show the frequency response function (FRF) amplitude and phase

for FS1 and FS2 in both vertical and horizontal directions.

Figure 9.5 Experimental setup for modal test


Experimental Set-up Natural Frequencies (Hz)

1st

2nd

3rd

4th

FS1 50.66 56.76 59.2 127.6

FS2 47 55.54 57.98 127


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(a) vertical direction (b) horizontal direction


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9.4.3 Signal processing

The CB and CT (computed as per Equations (9.7)-(9.8)) of the 20 sets of

measured vibration data for each of the 36 scenarios (Table 9.2) have been post-

processed with a MATLAB code using 95% overlap, frequency resolution (df) =

0.6104Hz, sampling frequency (fs) = 10000Hz, number of FT data points (N) =

16384 and 148 number of averages. Typical CB and CT plots of measured

vibration data for 4 scenarios (i.e. scenarios 1, 10, 19 and 28 in Table 9.2) are

shown in Figures 9.8-9.9. It can be observed that a distinction exists between the

reference (scenarios 1 and 19) and fault (scenarios 10 and 28) scenarios, and this

observation was fairly consistent for all other scenarios. In the CB plots (Figure

9.8), the reference scenarios (Figures 9.8(a)-(b)) only contained relatively small

B11 and B12=B21 CB components, due to inherent residual misalignments. On the

contrary, the fault scenarios (Figures 9.8(c)-(d)) were associated with several CB

components (e.g. B11, B12=B21, B13=B31, B33, etc.) of significantly higher amplitudes

than observed in the reference scenarios.

Table 9.2 Experimental scenarios for FS1 and FS2

Rig Speed

Scenarios

FS1 FS2

HRM BS SC LB SM SR HRM BS SC LB SM SR

20 Hz 1 4 7 10 13 16 19 22 25 28 31 34

30 Hz 2 5 8 11 14 17 20 23 26 29 32 35

40 Hz 3 6 9 12 15 18 21 24 27 30 33 36

It is vital to note that the amplitude of each CB peak in Figure 9.8 is a function of 2

frequency components, usually plotted in the xyz orthogonal axes, with axes x and

y respectively representing frequencies, while the amplitude of the CB component

is plotted on the z axis. For instance, the appearance of a B11 CB peak indicates

that the pCCS frequency components and (plotted on both x and y

orthogonal axes) shown in Equation (9.7) are both equal to the machine speed

(also known as 1x). Therefore, the B11 CB peak is a representation of the relation


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between (1x), (1x) and (2x). Similarly, each B12=B21 CB peak indicates

that the pCCS frequency components and shown in Equation (9.7) are

respectively equal to 1x machine speed and its second harmonic (2x) or vice

versa, while is equivalent to their sum (3x). Hence, each B12=B21 CB peak

shows the relation between 1x, 2x and 3x frequency components. Similarly, the

CT plots (Figure 9.9) for the reference (scenarios 1 and 19) and fault (scenarios 10

and 28) scenarios are different. The reference scenarios contain only T111 CT

component (due to some residual misalignment associated with the scenario),

while the fault scenarios contained T111, T113=T131=T311, etc. This observation was

also consistent for all the 36 experimentally simulated scenarios.

Figure 9.8 Typical CB plots for FS1 and FS2 at 1200RPM (a) HRM (FS1), (b)

HRM (FS2), (c) LB (FS1), (d) LB (FS2)

Unlike the CB, each CT component is a function of 3 pCCS frequency

components, therefore requiring a 4-dimensional plot. In this study, the spherical

plot method earlier suggested by Collis et al. [98] is adopted. In this method, the


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exists between the pCCS frequency components at that location. Furthermore, the

size of each sphere is a representation of the amplitude of that particular CT

component. Hence, T111 CT component in Figures 9.9(a)-(b) is a representation of

the relation between (1x), (1x), (1x) and (3x). Also, each

T113=T131=T311 CT component in Figures 9.9(c)-(d) indicates that the pCCS

frequency components , and shown in Equation (9.8) are respectively equal

to 1x, 1x and 3x (third harmonic of the machine speed) or vice versa, while

is equivalent to their sum (5x).

Figure 9.9 Typical CT plots for FS1 and FS2 at 1200RPM (a) HRM (FS1), (b) HRM

(FS2), (c) LB (FS1), (d) LB (FS2)


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9.5 Faults Diagnosis

It is clear from Figures 9.8-9.9 that the CB and CT plots provided distinct features

for each of the experimentally simulated scenarios. However, faults diagnosis

based on visual observation of the CB and CT plots alone can be extremely

difficult and sometimes subjective. This is due to the appearance of several

components in the plots. Hence, the core of the current study is focussed on

eliminating or significantly reducing such subjectivities, through the application of

the proposed unified fault diagnosis technique described in Section 9.3.

9.5.1 Data preparation

The proposed fault diagnosis process was simplified by preparing the feature

matrix in stages. Firstly, a matrix was constructed for a particular flexible

foundation at a single machine speed, for instance . The 20 sets of

vibration measurements for each scenario in Table 9.2 were classified as

observations (i.e. rows). Each observation was then used to compute 2 CB (B11

and B12) and 2 CT (T111 and T112) components amplitudes as per Equations (9.7)-

(9.8). The computed CB and CT components then represented the features of the

matrix (columns). Hence, a matrix containing 4 features (B11, B12, T111 and T112)

and 120 observations (20 observations per scenario) was obtained, as detailed by

Equation (9.18). The second stage is concerned with fault diagnosis under multiple

machine speeds for a single setup (e.g. ), where the

feature matrix is characterised by 12 features (i.e. 2 CB and 2 CT features at each

machine speed) and 120 observations. The third and final stage of the data

preparation involves the harmonisation of all the features obtained from the

second stage for each machine setup. At this stage, a feature matrix containing

120 observations and 24 features (i.e. 12 features each for FS1 and FS2) is

constructed. During each of the stages, the constructed feature matrix is

eventually fed into a PCA algorithm that computes the PCs. Since maximum

representation can be obtained from the first few PCs, a graphical plot of the first


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and second PCs (Figure 9.10) is then used for classification of the different

scenarios.

(9.18)


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9.5.2 Results and discussions

Results of the proposed fault diagnosis method for multiple speeds on FS1 and

FS2 rigs are respectively shown in Figures 9.10(a)-(b). With the exception of the

slight overlap between the scenarios associated with HRM and SM machine

conditions (cases), there was a good separation between all the experimentally

simulated cases. However, this overlap was adjudged to be due to the low severity

of induced misalignment (i.e. 0.4mm) as well as the presence of residual

misalignment in the HRM case. However, the results of the multiple speeds and

multiple foundations diagnosis shown in Figure 9.10(c) provided an even better

separation for all scenarios, although a relatively small amount of overlap is still

evident between the scenarios associated with HRM and SM cases. Hence, the

proposed fault diagnosis technique may be useful for significantly reducing the

rigour associated with conducting separate analysis for each machine, and at

different speeds.


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Figure 9.10 Proposed faults diagnosis (a) multiple speeds – FS1 setup (b) multiple speeds – FS2 foundation (c) multiple speeds

and multiple foundations


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Akilu Yunusa-Kaltungo 249 249


9.5.3 Comparison with Earlier Method

Figure 9.11 shows the results of similar analyses conducted using CB and CT

components amplitudes that were computed based on the earlier method

(Equations (9.4)-(9.5)). Although appreciable separation was also achieved using

the earlier method, however, significantly better results were obtained with the

improved method.


