Data fusion based diagnosis and prognosis of ball bearings

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DATA FUSION BASED DIAGNOSIS AND PROGNOSIS OF BALL BEARINGS

PIYUSH SHAKYA

DEPARTMENT OF MECHANICAL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY DELHI

DECEMBER, 2015

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DATA FUSION BASED DIAGNOSIS AND PROGNOSIS OF BALL

BEARINGS

by

PIYUSH SHAKYA

DEPARTMENT OF MECHANICAL ENGINEERING

Submitted

in fulfillment of the requirements of the degree of Doctor of Philosophy to the

INDIAN INSTITUTE OF TECHNOLOGY DELHI

DECEMBER, 2015

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(

Srimad Bhagavad Gita, Chapter 2, Verse 47)

You only have the right of performing actions, but never at any time

in their results. You should not be motivated by the results of the performed

actions and never be attached to not doing your Karmas.

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This thesis is dedicated to my family

&

To the spirit of detached Karma

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CERTIFICATE

This is to certify that the thesis entitledDATA FUSION BASED DIAGNOSIS AND PROGNOSIS OF BALL BEARINGSsubmitted byPIYUSH SHAKYAto the Indian Institute of Technology Delhi for the award of the degree of Doctor of Philosophy is a bonafide record of research work carried out by him under our supervision. This thesis has been prepared in conformity with the rules and regulations of the Indian Institute of Technology Delhi. We further certify that the thesis has attained a standard required for a degree Doctor of Philosophy. The research reported and the results presented in the thesis, in full or in parts, have not been submitted to any other Institute or University for the award of any degree or diploma.

Dr. A. K. Darpe Dr. M. S. Kulkarni

Associate Professor Associate Professor

Department of Mechanical Engineering Department of Mechanical Engineering Indian Institute of Technology Delhi Indian Institute of Technology Delhi

New Delhi-110016, India New Delhi-110016, India

Date Date

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ACKNOWLEDGEMENTS

First, I would like to express my deepest gratitude to my supervisors Dr. A. K. Darpe and Dr. M. S. Kulkarni. They were always accessible throughout the doctoral program and the most appreciable aspect of their behavior was their humane demeanor. Their simple but elegant and focused approach towards solving complicated problems always inspired me.

Their unwavering dedication and commitment to the project was always a motivating factor for me during the times when I felt discouraged and tired. I would also like to recall their heartily care and benevolence experienced during the crisis faced on the personal fronts.

This doctoral work would not have been possible without the crucial suggestions and relevant feedbacks provided by SRC memebers Prof. S. P. Singh (Chairman), Prof. J. K.

Dutt, and Prof. N. Tandon. Their invaluable suggestions helped greatly to improve the doctoral work and bring it to the current level.

I would also like to thank Prof. K. Gupta for his gentle support and encouragement throughout the doctoral program. I would like to admire Mr. K. N. Madhu for his genial nature and for making the Vibration research laboratory environment homely, pleasant, and conducive for research. During my interactions with him, I always found him willing to help all the research scholars at professional and personal fronts. It was because of his timely help on several occasions that I was able to devote time to the research.

I am also indebted to respected members of Project review and monitoring committee (PRMC), Prof. N. K. Mehta (Chairman), Prof. C. Amarnath, Dr. R. K. Biswas, Shri P. J.

Mohanram, Shri Neeraj Sinha, Shri N. K. Dhand, and Shri Kapil Dhand. I am also grateful to Shri Dinesh and Shri Rakesh Yadav of MGTL for their contributions for my project. Regards are also due to the Government of India for funding the project “Development of New Model using Dynamic Stress Profiles for A) Prediction of Bearing Residual life and B) Deciding Optimal Condition Monitoring Intervals” through which I was hired as project associate

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to work. I am grateful to the Government of India and MHRD for providing scholarship, enabling me to undertake PhD program.

I was also blessed with the company of friendly and considerate fellow research scholars, Dr. Skylab Bhore, Dr. Apurba Mandal, Dr. Suresh Babu, Dr. Sukesh Babu, Mr. Sanjeev Sood, Mr. Ashish Purohit, Mr. Asjad Mokhtar, Mr. Anvesh Reddy, and Mr. Jaskaran Singh.

I was also benefitted by the friendly research scholars of other labs Mr. Amit Upadhayay, Mr. Arun Dayal Udai, Mr. Ashok Bagha, Mr. Deepak Nehte, Mr. Sachin, Dr. Prashant Ambad, Mr. Pankaj Zine, Mr. B. M. Ningegowda, and Mr. Kuldeep Dagar for their friendly demeanor and encouragement throughout the doctoral program. In addition, I would like to thank Mr. Binu, Mr. Manmohan, Mr. Arvind, Mr. Ali, Ms. Hiral, Mr. Dheer, Mr.

Jagatpreet, Mr. Sachin, Mr. Mahesh, Mr. Ramesh, Mr. Kapil, and Mr. Virender of the Vibration Research Laboratory for their friendliness in their interaction with me.