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Figure 9.11 Faults diagnosis with earlier CB and CT method (a) multiple speeds – FS1 setup (b) multiple speeds – FS2 setup (c)

multiple speeds and multiple foundations


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9.6 Practical application of the proposed FD technique

In practice, VFD of rotating machines often involves the analysis of measured

vibration data that represent the state(s) of a particular machine or group of

machines. These measured vibration data are often acquired after pre-defined

machine operation periods (also referred to as condition monitoring interval), so as

to determine whether a change in machine health has occurred. In order to

examine the ability of the proposed technique to diagnose machine faults on a

continuous basis, 3 additional fault diagnosis scenarios (FDS) were considered.

The first 2 fault diagnosis scenarios (FDS1 and FDS2) consider that additional

vibration measurements were collected from FS1 and FS2 rotating machines with

cracked shafts at 1800RPM machine speed (i.e. scenarios 8 and 26 in Table 9.2).

The newly acquired vibration data were then used to compute CB (B11 and B12)

and CT (T111 and T112) components as per Equations (9.7)-(9.8) for FDS1 and

FDS2. The computed CB and CT components were then added to the already

existing PCA feature matrices described in Equation (9.13). A combination of the

above additional scenarios (FDS1 and FDS2) is also considered for the combined

approach (multiple speeds and multiple foundations). The predictions are once

again consistent as shown in Figure 9.12.


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Figure 9.12 Continuous faults diagnosis, (a) Multiple speeds - FS1 setup (b) Multiple speeds - FS2 foundation (c) Multiple speeds

and multiple foundations


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9.7 Summary

The chapter proposes a novel vibration-based fault diagnosis (VFD) technique for

detecting and distinguishing common rotor-related faults in rotating machines,

which is independent of the machine foundation flexibility and operating speed.

The proposed technique aims to significantly minimise the rigour and complexities

associated with the common practise of performing separate vibration-based

analysis for identically configured ‘as installed’ rotating machines on industrial sites

(owing to variations in the flexibilities of foundations and operating speeds). In this

study, several sets of vibration data were collected from 2 identical rotating rigs

with different foundation flexibilities and at various machine speeds, through the

aid of only 4 vibration sensors (1 per bearing location). For each of the

experimental rigs, the measured vibration data under each machine operating

condition and speed were then used to independently compute composite

bispectrum (CB) and composite trispectrum (CT) components. The computed CB

and CT components were then used as the features of a principal component

analysis (PCA) based algorithm, so as to develop the multiple-speeds and

multiple-foundations faults diagnosis technique. The current research presents an

integrated VFD method for rotating machines, and further emphasizes the

relevance of data combination approaches in the minimisation of the level of

subjectivity and human judgements associated with popular techniques such as

ordinary amplitude spectra. Hence, the proposed VFD technique presents the

potential to significantly enhance maintenance and overall reliability of industrial

rotating machines through these summarised advantages:

Usefulness: with the proposed VFD technique, diagnosis results from 1

rotating machine are directly applicable to another identically configured

rotating machine despite variations in foundation flexibilities and

operating speeds. This approach aims to eliminate the common practise

of conducting separate analysis for individual rotating machine at

different speeds. Hence, historical data and diagnosis results from 1

rotating machine could be used for fault detection on an identical ‘as

installed’ rotating machine.


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Computational time: in condition monitoring, the computational duration

of any chosen technique is very vital, as it may significantly influence the

ability to prevent the occurrence of catastrophic machine failures. The

proposed VFD technique applies CB and CT components as features in

a PCA-based algorithm, which implies that a single composite spectrum

is adequate for describing the entire machine dynamics. This significantly

reduces the computational rigour and time, when compared to the

common practise of computing different spectra at individual vibration

measurement locations.

Interpretation: interpretation of the results obtained from the proposed

VFD technique is quite simple and does not require the services of an

expert, since the classification of different machine conditions are very

visible.

Practical application: for any new machine fault diagnosis, the computed

features from measured vibration data must be fed into the PCA

database. Upon the introduction of the new data, analysis will then be

performed to observe the classification of new machine state (healthy or

faulty). This diagnosis approach is already demonstrated in the present

study.

Furthermore, a comparison of the diagnosis results from CB and CT components

computed using the earlier CS method and the improved poly coherent composite

spectra (pCCS) was also conducted, and it was clearly observed that CB and CT

components derived from the pCCS method offered better discrimination between

the different experimentally simulated scenarios. In general, the proposed VFD

technique is versatile, non-intrusive and computationally efficient, which therefore

enhances its potential for usage in industries. However, in order to further confirm

the robustness and reliability of the technique, the investigation of more faults with

different severities are planned for the near future.

Sensitivity Analysis of Higher Order Coherent Spectra in Machine Faults Diagnosis

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10 Chapter 10 SENSITIVITY ANALYSIS OF

HIGHER ORDER COHERENT SPECTRA IN MACHINE FAULTS DIAGNOSIS

----------------------------------------------------------------------------------------------


Paper title: Sensitivity analysis of higher order coherent spectra in machine

faults diagnosis


Submitted to: Structural Health Monitoring Journal

Abstract

In an earlier study, the poly coherent composite higher order spectra (i.e. poly

coherent composite bispectrum and trispectrum) frequency domain data fusion

technique was proposed to detect different rotor related faults. All earlier vibration-

based faults detection (VFD) involving the application of poly coherent composite

bispectrum (pCCB) and trispectrum (pCCT) have been solely based on the notion

that the measured vibration data from all measurement locations on a rotating

machine are always available and intact. However, practical industrial scenarios

sometimes deviate from this notion, owing to faults and/or damages associated

with vibration sensors or their accessories (e.g. connecting cables). Sensitivity

analysis of the method to various scenarios of measured vibration data availability

(i.e. complete data from all measurement locations and missing/erroneous data


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from certain measurement locations) is also examined through experimental and

industrial cases, so as to bring out the robustness of the method.

Keywords

Rotating machines, induced draft fan, data fusion, poly coherent composite

bispectrum, poly coherent composite trispectrum, sensitivity analysis

10.1 Introduction

In recent years, several research efforts have been invested into the development

of simplified but yet robust vibration-based fault detection (VFD) techniques. One

of such VFD approaches is the recently developed poly coherent composite higher

order spectra frequency domain data fusion method [251], whereby the dynamic

behaviour of a typical rotating machine can be described using a single poly

coherent composite bispectrum (pCCB) and/or trispectrum (pCCT), irrespective of

the number of vibration data measurement locations on the monitored machine.

Based on the results obtained from initially conducted experimental investigations,

pCCB and pCCT showed that it was possible to significantly reduce the rigour

often associated with the computation and analysis of separate higher order

spectra (mainly bispectrum and trispectrum) for vibration data collected from

individual measurement locations, which can be significant for large industrial

rotating machines supported by several bearings (e.g. large industrial turbines or

multi-shaft drive assemblies).

Besides the noteworthy ability of using a single pCCB or pCCT to effectively

distinguish different rotating machine conditions, the recent study conducted by

Yunusa-Kaltungo et al. [251] further highlighted the possibilities of developing a

hybrid data fusion (i.e. data fusion at both sensor and feature levels) method that

can detect and classify different operating conditions in identically configured

rotating machines irrespective of their foundation flexibilities and speeds, which

may foster the sharing of measured vibration data between identical ‘as installed’

rotating machines. While it is commendable that enormous research and practical


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efforts are continuously aimed at improving VFD of rotating machines, it is also

well-known that the successful operation of any VFD system is a direct function of

the proper integration of its 3 fundamental stages, namely; data collection, signal

processing and fault diagnosis. The data collection stage of a typical VFD system

provides the vibration data from which features (e.g. kurtosis, peak-to-peak

amplitude, 1x, 2x, 3x, etc.) are extracted during signal processing, before

eventually matching the various identified features with corresponding machine

conditions during fault diagnosis. The adverse conditions under which most

industrial rotating machines operate as well as the fragility of VFD instruments

sometimes restrict the availability of measured vibration data, which often affects

the effectiveness of the entire VFD system.

Until now however, studies on VFD of rotating machines have been significantly

based on the premise that vibration data from all sensors are intact and available,

irrespective of whether the measured vibration data will be separately analysed for

individual measurement locations with known techniques such as spectrum

analysis [55], [57], [252]–[254], wavelet analysis [208], [209], [255]–[260], higher

order statistical analysis [98], [106], [158], [204], [206], [261], etc., or fused

together for all measurement locations to generate a single but representative poly

coherent composite spectrum [251]. In practise however, the amount of data

available for faults diagnosis of some rotating machines may be limited at certain

instances, owing to faults/damages associated with the sensors or connecting

cables during auxiliary activities in the plant such as machine cleaning or general

maintenance, especially when dealing with critical industrial rotating machines that

are installed in highly remote and/or restricted plant locations (e.g. river gallery

pumps in water generation plants or drilling machines in mines). Hence, such

damages usually lead to the loss of vibration data from certain measurement

locations on these critical rotating machines.

However, owing to the operational demands as well as extremely low tolerances

for equipment downtime in most industrial plants, the VFD analyst may be

sometimes confined to conducting faults diagnosis based on limited measured

vibration data, as it may not be always feasible to recollect the vibration data


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representing the behaviours of such critical industrial rotating machines. Based on

this premise, it will be very useful to develop a VFD technique that possesses the

capability to identify incipient changes in the operating conditions of a rotating

machine due to the emergence of different faults, despite the unavailability of

measured vibration data from certain measurement locations on the machine.

In the current study, the concepts of pCCB and pCCT are applied to 2 examples –

laboratory scale experimental rig and critical cement manufacturing process fan.

Although vibration measurements were obtained from all the 4 bearing locations in

both examples, however, practical instances sometimes arise when some of the

measurements acquired from some sensors may be faulty. However, timely

machine fault diagnosis is often a requirement for all plants, irrespective of the

completeness of the measured data. In the current study however, measured

vibration data under different scenarios of data availability are analysed with the

method so as to understand its sensitivity and robustness in faults classification for

both examples, which generally leads to faults diagnosis. Hence, the current paper

explains;

The computational concepts of pCCB and pCCT.

The experimental and industrial examples considered.

The laboratory experiments conducted as well as on-site measurements in

the cement plant.

The data analysis, especially the sensitivity analysis for faults classification

based on both experimental and industrial examples.

10.2 poly-Coherent Composite Spectra

Equations (10.1)-(10.3) respectively provide the mathematical computations of the

poly Coherent Composite Spectra for an entire rotating machine with “b” number

of vibration measurement locations, which has already been extensively described

in an earlier study by Yunusa-Kaltungo et al. [242], [251].


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(10.1)

(10.2)

(10.3)

In Equation (10.1), ,

, ,

, ...., and

respectively denote the Fourier transformation (FT) of the rth segment at

frequency of the vibration responses at bearings 1, 2, 3, 4, ...., (b-1) and b.

Similarly, ,

, , ....,


between bearings 1-2, 2-3, 3-4, …, (b-1)-b. is the poly-Coherent

Composite Spectrum (pCCS) at frequency, .

The shown in Equations (10.2)-(10.3) represents the poly coherent

composite FT for a particular segment ‘r’ of the measured vibration data from ‘b’

bearing locations at a particular frequency, , which was also computed as [242];

(10.4)

In order to enhance proper understanding of the current study, a brief re-iteration

of the steps involved in the computations of pCCB and pCCT VFD method are

again illustrated by the flowchart shown in Figure 10.1.


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Figure 10.1 Schematic representation of pCCS computational process


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10.3 Example 1: Laboratory Scale Experimental Rig

The laboratory scale experimental rig consists of two rigidly coupled shafts (S1

and S2) and three identical balance discs (D1, D2 and D3). D1 and D2 are

mounted on S1, while D3 is mounted on S2. S1 was then flexibly coupled (FC) to

an electric motor (EM), and the complete rig assembly is supported by 4 bearings

(B1-B4). Figure 10.2 shows a photograph of the experimental rig, while Table 10.1

provides the specifications of its main components. On this experimental rig [251],

the 5 experimentally simulated cases (C1-C5) detailed in Table 10.2 were studied

at a machine speed of 1800 RPM (30 Hz). Under each case, 20 sets of vibration

measurements were collected through the aid of 4 accelerometers (A1-A4).


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Figure 10.2 Laboratory scale experimental rig


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Table 10.1 Experimental rig components and their specifications

S/No. Rig Component Parameter Specification

1 S1

Material type Mild steel

Length (mm) 1000

Diameter (mm) 20

2 S2


Length (mm) 500

Diameter (mm) 20

3 D1-D3


External diameter (mm) 125

Internal diameter (mm) 20

4 B1-B4 Type Flange mounted ball bearings

Bore (mm) 20

5 EM

Type 3-phase induction motor

Power (kW) 0.75

Speed (RPM) 3000

6 FC

Type Flexible

Length (mm) 55



7 RC

Type Rigid

Length (mm) 65




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Table 10.2 Experimentally simulated cases

S/No. Case Abbreviation Severity and Location

1 Healthy with residual misalignment

C1 Possible residual misalignment at couplings (FC & RC)

2 Bent shaft C2 3.4mm axial run-out was created at the centre of S1

3 Shaft misalignment C3 0.4mm mild steel shim beneath the left-hand-side (LHS) of B1foundation

4 Shaft rub C4 Rub using a brass sleeve of 21mm on S1, near D2

5 Cracked shaft C5 4mm (depth) x 0.25mm (width) crack on S1, at 160mm from B1

10.3.1 Earlier Faults Detection Method [251]

The earlier study conducted by Yunusa-Kaltungo et al. [251] has already provided

significant details about the capabilities of the method to detect several rotor

related faults at different machine speeds. However, it is anticipated that a brief

recap of the earlier observations will significantly buttress the understanding and

relevance of the current study. Using C1 and C2 cases as illustration, the signal

processing parameters in Table 10.3 were used to compute pCCB and pCCT for a

set of measured vibration data. It is clearly visible from Figure 10.3 that the pCCB

features for both cases are significantly different. For instance, the C1 case

(Figure 10.3(a)) contained a slightly prominent B11 pCCB peak and very negligible

B12=B21 and B22 peaks while the C2 (Figure 10.3(b)) case contained several pCCB

components (B11, B12=B21, B22, B13=B31 and B23=B32) with significantly larger

amplitudes. Similarly, the computed pCCT features (Figure 10.4) for C1 and C2

cases are very different. The C1 case (Figure 10.4(a)) contains only T111 pCCT

component. As observed with pCCB (Figure 10.3), the C2 case (Figure 10.4(b))

contained several pCCT components (T112=T121=T211, T122=T212=T221, T222,

T113=T131=T311 and T333).