I am also grateful to my friends and relatives, for their strong moral support and an understanding approach towards me at several occasions when I was unable to fulfill my responsibilities and duties towards them due to paucity of time. I am also thankful to several others who helped my parents in meeting various commitments in which additional support was required due to my conspicuous absence. I would like to mention a special thanks to Mr.

Sarvesh Kumar Verma and Mr. Narendra Kumar Maurya and their families in this regard.

This thesis would not have been possible without the perennial encouragement and inspiration provided by my family who virtually coerced me to complete the entire project with the utmost dedication. Though they suffered several hardships due to my absence on many crucial social occasions with a smile on their faces, they never complained or did anything to make me aware about those situations.

Last but not the least, I owe this work to almighty God, who gave me strength to crawl through several rough patches, times when I wanted to give up the entire project and leave.

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He/She taught me through several indications that there are many other facets of the life, which at times can assume much more importance than the research and that the research is not the only aspect of life. It is due to His/Her willingness that this work has seen the light of the day.

Piyush Shakya

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ABSTRACT

The data fusion based diagnosis and prognosis of ball bearings with naturally induced and progressed defect has been systematically attempted. Initially, various vibration signal based damage identification parameters along with the fused parameter Mahalanobis distance are ranked on the counts of robustness, sensitivity, early detectivity, and overall basis for seeded defects. The study concludes that the Mahalanobis distance is one of the best overall parameters for diagnosis of ball bearing.

Two methodologies based on Mahalanobis distance are proposed for online identification of the health status and type of defect for bearings with naturally induced and progressed defects. The methodologies are validated from simulation data/vibration data acquired from multiple sources (test rigs) for bearings with seeded and naturally progressed defects. Identifi- cation of exact condition of the bearing reduces the cost of condition monitoring by modifying the data acquisition frequency. Another instantaneous energy density based methodology is proposed for classification of the type of the defect in bearing, also validated by data from multiple sources.

Application of alternate sensors for bearing diagnosis is explored. Variety of sensors such as proximity pickup and pressure microphone is used. The application of multiple sensors increases the robustness of the bearing diagnosis. In the end, a simulation study is conducted to generate damage identification parameters for a large number of bearings. Two third of the dataset is used for training, and remaining one third is used for quantification of the prediction accuracy. Effect of various inputs on the prediction accuracy of the ANNs is studied. A Weibull distribution based methodology is proposed to address several issues/shortcomings in the prediction by ANNs such as negative and non-monotonic remaining useful life. The Weibull distribution based method is found superior in prediction of remaining useful life towards the end of the bearing life, where the accuracy of prediction required is higher.

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315

Appendix

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LIST OF FIGURES

Figure 2.1: Vibration data from test rig with an implanted inner race defect . . . . 14

Figure 2.2: Bearing inner race defect vibration data band passed 20-40 kHz . . . . 15

Figure 2.3: Probability density functions for bearing acceleration . . . 17

Figure 2.4: Typical trends of time domain parameters with fault development. . . . 18

Figure 2.5: The operations involved in the HFRT and the form of the signal pro- duced. . . 23

Figure 2.6: Movement of defect in case of inner race defect . . . 24

Figure 2.7: Typical signals and envelop signals from local faults in bearing . . . 24

Figure 2.8: Illustrative prognostic dynamic Bayesian Network . . . 43

Figure 2.9: Five state left to right HMM used for tool wear prediction . . . 45

Figure 2.10: HMM based fault diagnosis algorithm . . . 46

Figure 3.1: Experimental set up (a) Test rig (courtesy: N.E.I., Jaipur) (b) Test bearings with defect size of 500µm on the outer race (c) Test bearings with defect size of 500µm on the inner race . . . 64

Figure 3.2: The loading diagram of experimental set up . . . 65

Figure 3.3: Variation of RMS value with defect severity for bearing with (a) Outer race defect (b) Outer race defect (side view) (c) Inner race defect (d) Inner race defect (side view) . . . 67

Figure 3.4: Variation of Peak amplitude with defect severity for bearing with (a) Outer race defect (b) Outer race defect (side view) (c) Inner race defect (d) Inner race defect (side view) . . . 68

Figure 3.5: Variation of Crest Factor with defect severity for bearing with (a) Outer race defect (b) Outer race defect (side view) (c) Inner race defect (d) Inner race defect (side view) . . . 70

Figure 3.6: Variation of Kurtosis with defect severity for bearing with (a) Outer race defect (b) Outer race defect (side view) (c) Inner race defect (d) Inner race defect (side view) . . . 71

Figure 3.7: FFT spectrum of healthy bearing . . . 74 xiii

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Figure 3.8: FFT spectra of outer race defect bearings (a) 500µm size (b) 1000µm size (c) 1500µm size (d) 2000µm size . . . 74 Figure 3.9: FFT spectra of inner race defect bearings (a) 500µm size (b) 1000µm

size (c) 1500µm size (d) 2000µm size . . . 75 Figure 3.10: Enlarged FFT spectrum of healthy bearing . . . 75 Figure 3.11: Enlarged FFT spectrum of outer race defect bearings (a) 500µm size

(b) 1000µm size (c) 1500µm size (d) 2000µm size . . . 78 Figure 3.12: Enlarged FFT spectrum of inner race defect bearings (a) 500µm size