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Figure 10.3 Typical pCCB plots (a) C1 (b) C2

Figure 10.4 Typical pCCT plots (a) C1 (b) C2

Figures 10.3-10.4 clearly indicate the capabilities of pCCB and pCCT plots to

provide distinctions between different machine conditions. However, the earlier

study by Yunusa-Kaltungo et al. [251] proposed the combination of the amplitudes

of pCCB and pCCT, owing to the rigour and subjectivities associated with limiting

faults detection to visual inspection of numerous and sometimes highly diverse

pCCB and pCCT components that emerge as a result of continuous measurement

and analysis of vibration data during routine condition monitoring (CM) activities.

Hence, Figure 10.5 again shows the benefits of such a combined approach based

using 20 sets of measured vibration data for each experimentally simulated case.


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It is visible from Figure 10.5 that data related to each case are clustered together

and separated from the clusters of other cases.


components for all cases under ideal laboratory scenario (LS0) of complete data

10.4 Sensitivity Analysis Based on Experimental Data

In Figure 10.5, the faults classification based on the combination of the computed

B11 pCCB and T111 pCCT components for all 100 sets (i.e. 20 sets of data per

case) of measured vibration data for C1-C5 cases solely assumes an ideal

laboratory scenario (LS0), where the data from all 4 measurement locations are

available and intact. However, this scenario may not always be practicable in “real

life” industrial machines, owing to the possibilities of damages to sensors or their

accessories at certain instances. Therefore, in order to ascertain the robustness

and sensitivity of this technique under changing conditions of measured vibration

data availability, the 4 additional scenarios (LS1-LS4) described in Table 10.4 have

been considered. In all 4 scenarios, vibration data from only 3 measurement

locations were used to compute the pCCB and pCCT components that produced


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the faults classifications shown in Figure 10.6. Based on the current experimental

rig and cases simulated, the omission of measured vibration data from certain

measurement locations did not have any significant effect on the faults

classification patterns. In fact, Figure 10.6 shows that data corresponding to each

of the 5 experimentally simulated cases consistently remained clustered together

and separated from the clusters of other cases under all scenarios of data

availability. For all scenarios, the C2 cluster consistently occupied the highest

position owing to its possession of significantly greater B11 pCCB and T111 pCCT

components amplitudes. Although C1, C4 and C5 cases for all scenarios

possessed relatively similar T111 pCCT components amplitudes, however, the

variations in their B11 pCCB components amplitudes still enabled appreciable

separations between them which further highlight the benefits of faults detection

based on the combination of pCCB and pCCT components. Similarly, the cluster

comprising of data related to the C3 case was positioned at the bottom left corner

of the plots for all scenarios due to its lower B11 pCCB and T111 pCCT components

amplitudes.

Table 10.3 Signal processing parameters for experimental data

Table 10.4 Description of laboratory scenarios

Scenario(s) Abbreviation Accelerometers Missing Data Location

1 LS1 123 Bearing 4

2 LS2 234 Bearing 1

3 LS3 124 Bearing 3

4 LS4 134 Bearing 2

S/No. Signal Processing Parameter(s)

1 Sampling frequency 10000 Hz

2 Number of data points (N) 8192

3 Frequency resolution (df) 1.2207 Hz

4 Number of averages 88

5 Segment overlap 95%


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components for all cases under different laboratory scenarios of missing data (a)

LS1 (b) LS2 (c) LS3 (d) LS4

In order to perform a more detailed examination of the consistency of the

clustering for individual cases under all the scenarios described in Table 10.4, B11

pCCB and T111 pCCT components amplitudes were then separately combined for

each experimentally simulated case for all scenarios (for example C1 for LS0-LS5

and so on). The results of the various combinations are shown in Figure 10.7,

where it was again observed that the clusters for individual cases for all the

considered scenarios appear around the same region. For instance, Figure

10.7(a)-(e) respectively show the clustering together of C1-C5 cases for scenarios

LS0-LS4. It is also interesting to note that the patterns and relative locations of the

clusters for the four scenarios representing missing data (i.e. LS1-LS4) cannot be

distinguished from that of the ideal scenario (LS0). Therefore, based on the current


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experimental data and scenarios considered, the combined pCCB and pCCT VFD

technique is robust enough to classify rotating machine faults despite the

unavailability of data from certain measurement locations.


components for individual cases for all scenarios (a) C1 (b) C2 (c) C3 (d) C4 (e)

C5


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10.5 Example 2: Industrial Fan

A fundamental rationale behind the development of any new rotating machines

VFD technique (or any other technique) is usually to enhance and/or simplify the

currently existing faults detection process in “real life” industrial machines. Based

on this premise, the current study similarly explored the capability and robustness

of pCCB and pCCT [251] in detecting changes in the operating conditions of a

very critical cement process rotary kiln induced draft fan (RKIDF), due to the

emergence of fault(s).

10.5.1 The Case Study (RKIDF)

The case study is a rotary kiln ID fan (RKIDF) for a cement process plant (Figure

10.8), which its main technical specifications are shown in Table 10.5. The RKIDF

is a twin inlet backward curved centrifugal fan that provides air draft across the

cement rotary kiln. The entire fan assembly is supported by 4 bearings, namely;

motor drive end (MDE), motor non-drive end (MNDE), fan drive end (FDE) and fan

non-drive end (FNDE) bearings as shown in Figure 10.8. The motor and fan shafts

are coupled by a very flexible spring-type coupling.

Table 10.5 Technical specifications of RKIDF [262]

S/No. Parameter Specification

1 Fan type 105 type – 12 double inlet

2 Fan serial number VW5/39231-02-01 & 02-02

3 Fan shaft length (m) 4.65

4 Impeller diameter (m) 2.697

5 Fan weight (kg) 5350

6 Number of impeller blades 11

7 Motor speed (RPM) 993

8 Power (kW) 656

9 Voltage (V)/current (A)/frequency (Hz) 690/674/50

10 Fan bearings Cooper self-aligning

11 Motor bearings Cooper self-aligning


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Figure 10.8 Schematic representation of RKIDF assembly [262]

The RKIDF performs 2 very critical functions in the cement manufacturing process.

Firstly, the draft of air needed for fuel combustion during clinker (the main

component of cement) production is provided by the RKIDF. Secondly, the hot kiln

exit gases used for drying and pre-heating fresh kiln feed are also conveyed by the

RKIDF. In order to increase the rotary kiln throughput, there has to be a

corresponding increase in the amount of fuel to be burnt, which is directly

dependent on the RKIDF speed (i.e. higher kiln feed requires more fuel; more fuel

requires more combustion air and more combustion air requires higher RKIDF

speed). Since the performance of cement process plants is most often judged by

the outputs from their rotary kilns (since this stage produces the clinker that is

eventually grinded into cement in the cement mills), hence, the optimum

performance and reliability of the RKIDF is very vital. The criticality of RKIDF to

this cement burning line is further compounded owing to its lack of built-in

redundancy (i.e. no standby available), as illustrated by Figure 10.9.