(b) 1000µm size (c) 1500µm size (d) 2000µm size . . . 79 Figure 3.13: Frequency-amplitude-time map for 1500µm outer race defect . . . 80 Figure 3.14: Enlarged Frequency-amplitude-time map for 1500µm outer race defect 81 Figure 3.15: Variation of defect frequency amplitude with defect severity for bearing

with (a) Outer race defect (b) Outer race defect (side view) (c) Inner race defect (d) Inner race defect (side view) . . . 83 Figure 3.16: Variation of 2^nd harmonics of defect frequency amplitude with defect

severity for bearing with (a) Outer race defect (b) Outer race defect (side view) (c) Inner race defect (d) Inner race defect (side view) . . . 84 Figure 3.17: Variation of 3^rd harmonics of defect frequency amplitude with defect

severity for bearing with (a) Outer race defect (b) Outer race defect (side view) (c) Inner race defect (d) Inner race defect (side view) . . . 85 Figure 3.18: HFRT spectrum of the healthy bearing . . . 87 Figure 3.19: HFRT spectrum of outer race defect (a) 500µm (b) 1000µm(c) 1500µm

(d) 2000µm . . . 88 Figure 3.20: HFRT spectrum of inner race defect (a) 500µm (b) 1000µm(c) 1500µm

(d) 2000µm . . . 89 Figure 3.21: Variation of HFRT spectrum DFA with defect severity for bearing with

(a) Outer race defect (b) Outer race defect (side view) (c) Inner race defect (d) Inner race defect (side view) . . . 90 Figure 3.22: CWT analysis of healthy bearing (a) 3D view (b) Time slice at reso-

nance frequency . . . 93 xiv

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Figure 3.23: 3D CWT analysis of outer race defect (a) 500µm (b) 1000µm (c) 1500µm (d) 2000µm . . . 94 Figure 3.24: 3D CWT analysis of inner race defect (a) 500µm (b) 1000µm (c) 1500µm

(d) 2000µm . . . 95 Figure 3.25: CWT analysis (a) 2000µm outer race defect 3D plot (b) Time slice at

resonance frequency for 2000 µm outer race defect (c) 2000 µm inner race defect 3D plot (d) Time slice at resonance frequency for 2000µm inner race defect . . . 96 Figure 3.26: Variation of RMS amplitude of time slice corresponding to resonance

frequency with defect severity for bearing with (a) Outer race defect (b) Outer race defect (side view) (c) Inner race defect (d) Inner race defect (side view) . . . 97 Figure 3.27: Variation of HFRT spectrum DFA of time slice corresponding to res-

onance frequency with defect severity for bearing with (a) Outer race defect (b) Outer race defect (side view) (c) Inner race defect (d) Inner race defect (side view) . . . 98 Figure 3.28: Hilbert Huang Spectrogram (HHS) of the healthy bearing . . . 100 Figure 3.29: HHS of outer race defect (a) 500µm (b) 1000µm (c) 1500µm (d) 2000µm101 Figure 3.30: HHS of inner race defect (a) 500µm (b) 1000µm (c) 1500µm (d) 2000µm102 Figure 3.31: HHS of outer race defect with respect to highest energy of 2000µm size

defect (a) 500µm (b) 1000µm (c) 1500µm (d) 2000µm . . . 103 Figure 3.32: HHS of inner race defect with respect to highest energy of 2000µm size

defect (a) 500µm (b) 1000µm (c) 1500µm (d) 2000µm . . . 104 Figure 3.33: Variation of HHS analytical signal maximum amplitude with defect

severity for bearing with (a) Outer race defect (b) Outer race defect (side view) (c) Inner race defect (d) Inner race defect (side view) . . . . 105 Figure 3.34: Comparison of HHT peak computed from basic HHT and HHT with

EEMD techniques. . . 118 Figure 4.1: Flow chart explaining the proposed methodology for online detection

of bearing health status . . . 135 xv

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Figure 4.2: MD variation with change in the number of data points considered as

healthy . . . 141

Figure 4.3: Expanded view of MD variation with change in number of data points considered as healthy . . . 142

Figure 4.4: Model of experimental setup for vibration data acquisition for naturally induced defect . . . 143

Figure 4.5: Trend of the MD with respect to data point (simulation study) . . . 145

Figure 4.6: Z-statistic of the MD of the simulated data . . . 145

Figure 4.7: MD for seeded defect in rolling element bearing . . . 146

Figure 4.8: Z-statistic of the MD of the seeded defect in rolling element bearing . . 146

Figure 4.9: RMS of the naturally progressed defect vibration data (experiment 1) . 148 Figure 4.10: Peak acceleration of the naturally progressed defect vibration data (experiment 1) . . . 148

Figure 4.11: MD for naturally induced and progressed defect in rolling element bearing (experiment 1) . . . 149

Figure 4.12: Comparison of percentage change in values of RMS, Peak and MD . . . 149

Figure 4.13: Z-statistic of the MD of the naturally progressing defect (experiment 1) 150 Figure 4.14: RMS of the naturally progressed defect vibration data (experiment 2) . 151 Figure 4.15: Peak acceleration of the naturally progressed defect vibration data (experiment 2) . . . 152