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Figure 10.9 Schematic representation of the burning line

10.5.2 On-site vibration measurements

During the on-site measurements, a total of 40 sets of vibration data were

collected from the RKIDF assembly at 600RPM (10Hz) fan speed. The first 20 sets

of vibration data were collected during the RKIDF fault condition, while the other

20 sets of vibration data were collected immediately after the conduction of a

corrective maintenance intervention to align the machine and remove heavy

limestone deposits from the impeller blades (Figure 10.10).

Figure 10.10 Limestone deposits on RKIDF impeller and blades [263]


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During these measurements (Figure 10.11), 4 diagonally mounted PCB

accelerometers (i.e. 1 per bearing) were used for collecting vibration data at a

sampling frequency (fs) of 10000Hz onto a PC, through the aid of a 16 channels

16-bit analogue-to-digital converter (ADC), as shown in Figure 10.11. In Figure

10.11, PC, ADC and A1-A4 respectively denote personal computer, analogue-to-

digital converter and accelerometers 1-4.

Figure 10.11 Photograph of on-site vibration measurement setup [263]

10.5.3 Detection and Classification of RKIDF Operating Conditions using

Earlier Method

As performed with the experimentally acquired data, (Section 10.3.1), the earlier

method was also used to analyse one set of vibration data measured on the


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RKIDF under faulty and healthy conditions. As anticipated, Figures 10.12-10.13

respectively display distinct pCCB and pCCT faults diagnosis for both cases. The

faulty case (Figure 10.12(a)) contains a very dominant B11 pCCB peak along with

smaller B12=B21 and B13=B31 pCCB peaks, while the healthy case (Figure 10.12(b))

only contained very negligible B11 and B12=B21 pCCB components. Similarly, the

pCCT components shown in Figure 10.13 are different for both RKIDF cases. The

healthy case (Figure 10.13(b)) contained a single T111 pCCT component, while the

faulty case (Figure 10.13(a)) contained several pCCT components (T112=T121=T211

and T113=T131=T311) in addition to a large T111 pCCT component.

Figure 10.12 Typical pCCB plots (a) faulty (b) healthy

Figure 10.13 Typical pCCT plots (a) faulty (b) healthy


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Similarly, the combined amplitude approach described earlier [251] was also

explored for the classification of 40 sets (i.e. 20 sets for faulty and 20 sets for

healthy cases) of vibration data acquired from the RKIDF, where it is again visible

from Figure 10.14 that all data sets related to the faulty case are grouped in the

same cluster and separated from the cluster comprising of data sets measured

during the healthy RKIDF condition.


components for all cases under ideal industrial scenario (IS0) of complete data

10.6 Sensitivity Analysis Based on Industrial Data

The faults classification shown in Figure 10.14 is based on an ideal industrial

scenario (IS0) of total data availability from all measurement locations, which might

not always be the case. However, 4 additional industrial scenarios (IS1-IS4) similar

to those described in Table 10.4 have been considered with the industrial data,

and the result of the faults classification for each scenario is shown in Figures

10.15(a)-(d). As observed in the experimental example (Section 10.4), the healthy

and faulty conditions were separately clustered for all scenarios (Figure 10.15),


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which could be an indication of the industrial applicability of the technique in the

near future.


components for all cases under different industrial scenarios of missing data (a)

IS1 (b) IS2 (c) IS3 (d) IS4

Figures 10.16(a)-(b) respectively show the separate combination of all faulty and

healthy data for the different scenarios (IS1-IS4) listed in Table 10.3, including the

ideal scenario of complete measured vibration data from all measurement

locations (IS0). The observations were quite similar and consistent with the

experimental example, with the clusters relating to each of the machine conditions

from all scenarios retaining their unique and respective regions.


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components for individual cases for all scenarios (a) all faulty (b) all healthy

10.7 Summary

The quantity of measured vibration data available for classifying an industrial

rotating machine as healthy or faulty could be sometimes hampered by damages

to VFD sensors during routine field activities such as machine cleaning and

general maintenance. The avenues for ensuring the integrity of installed VFD

sensors such as accelerometers prior to each instance of data acquisition is

sometimes restricted by the immense production requirements, especially when

dealing with an on-line condition monitoring system for critical rotating machines

situated in isolated plant locations. Based on this premise, faults classification of

rotating machines (which generally leads to faults diagnosis) may be performed

based on the available vibration data from only certain measurement locations. In

the current study, several sets of measured vibration data from an experimental rig

and a critical induced draft fan of a cement manufacturing company have been

collected under different operating conditions. The results of the faults

classification performed using a combination of the amplitudes of poly coherent

composite bispectrum and trispectrum components for different scenarios of

measured vibration data (i.e. complete and incomplete data), indicated that the

proposed technique is able to separately classify the different cases. This however

shows the robustness and insensitivity of the technique to variations in the

availability of measured vibration data, which may be very useful for faults


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identification in critical industrial rotating machines, especially those installed in

remote and isolated locations, where the frequency of machine inspection is very

low. Future considerations for the current study will be aimed at observing the

impact of varying fault severities and locations on the cluster patterns for different

faults.

Concluding Remarks and Future Research

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11 Chapter 11 CONCLUDING REMARKS AND

FUTURE RESEARCH ----------------------------------------------------------------------------------------------

11.1 Overall Summary

Rotating machines are indispensable parts of most industrial processes including

power generation turbines, cement manufacturing rotary kilns, water transport

pumps, instrument air compressors, hotel and hospital ventilation fans, etc.

Failures of critical rotating machines can lead to catastrophic outcomes including

significant plant downtimes and fatalities, which makes early fault detection

imperative. Over the years, the reliability and quality of products/services delivered

by these critical machines have always been ensured through maintenance

activities whereby CM has been identified as one of the most efficient strategies.

Amongst the very popular rotating machine CM techniques, VCM is the most pre-

potent. The popularity of VCM in research and practise is largely owed to its ability

to offer the longest lead-time to machine failure as well as the relative

computational simplicity and sensitivity of standard VCM techniques such as

amplitude spectrum and rotor orbit analyses to various machine conditions.

While the advancements recorded through the application of amplitude spectrum

analysis for rotating machine faults detection has been immense, however, the

ability of the technique to provide simple, reliable, consistent and conclusive

results still remains questionable due to 2 main reasons. Firstly, the conventional

spectrum analysis process often entails the acquisition of vibration data from

several orthogonal directions of each measurement location (mostly the bearing

pedestal), which results in the accumulation of large volumes of data sets requiring

processing and interpretation. Secondly, the loss of phase information resulting


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from the computation of the final amplitude spectrum greatly limits its ability to

accurately distinguish certain machine conditions. A combination of these

limitations is a fundamental inducement for applying spectrum analysis in

conjunction with other standard VCM techniques such as rotor orbits analysis.

Although some useful results have been achieved, this amalgamation of

techniques makes the fault diagnosis process very complex, time-consuming,

costly, subjective and solely dependent on the expertise of an experienced

analyst. Besides the complexity of combining various standard VCM techniques

such as amplitude spectrum and rotor orbits analyses during fault diagnosis, it has

been experimentally observed that even rotor orbits for different machine

conditions sometimes appear similar thus making the entire diagnosis process

indeterminate.

By taking advantage of the recent and fast-growing computational advancements,

some researchers have explored other VCM approaches including model-based,

AI, higher order signal processing (mainly HOS and HOC) and data fusion

techniques. Although several studies have shown that it is possible to gain

intricate understanding about the dynamics of rotating machines through model-

based techniques, however, the possibility of generating FE models that would

accurately represent complex industrial rotating machines is still a topic of intense

debates. AI techniques on the other hand have recorded significant strides in an

attempt to reduce subjectivities arising from over-reliance on human experience.

However, popular AI techniques such as ANN and SVM are respectively limited by

lack of clearly defined guidelines for acquiring training data and Kernel function

selection.

Amongst all the emerging techniques currently available in the literature, higher

order signal processing appeared the most likely to overcome all the limitations

associated with the commonly used amplitude spectrum analysis. This is based on

the premise that HOS or its normalised form (i.e. HOC) provides information about

both amplitude and phase relationships that exist between the frequency

components of measured vibration signals. Without necessarily compromising the

fault diagnosis process, the phase and amplitude retaining capabilities of HOS and


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HOC offer the opportunity to reduce the number of sensors required for VCM of

rotating machines, which in turn leads to tangible reductions in the number of

measured data sets to be processed and interpreted. A detailed investigation of

the available literature indicates that right up till this moment, most of the current

efforts involving the application of higher order signal processing tools are

significantly skewed towards HOC, with no clarity on whether the features from

both classes (i.e. HOS and HOC) are exactly the same or whether one class

supersedes the other. Also, the very few studies that have explored fault diagnosis

with HOS are restricted to very simple experimental rigs and limited machine

faults. However, real life machines possess various levels of complexity and are

susceptible to several faults. Hence, there is a need to compare the capabilities of

HOS and HOC, so as to adequately justify the selection of what class to use. Also,

ample opportunities still exist to further examine the robustness of HOS on

different kinds of rotating machines and faults.

Maintenance cost effectiveness in the industry refers to any approach to

maintenance that would sustainably reduce maintenance cost, which includes the

rationalisation of rotating machines’ spares. A popular approach for rationalising

maintenance spares is the standardisation of plant machines, which implies that

there would be several identical rotating machines available in a typical plant.

Despite the similarities in configuration (e.g. components), the natural frequencies

of these rotating machines often differ due to variations in the flexibilities of their

foundations. Currently existing fault detection approaches are restricted to a

particular rotating machine, which means that separate analysis needs to be done

for individual rotating machines. Therefore, the development of a robust data

fusion approach that permits the application of measured vibration data from one

rotating machine on another identical rotating machine is highly warranted by the

industry and academia.

Through several experimental and numerical simulations, the current study

proposes a fault diagnosis approach that is capable of detecting and classifying

rotating machine faults irrespective of the variations in foundation flexibilities and

operating speeds. Based on the experimental results obtained, the current


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approach evades the lack of phase and need for multiple measurement locations

that often complicate the commonly used amplitude spectrum analysis.

11.2 Achieved Objectives

This section provides a description of how each of the 5 objectives defined in the

introductory chapter (Section 1.2) of this thesis were precisely achieved.

1. Compare higher order spectra and higher order coherences in order

to determine the usefulness of either class of signal processing tools.

Several studies have reported the abilities of higher order spectra (HOS)

and their normalised forms, higher order coherences (HOC) to establish the

amplitude and phase relationships that exist between several frequency

components of a measured vibration signal. All the studies currently

available in the literature portray both classes of tools as similar, with no

justifications for the selection of one class ahead of the other. Also, most of

the studies involving higher order signal processing tools have been

centred on HOC (i.e. bicoherence and tricoherence). Therefore, in order to

truly justify the choice of tool to use in the current study, a comparative

study was initially conducted to ascertain the usefulness of HOS and HOC.

In the study, a total of 4 cases were numerically simulated. Although the

frequency components for the 4 cases were same, each case possessed

different amplitudes and phases (representing a typical rotating machine

operating at same speed under different conditions of health). The HOS

and HOC components were then computed for each of the 4 cases under 4

different noise levels, so as to reflect industrial situations where

measurement noise is always an integral part of vibration signals measured

from rotating machines. The comparison showed that HOS components

adequately responded to amplitude and phase changes irrespective of the

measurement noise levels. On the contrary, HOC components varied


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inversely with measurement noise contents. This therefore implies that

HOC components are not only affected by amplitude and phase changes

but by measurement noise which can yield misleading diagnosis results in

practice.

2. Observe the dynamics of different rotating machine faults with

reduced sensors, using higher order spectra.

The capability of HOS (bispectrum and trispectrum) components to respond

to amplitude and phase change has already been established. On a

relatively rigid experimental rig and using significantly reduced sensors (1

accelerometer per bearing pedestal), vibration measurements were

acquired under 4 machine conditions at 2 machine speeds. Although the

computed amplitude bispectrum was relatively distinct for most machine

conditions at the 2 speeds, the healthy and shaft rub conditions at the

higher machine speed were quite similar. On the contrary, the computed

amplitude trispectra were clearly different for all machine conditions at both

speeds. Most importantly, the trispectrum features for each machine

condition were fairly consistent at both machine speeds, which is very

valuable for rotating machine fault diagnosis. It is a widely held view that the

appearance of different harmonics in vibration response is often associated

with the changing state of health of any typical rotating machine, which is

expected to be unique in terms of amplitude and phase at respective

harmonic components for every condition. Hence, these observations

provide clear indications that despite the reduced number of measurement

sensors (which significantly reduces fault diagnosis time and equipment

downtime), fault diagnosis is very possible with HOS. In order to increase

robustness of the fault diagnosis process, a combination of both bispectrum

and trispectrum components are proposed for defining machine health

indicators with the hope that the limitations of bispectrum would be

accounted for by the strengths of trispectrum and vice versa.


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3. Improve the existing frequency domain data fusion technique used for

constructing a single composite spectrum for a rotating machine, so

as to ease and enhance the accuracy of fault diagnosis.

Large and complex industrial rotating machines with multiple shafts are

always associated with numerous bearings. VCM of rotating machines

requires the collection of vibration data from each of the bearing pedestals.

During fault diagnosis, the measured vibration data from each bearing

pedestal is individually analysed for several machine faults and speeds.

This approach can be very demanding, especially when dealing with very

large rotating machines with several bearings. Based on this premise, the

concept of constructing a single composite spectrum (CS) that would be

independent on the number of measurement locations was proposed by

earlier studies. The results obtained from CS frequency domain data fusion

approach were quite encouraging, especially in terms of its ability to ease

fault diagnosis and significantly reduce equipment downtime. However, the

cross-power spectrum density (CSD) approach adopted for fusing the

measured vibration data led to a loss of phase information at intermediate

measurement locations. Also, the final CS is totally phase blind as a result

of the product of the coherent composite Fourier transformation (FT) and its

complex conjugate. As a consequence, fault diagnosis with earlier CS leads

to an extreme reliance on the amplitudes at the different harmonics.

In order to obviate the limitations of CS, an improved poly coherent

composite (pCCS) frequency domain data fusion technique was proposed

to provide a better representation of machine dynamics. Still based on the

concept of CSD, however, it was modified to incorporate all signals as

opposed to just a few signals considered in the earlier CS. The proposed

pCCS therefore guarantees better representation of machine dynamics,

owing to its retention of amplitude and phase information at all

measurement locations. The proposed pCCS was then used to diagnose

faults on an experimental rig where it was observed that the amplitude and

phase information at the operating speed or any higher harmonic can offer


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better and easier diagnosis, especially when compared to CS that relied on

only the amplitudes of several harmonics of the machine speed.