Figure 4.16: MD for naturally induced and progressed defect in rolling element bearing (experiment 2) . . . 152

Figure 4.17: Z-statistic of the MD of the naturally progressing defect (experiment 2) 153 Figure 4.18: Flow chart explaining the methodology proposed for defect type identification . . . 157

Figure 4.19: Trends of gain value of all the DIPs (outer race 500µm defect) . . . 159

Figure 4.20: Trend of MD for outer race 500µm defect after excluding negative gain parameters . . . 159

Figure 4.21: Trends of GSVs of the frequency domain DIPs having positive gain (outer race 500µm defect) . . . 160

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Figure 4.22: DOIs of outer race and ball defect (outer race 500µm defect) . . . 161

Figure 4.23: Trends of gain value of all the DIPs (inner race 500µm defect) . . . 163

Figure 4.24: Trend of MD for inner race 500µm defect after excluding negative gain parameters . . . 163

Figure 4.25: Trends of GSVs of the frequency domain DIPs having positive gain (inner race 500µm defect) . . . 164

Figure 4.26: Amplitudes of defect frequencies in FFT and HFRT spectrum for healthy data and inner race 2000µm defect size . . . 164

Figure 4.27: Trends of gain value of all the DIPs (outer race 175µm defect) . . . 166

Figure 4.28: Trend of MD for 175µm size outer race defect after excluding negative gain parameters . . . 167

Figure 4.29: Trends of GSVs of the frequency domain DIPs having positive gain (outer race 175µm defect) . . . 167

Figure 4.30: Trends of gain value of all the DIPs (inner race 175µm defect) . . . 168

Figure 4.31: Trend of MD for 175µm size inner race defect after excluding negative gain parameters . . . 168

Figure 4.32: Trends of GSVs of the frequency domain DIPs having positive gain (inner race 175µm defect) . . . 169

Figure 4.33: DOIs of various types of defects (inner race 175µm defect) . . . 169

Figure 4.34: Trends of gain value of all the DIPs (ball defect 525µm) . . . 170

Figure 4.35: Trend of MD and Peak vibration values (ball defect 525µm) . . . 170

Figure 4.36: Trends of GSVs of the frequency domain DIPs having positive gain (ball defect 525µm) . . . 171

Figure 4.37: Trend of MD for accelerated life test data after excluding negative gain parameters . . . 173

Figure 4.38: Z-statisticsof the MD for the accelerated life test data . . . 174

Figure 4.39: Trends of gain value of all the DIPs for accelerated life test data . . . . 175

Figure 4.40: Trends of GSVs of the frequency domain DIPs having positive gain for accelerated life test . . . 175

Figure 4.41: DOIs of outer race and ball defect for accelerated life test . . . 176 xvii

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Figure 4.42: Picture of (a) Three balls with defect (accelerated test bearing); (b) a

healthy ball . . . 177

Figure 5.1: Time domain data for outer race defect of 1500µm size . . . 182

Figure 5.2: Time domain data for inner race defect of 1500µm size . . . 182

Figure 5.3: The load distribution of a bearing . . . 184

Figure 5.4: Effect of unbalance for the inner race defect . . . 187

Figure 5.5: Effect of unbalance for the outer race defect . . . 188

Figure 5.6: Simulated ideal outer race defect (a) Time domain signal; (b) FFT spectrum; (c) FFT spectrum for low frequency region. . . 191

Figure 5.7: Simulated outer race defect with radial load variation and unbalance (a) Time domain signal; (b) FFT spectrum; (c) FFT spectrum for low frequency region. . . 192

Figure 5.8: Simulated outer race defect with shaft speed variation and unbalance (a) Time domain signal; (b) FFT spectrum; (c) FFT spectrum for low frequency region. . . 192

Figure 5.9: Simulated outer race defect with shaft speed variation, load variation and unbalance (a) Time domain signal; (b) FFT spectrum; (c) FFT spectrum for low frequency region. . . 193

Figure 5.10: Simulated outer race defect with shaft speed variation, load variation, unbalance, and noise (SNR:-7.5 dB) (a) Time domain signal; (b) FFT spectrum; (c) FFT spectrum for low frequency region. . . 193

Figure 5.11: Simulated ideal inner race defect (a) Time domain signal; (b) FFT spectrum; (c) FFT spectrum for low frequency region. . . 195

Figure 5.12: Simulated inner race defect with shaft load variation and unbalance (a) Time domain signal; (b) FFT spectrum; (c) FFT spectrum for low frequency region. . . 195

Figure 5.13: Simulated inner race defect with shaft speed variation and unbalance (a) Time domain signal; (b) FFT spectrum; (c) FFT spectrum for low frequency region. . . 196

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Figure 5.14: Simulated inner race defect with shaft speed variation, load variation, and unbalance (a) Time domain signal; (b) FFT spectrum; (c) FFT spectrum for low frequency region. . . 197 Figure 5.15: Simulated inner race defect with shaft speed variation, load variation,

unbalance, and noise (SNR:-7.5 dB) (a) Time domain signal; (b) FFT spectrum; (c) FFT spectrum for low frequency region. . . 198 Figure 5.16: HHS of simulated ideal defect signal: (a) Outer race; (b) Inner race. . . 199 Figure 5.17: For simulated ideal outer race defect (a) The IE; (b) Autocorrelation;