4. Develop a faults diagnosis method that is independent of machine

speeds and foundation flexibilities, using composite spectra.

Nowadays, a significant number of plants have adopted equipment

standardisation strategies, so that the cost-effectiveness of their operations

can be enhanced. A notable consequence of such strategies is the

existence of several identical (similar components and configurations)

rotating machines on plant sites. Despite the similarities in configurations

and components, it has been observed that these identical rotating

machines often exhibit different natural frequencies, owing to variations in

their foundation flexibilities. Previously, all fault diagnosis efforts involving

identical rotating machines with different foundations requires the

independent collection and analysis of vibration data from each machine.

The complexity of the fault diagnosis process becomes even bigger if the

considered rotating machines operate at various speeds.

Hence, a similar scenario was experimentally simulated using 2 identical

rotating rigs with 2 different foundations. On both experimental rigs, several

sets of vibration data were collected under a wide range of machine health

conditions and at 3 separate speeds. For each of the experimental rigs, the

measured vibration data under each machine operating condition and

speed were then used to independently compute poly coherent composite

bispectrum (pCCB) and poly coherent composite trispectrum (pCCT)

components. The computed pCCB and pCCT components were then used

as the features of a multiple-speeds and multiple-foundations algorithm,

which was able to group data corresponding to the various machine

operating conditions into their respective clusters irrespective of speed or

foundation. The proposed technique therefore presents an integrated VCM

method that minimises the level of subjectivity and human judgements


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associated with commonly used techniques such as amplitude spectrum

analysis.

5. Determine the sensitivity of composite higher order spectra to various

scenarios of data availability.

Over the years, VCM of rotating machines has always been based on the

premise that measured vibration data from all sensors are intact and

available for processing. In reality though, the quantity of measured

vibration data available for classifying industrial rotating machines as

healthy or faulty is sometimes hampered by damages to VCM sensors

during routine field activities including cleaning, general maintenance and

sabotage. The immense production requirements and extremely low

tolerance for plant downtime sometimes limits the practicability of always

ensuring the integrity of all VCM sensors prior to each instance of vibration

measurement. Consequently, fault detection is sometimes performed using

vibration data available from only certain measurement locations.

In an attempt to examine the abilities of pCCB and pCCT to adequately

classify rotor-related faults despite the unavailability of data from certain

measurement locations, several sets of vibration data were acquired from

an experimental rig and critical cement manufacturing process fan under

different conditions of health. The results showed that a combination of

pCCB and pCCT components is able to consistently classify machine

conditions under all the tested scenarios (complete and incomplete data).

This therefore shows the robustness and insensitivity of the technique to

variations in the availability of measured vibration data, which is valuable for

fault identification in critical industrial rotating machines, especially those

installed in remote and isolated locations, where the frequency of machine

inspection is very low.


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11.3 Concluding Remarks

In an attempt to enhance the robustness and simplicity of vibration based

condition monitoring (VCM) of rotating machines, the current study proffers a novel

approach that is capable of detecting and classifying a wide range of rotor-related

faults on identical rotating machines with different foundations and operating at

different speeds. The current study showed how the proposed approach is able to

evade the complexities, rigour and over reliance on human experience often

associated with the application of standard VCM techniques such as amplitude

spectrum and rotor orbits analyses by allowing the transfer of measured vibration

data from one rotating machine to another identical rotating machine. Although

most of the findings from the current study are based on experimental

observations gathered from 3 separate rotating rigs with different faults and

speeds, the sensitivity of the proposed technique to different scenarios of data

availability was also validated with vibration data collected from a very critical

industrial rotating machine. Based on these initially observed eminences, the

proffered technique might be a feasible contender for industrial deployment in the

near future.

11.4 Future Research

The current study has clearly shown the potentials and merits of the proposed

VCM technique over the standard techniques such as amplitude spectrum and

rotor orbit analyses. However, the success and sustainability of this technique as

well as any other technique significantly depends on continuous improvement

strategies planned for the future. Therefore, the viability of the proposed approach

would be greatly enhanced by exploring the following research areas in the near

future.

1. All of the measured vibration data analysed using the VCM technique

proposed in the current study were acquired from rotating machines


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supported by anti-friction ball bearings. However, several industrial rotating

machines are supported by fluid film bearings. Therefore, it will be very

useful to equally conduct similar faults diagnosis activities on vibration data

measured from several identical rotating machines that are supported by

fluid film bearings under different operating conditions.

2. The current study was principally based on detecting the existence of faults

as well as classifying measured vibration data related to certain rotor-

related faults. However, knowledge of faults severities is a very vital aspect

of VCM of rotating machines especially when dealing with very critical

industrial machines with costly downtime implications. Therefore, using the

techniques proposed in the current study to analyse more measured

vibration data acquired from rotating machines under different faults

severities will provide very useful information about the sensitivity of the

proposed technique to different fault severities.

3. Based on the considered experimental test rigs and experimentally

simulated cases considered for the current study, the proposed VCM

techniques successfully detected, differentiated and classified different

rotating machines operating conditions. However, it is strongly believed that

better and more precise theoretical understanding of the dynamic

behaviours of the considered rotating machines in certain ways can be

achieved through the development of mathematical models of the different

rigs as well as the experimentally simulated faults.

4. It well-known that a fundamental objective of academic research is usually

to enhance and/or simplify currently existing industrial processes, so as to

enhance efficiency and overall effectiveness. Based on this premise, it is

anticipated that the confidence level of the VCM approaches proposed in

the current study will be significantly enhanced through its application on

several identical industrial rotating machines with different foundation

flexibilities.

References

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Appendix A

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APPENDIX A

APPENDIX A THEORETICAL BACKGROUND OF SPECTRUM BASED SIGNAL

PROCESSING TOOLS ----------------------------------------------------------------------------------------------

A.1 Overview of Frequency Domain Signal Processing

During faults diagnosis, it is often desired to convert a time domain signal into the

frequency domain so as to observe the various frequency components within such

a signal. This conversion from time into the frequency domain (often achieved

through the Fourier transformation (FT) process) significantly enhances the

understanding of the physical behaviour of the studied system through a plot of the

vibration amplitude against frequency, also known as the spectrum of the signal.

A.2 Power Spectrum

The power spectrum can be arguably regarded as one of the most commonly used

signal processing tool, and this is evident from the huge body of literature

published with regards to its applications [21], [98], [159]. The power spectrum is a

second-order measure of stationary random processes, which can be

mathematically defined as [98];

(A.1)

Appendix A

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where and are respectively the Fourier transformation (FT) and the

complex conjugate of a time domain signal at a particular frequency.

During the computation of the FT for experimentally measured time domain data,

the direct application of Equation (A.1) is often limited by the following reasons

[21]:

Measured time domain data is often associated with noise

Accurate definition of the time period (T) of the signal

Obtaining the digital form of the data with sampling frequency

Therefore, it is often required to artificially define T, compute the frequency

resolution (d =

) and divide the measured time domain data into equal

segments ( for averaging where the segment size is guided by the number of

data points (N). Based on this premise, Equation (A.1) can also be written as:

(A.2)

where =

. Here, N denotes the number of data

points for FT analysis; represents the sampling frequency; is the frequency

resolution; is the number of equal segments with size N; and

respectively remain the FT and its complex conjugate at frequency for the rth

segment of the considered time domain signal , having a time length of t, with

sufficient amount of overlap.

Equations (A.1) and (A.2) clearly show that the power spectrum is a real quantity

owing to the magnitude squared operation (i.e. the product of and ).

Hence the power spectrum contains no phase information which is the reason why

faults diagnosis using power spectrum density is restricted to the comparison of

amplitudes at individual frequencies.

Appendix A

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A.3 Cross-power Spectrum

Equations (A.2) defines the averaged auto-power spectral density, for a

particular time domain signal at frequency . However, practical VCM of

rotating machines often entails the measurement of vibration data from several

machine locations. Therefore, it is sometimes required that the relationship

between 2 separate time domain signals ( and ) at a particular frequency

is established. The cross-power spectrum (which can be mathematically

computed using Equations (A.3)-(A.4)) is known to provide information about such

relationships.

(A.3)

The averaged cross-power spectrum can be similarly computed as:

(A.4)

where and respectively represent the FT and the complex conjugate

of the FT at frequency for the rth segment of the signals and , while

is the averaged cross-power spectrum for number of segments.

A.4 Ordinary Coherence

The vibration responses acquired from rotating machines and structures in general

are known to be contaminated by noises generated by the measurement sensors

and the monitored structures. The coherence between 2 vibration signals, and

at a frequency provides an indication of the linear correlation between

Appendix A

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them. Coherence values are always bounded between 0 and 1. A coherence value

of 0 at a frequency indicates a lack of relation between the 2 signals, while a

coherence value of 1 indicates a perfect relation between them. According to a

study by Suryam et al. [156], the following can be inferred about coherence:

Coherence value increases as the linear correlation between input

excitation and response increases.

Coherence value may decrease with increase in measurement noise

A nonlinear relation between input excitation and response leads to

reduction in the coherence value

Hence, the ordinary coherence between 2 vibration signals, and at a

frequency is defined as [21]:

(A.5)

Similarly, the averaged coherence can be computed as:

(A.6)

A.5 Higher Order Signal Processing Tools

Equation (A.2) has shown that all phase information is lost during the magnitude

squared operation leading to the computation of the power spectrum, which is why

the power spectrum is only capable of comparing the magnitudes at individual

frequencies. However, the outcomes of analysing measured vibration signals

Appendix A

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(especially during VCM of rotating machines) based on the comparisons of

magnitudes at individual frequencies for different operating conditions is

sometimes unreliable, owing to the possibilities of generating identical power

spectral patterns for various machine conditions. Hence, the establishment of the

level of interaction between several frequency components in a time domain signal

through the application of higher order signal processing tools is desirable for

faults diagnosis.

A.5.1 Bispectrum

Just as the power spectrum provides information about the decomposition of the

power of a measured time domain signal, the bispectrum provides information

about the third order moment [98]. Consequently, the bispectrum can be regarded

as a function of 2 frequency components (each containing amplitude and phase),

say and . The bispectrum provides information about the relations that exist

between , and the complex conjugate of their sum , which can be

mathematically represented as:

(A.7)

A.5.2 Trispectrum

Similarly, the trispectrum of a time domain signal , involves the combination of

3 frequencies (each having amplitude and phase) , and with a fourth

frequency that is equivalent to the sum of the initial 3, and was

computed as [98], [159]:

(A.8)

Appendix A

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In contrast to the bispectrum, each trispectrum component is a function of 3

frequencies, requiring a 4-dimensional plot. Therefore, the spherical plot method

earlier suggested by Collis et al. [98] is adopted here, where the appearance of

individual spheres at certain locations signifies the coupling that exists between

the frequencies at that location and the sizes of the spheres relate to the

amplitudes of the trispectrum components for individual cases.

A.6 Normalisation of Higher Order Signal Processing Tools

Another popular class of higher order signal processing tools are the normalised

forms of higher order spectra (HOS), also known as higher order coherences

(HOCs). HOCs represent the amplitude normalisation of HOS between a range of

0 and 1. The 2 most common classes of HOCs are the bicoherence and

tricoherence.

A.6.1 Bicoherence

The bicoherence is the amplitude normalisation of bispectrum, and can be

computed as [98]:

b2 ( , ) =

(A.9)

A.6.2 Tricoherence

Similarly, the tricoherence is the amplitude normalisation of the trispectrum which

can be computed as [98]:

Appendix A

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t2 =

(A.10)

In order to further boost the understanding of HOS and their normalised forms

(HOCs), their mathematical derivations provided in an earlier study by Howard

[159] is again repeated here.

Let’s consider a time domain signal, , where

. By

applying the exponential form of the Fourier series, the coefficients can be

represented by:

(A.11)

In general, m=0, , , , etc. Hence the positive and negative Fourier series

coefficients of m are determined. The expansion of the time domain signal

can be achieved by using Euler’s theorem as follows:

(A.12)

Substituting Equation (A.12) into Equation (A.11), we obtain:

(A.13)

Appendix A

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Substitute

and

into Equation (A.13) to obtain:

(A.14)

Let’s assume a specific case where , Equation (A.13) can be rewritten to

obtain the positive and negative frequency components for ,

and

, then:

(A.15)

This therefore yields

and

for the positive and negative

Fourier series coefficients respectively.

Since vibration data measured from real structures is often a combination of

several periodic waves due faults, let’s then consider other time domain signals

with period T, say:

and

and are respectively equivalent to

and

, where

Appendix A

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By applying the procedure earlier described, the Fourier series coefficients can be

determined as:

,

and

,

Therefore, the averaged normalised bispectrum for a time domain signal with

equal FT segments can be similarly obtained from the positive and negative

Fourier series coefficients as:

(A.16)

where the bispectrum,

During the computation of the bicoherence, it more convenient to separately

compute the numerator and denominator of Equation (A.16).

Solving for the first denominator term, we have:

(A.17)

Appendix A

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Using a similar approach to solve for the second denominator term, we have:

(A.18)

The numerator on the other hand gives:

(A.19)

By expansion of Equation (A.19), we get:

(A.20)

A very similar approach to that shown in Equation (A.16) is adopted for the

averaged tricoherence for a time domain signal with equal FT segments except

that 4 frequency components ( , and ) are involved, with each having

amplitudes ( , , and ) and phases ( , and ). Hence, the

tricoherence can be computed as:

(A.21)

Appendix A

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where the trispectrum,

In the case of bispectrum and bicoherence, , and are the amplitudes of

the signal components at frequencies , and respectively, while , and

( = + ) are the respective random phases of the signal components at

frequencies , and respectively. Although only the positive frequency

components have been used in the above derivations, however, the same would

apply for the negative frequency components.

The outcome of the trispectrum and tricoherence are similar to those of the

bispectrum and bicoherence except that 4 frequency components ( , , and

) with amplitudes , , and and phases , , and ( = +

) are considered. Each of the bispectrum components amplitude is a

function of 2 frequencies, usually plotted in the xyz orthogonal axes, with axes x

and y respectively representing frequencies, while the amplitude of the bispectrum

is plotted on the z axis. On the other hand, each trispectrum component is a

function of three frequencies, requiring a 4-dimensional plot. Therefore, the

spherical plot method suggested by Collis et al. [98] is often adopted, where the


exists between the frequencies at that location and the sizes of the spheres relate

to the amplitudes of the trispectrum components.

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