(c) Expanded view of autocorrelation. . . 200 Figure 5.18: For simulated ideal inner race defect (a) The IE; (b) Autocorrelation;

(c) Expanded view of autocorrelation. . . 200 Figure 5.19: (a) Unfiltered variation of IE with time (outer race); (b) Filtered IE

based on adaptive filtering (outer race); (c) Histogram of IE (outer race); (d) Filtered IE based on adaptive filtering (inner race); (e) His- togram of IE (inner race). . . 204 Figure 5.20: Simulated outer race defect with noise (SNR:-7.5 dB): (a) Actual IE;

(b) ACs with varying lags; (c) Expanded view of ACs with varying lags;

(d) Filtered IE; (e) Histogram of filtered IE. . . 212 Figure 5.21: Simulated inner race defect with noise (SNR:-7.5 dB): (a) Actual IE;

(b) ACs with varying lags; (c) Expanded view of ACs with varying lags;

(d) Filtered IE; (e) Histogram of filtered IE. . . 213 Figure 5.22: Simulated inner race defect with load variation, shaft speed variation,

and unbalance (for θ_max = 180^◦) : (a) Time domain signal; (b) FFT spectrum; (c) FFT spectrum for low frequency region . . . 214 Figure 5.23: Simulated inner race defect for θ_max = 180^◦: (a) Actual IE; (b) ACs

with varying lags; (c) Expanded view of ACs with varying lags; (d) Filtered IE; (e) Histogram of IE . . . 215 Figure 5.24: Simulated healthy data with shaft speed variation, unbalance, and noise

(SNR:-7.5 dB): (a) Time domain signal; (b) FFT spectrum; (c) FFT spectrum for low frequency region . . . 216

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Figure 5.25: Simulated healthy data with shaft speed variation, unbalance, and noise (SNR:-7.5 dB): (a) ACs with varying lags; (b) Expanded view of ACs with varying lags . . . 217 Figure 5.26: Simulated inner race defect with shaft speed variation, unbalance, and

noise of (SNR:-7.5 dB) with five resonance frequencies: (a) Time domain signal; (b) FFT spectrum; (c) FFT spectrum for low frequency region . 218 Figure 5.27: For simulated inner race defect with shaft speed variation, unbalance,

and noise of -7.5 dB with five-resonance frequencies, application of (a) Fast Kurtogram (b) HFRT . . . 219 Figure 5.28: For simulated inner race defect signal with shaft speed variation, un-

balance, and noise of -7.5 dB with five-resonance frequencies: (a) CWT (b) time slice at resonance frequency (c) Envelope analysis at time slice at resonance frequency . . . 221 Figure 5.29: Comparison of HFRT of CWT slice with different mother wavelet . . . 221 Figure 5.30: HHS of the simulated inner race defect with shaft speed variation, un-

balance, and noise (SNR:-7.5 dB) with five resonance frequency regions 222 Figure 5.31: EEMD based HHS of the simulated inner race defect with shaft speed

variation, unbalance, and noise (SNR:-7.5 dB) with five resonance frequency regions . . . 222 Figure 5.32: Comparison of Instantaneous energy for basic HHT and HHT with

EEMD technique for simulated inner race defect with five resonance frequency regions . . . 223 Figure 5.33: Marked EEMD based HHS of the simulated inner race defect with shaft

speed variation, unbalance, and noise (SNR:-7.5 dB) with five resonance frequency regions . . . 223 Figure 5.34: Application of the proposed methodology simulated inner race defect

with shaft speed variation, unbalance, and noise (SNR:-7.5 dB) with five resonance frequency regions: (a) Actual IE; (b) ACs with varying lags; (c) Expanded view of ACs with varying lags; (d) Filtered IE; (e) Histogram of IE . . . 225

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Figure 5.35: IMF 1 for 500µm size inner race defect: (a) Time domain; (b) FFT; (c) IE . . . 228 Figure 5.36: IMF 2 for 500µm size inner race defect: (a) Time domain; (b) FFT; (c)

IE . . . 228 Figure 5.37: IMF 3 for 500µm size inner race defect: (a) Time domain; (b) FFT; (c)

IE . . . 229 Figure 5.38: 500µm outer race defect: (a) Actual IE; (b) ACs with varying lags; (c)

Expanded view of ACs with varying lags; (d) Filtered IE; (e) Histogram of IE . . . 230 Figure 5.39: 1000µm outer race defect: (a) Actual IE; (b) ACs with varying lags; (c)

Expanded view of ACs with varying lags; (d) Filtered IE; (e) Histogram of IE . . . 232 Figure 5.42: 500µm inner race defect: (a) Actual IE; (b) ACs with varying lags; (c)

Expanded view of ACs with varying lags; (d) Filtered IE; (e) Histogram of IE . . . 235 Figure 5.45: 2000µm inner race defect: (a) ACs with varying lags; (b) Expanded

view of ACs with varying lags . . . 236 xxi

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Figure 5.46: Healthy data: (a) Time domain signal; (b) FFT spectrum; (c) FFT spectrum for low frequency region . . . 237 Figure 5.47: Healthy data: (a) ACs with varying lags; (b) Expanded view of ACs

with varying lags . . . 238 Figure 5.48: 175µm outer race defect: (a) Actual IE; (b) ACs with varying lags; (c)

Expanded view of ACs with varying lags; (d) Filtered IE; (e) Histogram of IE . . . 240

Figure 6.1: Diagram showing the position of the proximity probe and accelerometer 247 Figure 6.2: Proximity probe (a) time-domain displacement data; (b) FFT spec-

trum; (c) FFT spectrum for low frequency region . . . 247 Figure 6.3: Histogram for speed signal . . . 249 Figure 6.4: Flow chart of the proposed TSA based methodology . . . 249 Figure 6.5: Proximity Probe (a) Time synchronous averaging; (b) FFT of original

signal;(c) FFT of averaged signal (after TSA); (d) Time domain signal after subtracting the averaged signal from the original signal . . . 251 Figure 6.6: FFT of the final signal for vibration data acquired by proximity probe . 252 Figure 6.7: Failed bearing after dismantling . . . 253 Figure 6.8: Time Synchronous Averaging for healthy data . . . 253 Figure 6.9: Results after the application of the method proposed on the data from

healthy bearing . . . 254 Figure 6.10: FFT spectrum of the data acquired from proximity probe for low fre-

quency region . . . 256 Figure 6.11: FFT spectrum of the data acquired from accelerometer for low fre-

quency region . . . 256 Figure 6.12: IRDF amplitude and ORDF amplitude for data acquired by proximity

probe . . . 257 xxii

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Figure 6.13: IRDF amplitude and ORDF amplitude for vibration data acquired by accelerometer . . . 258 Figure 6.14: Picture of the inner race with defect (naturally induced and progressed

defect) . . . 258 Figure 6.15: Picture of the outer race with defect (naturally induced and progressed

defect) . . . 259 Figure 6.16: Diagram showing the position of the pressure microphone and accelerom-

eter . . . 260 Figure 6.17: Time domain data for the outer race defect of 300µm size (a) accelerom-

eter; (b) pressure microphone; (c) comparison of accelerometer and microphone . . . 261 Figure 6.18: FFT spectra for the outer race defect of 300µm size (a) accelerometer;

(b) pressure microphone; (c) comparison of accelerometer and microphone261 Figure 6.19: Time domain data for the inner race defect of 300µm size (a) accelerom-

eter; (b) pressure microphone; (c) comparison of accelerometer and microphone . . . 262 Figure 6.20: FFT spectra for the inner race defect of 300µm size (a) accelerometer;

(b) pressure microphone; (c) comparison of accelerometer and microphone263 Figure 6.21: FFT spectra for naturally induced and progressed defect (a) accelerom-

eter; (b) pressure microphone; (c) comparison of accelerometer and microphone . . . 264 Figure 6.22: The outer race defect on the naturally induced and progressed defect

bearing after dismantling . . . 265 Figure 6.23: Comparison of RMS trend for naturally induced and progressed defect

(accelerometer and pressure microphone) . . . 265 Figure 6.24: Comparison of Peak trend for naturally induced and progressed defect

(accelerometer and pressure microphone) . . . 266 Figure 6.25: Comparison of MD computed from accelerometer and proximity probe . 267 Figure 6.26: Comparison of MD computed from accelerometer and pressure micro-

phone . . . 268 xxiii

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Figure 6.27: Comparison of MD computed from accelerometer, pressure microphone,

proximity pickup and all sensors combined . . . 268

Figure 7.1: Comparison of the Erlang distribution with Weibull distribution for different number of stages (k) . . . 275

Figure 7.2: A sample RMS mean value trend . . . 278

Figure 7.3: RMS mean value trend for seeded defect study (outer race) . . . 279

Figure 7.4: Trend of the simulated RMS value corresponding to Figure 7.2 . . . 284

Figure 7.5: Predictions from the ANN trained on DIPs for a sample bearing lifing data . . . 291

Figure 7.6: The prediction error histogram for the ANN trained on DIPs . . . 291

Figure 7.7: Predictions from the ANN trained on MD for the sample bearing shown in Figure 7.5 . . . 292

Figure 7.8: The prediction error histogram for the ANN trained on MD . . . 293

Figure 7.9: Predictions from the ANN trained on MD only for defective stage data (for the sample discussed in Figures 7.5 and 7.7) . . . 294

Figure 7.10: The prediction error histogram for the ANN trained on MD (defective stage datasets only) . . . 294

Figure 7.11: RMSE with respect to percentage of actual life of bearing for ANN trained on MD values only from defective stage . . . 295

Figure 7.12: The fitted curve between percentage reduction inηvalue and percentage increase in RMS value for the training dataset . . . 299

Figure 7.13: RUL prediction for a sample dataset for Weibull distribution based prediction method . . . 299

Figure 7.14: RMSE with respect to percentage of actual life of the bearing for Weibull based method . . . 300 Figure 7.15: RUL prediction for the experimental dataset by parametric approach . 301

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LIST OF TABLES

Table 2.1: Fault recognition of rolling bearings using various methods . . . 47

Table 3.1: Geometry of the bearing AU1103M . . . 66

Table 3.2: Summary of central frequency and bandwidth using Fast Kurtogram approach . . . 86

Table 3.3: Summary of HFRT DFA obtained with different central frequency (bold and italic values show the highest HFRT DFA) . . . 91

Table 3.4: Robustness comparison of parameters (outer race) . . . 111

Table 3.5: Robustness comparison of parameters (inner race) . . . 111

Table 3.6: Sensitivity comparison of parameters (outer race) . . . 112

Table 3.7: Sensitivity comparison of parameters (inner race) . . . 112

Table 3.8: Early detectivity comparison of parameters (outer race) . . . 113

Table 3.9: Early detectivity comparison of parameters (inner race) . . . 113

Table 3.10: Overall ranking of parameters (outer race) . . . 114

Table 3.11: Overall ranking of parameters (inner race) . . . 114

Table 3.12: Early detectivity comparison of parameters (CWRU data) outer race . . 116

Table 3.13: Early detectivity comparison of parameters (CWRU data) inner race . . 117

Table 3.14: SNR calculation for every run (500µm outer race defect) . . . 121

Table 3.15: SNR calculation for every run (500µm outer race defect) . . . 122

Table 3.16: Gain for presence values with defect size (outer race defect) . . . 123

Table 3.17: Gain for presence values with defect size (inner race defect) . . . 123

Table 3.18: Mahalanobis distance comparison table for the outer race defect . . . 124

Table 3.19: Robustness comparison of parameters including Mahalanobis distance (outer race) . . . 125

Table 3.20: Robustness comparison of parameters including Mahalanobis distance (inner race) . . . 126

Table 3.21: Sensitivity comparison of parameters including Mahalanobis distance (outer race) . . . 126

Table 3.22: Sensitivity comparison of parameters including Mahalanobis distance (inner race) . . . 127

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Table 3.23: Early detectivity comparison of parameters including Mahalanobis dis-

tance (outer race) . . . 127

Table 3.24: Early detectivity comparison of parameters including Mahalanobis distance (inner race) . . . 128

Table 3.25: Overall ranking of parameters including Mahalanobis distance (outer race)128 Table 3.26: Overall ranking of parameters including Mahalanobis distance (inner race)129 Table 4.1: Details of simulated rolling element bearing damage identification parameters . . . 139

Table 4.2: Correlation coefficients of damage identification parameters (Par = Pa- rameter) . . . 140

Table 4.3: Summary of outer race seeded defect experiment (line defect) . . . 161

Table 4.4: Comparison of change in amplitude of characteristic frequency and GSV 162 Table 4.5: Summary of inner race seeded defect experiment (line defect) . . . 165

Table 4.6: Summary of seeded defect experiment (CWRU data) . . . 172

Table 5.1: Parameters of the simulation study . . . 190

Table 5.2: Summary of the results of seeded defect experiment (outer race) . . . 233

Table 5.3: Summary of the results of seeded defect experiment (inner race) . . . 236

Table 5.4: Summary of the results of 175µm defect size (CWRU data) . . . 239

Table 5.5: Summary of the sensitivity analysis for 175µm defect size (outer race) . 241 Table 5.6: Summary of the sensitivity analysis for 175µm defect size (inner race) . 241 Table 6.1: Comparison of data point of change in health status for different sensors 269 Table 7.1: Correlation coefficients of DIPs for healthy stage . . . 280

Table 7.2: Lower bounds of correlation coefficients of DIPs for healthy stage . . . . 280

Table 7.3: Upper bounds of correlation coefficients of DIPs for healthy stage . . . . 281

Table 7.4: Correlation coefficients of DIPs for seeded defect (outer race) . . . 281

Table 7.5: Lower bounds of the correlation coefficients of DIPs for seeded defect (outer race) . . . 282

Table 7.6: Upper bounds of the correlation coefficients of DIPs for seeded defect (outer race) . . . 283

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Table 7.7: Correlation coefficients of DIPs for seeded defect (inner race) . . . 285 Table 7.8: Lower bounds of the correlation coefficients of DIPs for seeded defect

(inner race) . . . 285 Table 7.9: Upper bounds of the correlation coefficients of DIPs for seeded defect

(inner race) . . . 287 Table 7.10: Summary of validation of methodology of online detection of bearing

health status . . . 288 Table 7.11: Summary of late detection for simulated lifing data . . . 288 Table 8.1: Summary of student’s publications . . . 311

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NOMENCLATURE AND ABBREVIATIONS

()^T Transpose of the vector

()^∗ Complex conjugate

()⁻¹ Inverse of the matrix

α error Type 1 error

α_c Contact angle

β Weibull shape parameter

χ² Chi square statistics

δ Dirac delta function

Load distribution factor

η Weibull scale parameter

λ Erlang rate parameter

µ Mean

ω(t) Instantaneous frequency

() Average

φ Phase of unbalance with defect

ψ(t) Phase of the analytical signal

σ Standard deviation

τ Variable

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θ Angle from maximum load position

θmax Angular extent for load zone

A(t) Amplitude of the analytical signal

a(t) Transfer function between defect and transducer

AC Autocorrelation coefficient

AIC Akaike Information Criterion

AN N Artificial Neural Network

AR Auto Regression

ARIM A Auto Regressive Integrated Moving Average

ARM A Auto Regressive Moving Average

BBN Bayesian Belief Network

BDF Ball defect frequency

BDF A Ball defect frequency amplitude

BN Bayesian Networks

C Correlation matrix

CV Coefficient of Variation

CW RU Case Western Reserve University

CW T Continuous Wavelet Transform

D Pitch circle diameter

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d(t) Impulse function

d0 Amplitude of the impulse

d_b Ball diameter

DBN Dynamic Bayesian Networks

DF A Defect frequency amplitude

DIP Damage identification parameter

DOI Defect occurrence index

DRAC Double row angular contact

DSV Defect severity value

DW N N Dynamic Wavelet Neural Network

E Expected group frequency

EEM D Ensemble Empirical Mode Decomposition

EM D Empirical Mode Decomposition

EP RI Electrical Power Research Institute

f frequency

F(t) Cumulative distribution function

fe(t) Erlang probability density function

f_w(t) Weibull probability density function

Few Sum of least squares of the error xxxi

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f_{shaf t} Shaft rotation frequency

F F N N Feed forward Neural Network

F F T Fast Fourier Transform

F T F Fundamental train frequency

G Total groups

GSP Gram-Schmidt orthogonalization process

GSV Gram-Schmidt Vector

h(t) Unit impulse response function

H[] Hilbert transform

HF RT High Frequency Resonance Technique

HHS Hilbert-Huang Spectrogram

HHT Hilbert Huang Transform

HM M Hidden Markov Modeling

HSM M Hidden Semi Markov Models

IE Instantaneous energy density

IM F Intrinsic Mode Functions

IRDF Inner race defect frequency

IRDF A Inner race defect frequency amplitude

kN N k Nearest Neighbour

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L₁₀ Rating life associated with 90% reliability

M D Mahalanobis distance

M F CC Mel-Frequency Complex Cepstrum

M QE Mean quantization error

M RL Mean remaining life

M SE Mean square error

M T GS Mahalanobis-Taguchi-Gram-Schmidt

M T S Mahalanobis-Taguchi system

N Distance in terms ofσ to define change in health stage

n Number of consecutive data point verified to avoid outliers

N_b Number of rolling elements

N_{f t} Data Point corresponding to ft (frequency type)

N oise(t) White gaussian noise

O Observed group frequency

OA Orthogonal Array

ORDF Outer race defect frequency

ORDF A Outer race defect frequency amplitude

P value Probability

Pnoise Power of the noise

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P_signal Power of the signal

P CA Principal Component Analysis

P DF Probability density function

P HM Proportional Hazard Modeling

P r Probability of event

Q Total data points in time series

q(t) Radial load distribution

q₀(t) Radial load

q_mean Mean radial load

q_s Amplitude of varying sinusoidal load

q_v Amplitude of variation in mean radial load

R(t) Reliability function

R² Coefficient of determination

R_k Deviation from T_d in the k^th impact

r_n Residual component

RBN Radial basis Neural Network

RM S Root Mean Square

RM SE Root mean square error

RU L Remaining useful life

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SN R Signal to noise ratio

SN R_dB Signal to noise ratio (dB)

SOM Self-organizing map

SV M Support vector machine

t time

T_d0 Exact time of occurrence of the impulse

T_d Reciprocal of defect frequency

T SA Time Synchronous Averaging

U_k Mutually perpendicular vector

W P D Wavelet Packet Decomposition

X Random variable

X(f) Signal in the frequency domain

x(t) Signal in the time domain

Y Time series

Z Z-statistic

Z(t) Analytical signal

Zk Standardized vector

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Data fusion based diagnosis and prognosis of ball bearings

DATA FUSION BASED DIAGNOSIS AND PROGNOSIS OF BALL BEARINGS

PIYUSH SHAKYA

DEPARTMENT OF MECHANICAL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY DELHI

DECEMBER, 2015

DATA FUSION BASED DIAGNOSIS AND PROGNOSIS OF BALL

BEARINGS

PIYUSH SHAKYA

DEPARTMENT OF MECHANICAL ENGINEERING

INDIAN INSTITUTE OF TECHNOLOGY DELHI

DECEMBER, 2015

Srimad Bhagavad Gita, Chapter 2, Verse 47)

You only have the right of performing actions, but never at any time

in their results. You should not be motivated by the results of the performed

actions and never be attached to not doing your Karmas.

This thesis is dedicated to my family

&

To the spirit of detached Karma

CERTIFICATE

ACKNOWLEDGEMENTS

ABSTRACT

CONTENTS

315

LIST OF FIGURES

LIST OF TABLES

NOMENCLATURE AND ABBREVIATIONS