NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Contract No. DE-AC36-08GO28308

Wind Turbine Gearbox Condition 

Monitoring Round Robin Study –

Vibration Analysis

S. Sheng, Editor

National Renewable Energy Laboratory

Technical Report

NREL/TP-5000-54530

July 2012
NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

National Renewable Energy Laboratory

15013 Denver West Parkway

Golden, Colorado 80401

303-275-3000 • www.nrel.gov

Contract No. DE-AC36-08GO28308

Wind Turbine Gearbox Condition 

Monitoring Round Robin Study –

Vibration Analysis

S. Sheng, Editor

National Renewable Energy Laboratory

Prepared under Task No. WE11.0305

Technical Report

NREL/TP-5000-54530

July 2012
NOTICE

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i

Acknowledgements

The National Renewable Energy Laboratory’s (NREL) contributions to this report were funded 

by the Wind and Water Power Program, Office of Energy Efficiency and Renewable Energy of 

the U.S. Department of Energy, under contract No. DE-AC02-05CH11231. The authors are 

solely responsible for any omission or errors contained herein. NREL wishes to acknowledge 

and thank the Office of Energy Efficiency and Renewable Energy and its staff who have 

supported this work from its inception. Specifically, NREL would like to thank Mark Higgins 

and Michael Derby for their support and guidance. 

NREL deeply appreciates the voluntarily support from all sixteen partners of the Wind Turbine 

Gearbox Condition Monitoring Round Robin project. One project partner estimates that the

value of the voluntary support from all partners would be worth $2 to $3 million.
ii

Nomenclature

Acronym Definition

A/D analog to digital

AM amplitude modulation

BPFI ball-passing frequency inner race 

BPFO ball-passing frequency outer race 

BSF ball-spinning frequency 

CF crest factor

CI condition indicator

CM condition monitoring

COE cost of energy

CRB cylindrical roller bearing

DAS data acquisition system

DOD Department of Defense

DOE Department Of Energy 

DSTO Defence Science and Technology Organisation (Australia) 

DTF Dynamometer Test Facility

EO energy operator

fcCRB full complement cylindrical roller bearing

FFT Fast Fourier Transform

FTF fundamental train frequency 

FM frequency modulation 

GE General Electric

GL Germanischer Lloyd 

GRC Gearbox Reliability Collaborative

GMF gear meshing frequency 

HS High speed

HSGM high-speed gear meshing stage

HSIS high-speed intermediate shaft

HSS high-speed shaft

ISGM intermediate speed gear meshing stage

IMS intermediate-speed shaft

IMS Intelligent Maintenance Systems

INT intermediate 

JTFA joint time frequency analysis 
iii

Acronym Definition

LS low speed

LSIS low-speed intermediate shaft

LSS low-speed shaft

MS main shaft

NASA National Aeronautics and Space Administration

NREL National Renewable Energy Laboratory

NWTC National Wind Technology Center

O&M operation and maintenance

PGSF spin frequency of the planetary gear

PLC planet carrier 

PLTGM planetary gear meshing stage

RMS root mean square

RPM revolutions per minute

SER sideband energy ratio

SF severity factor 

SH shaft

SK spectral kurtosis 

SO shaft order

TRB tapered roller bearing

TSA time synchronous averaging 
iv

Executive Summary 

Utility-scale wind turbines have historically experienced premature component failures, which 

subsequently increase the cost of energy. The majority of these failures are caused by faults in 

the drivetrain, led by the main gearbox. To understand the possible causes for gearbox failures 

and recommend practices for improvement, the National Wind Technology Center (NWTC), at

the National Renewable Energy Laboratory (NREL), started a project called the Gearbox 

Reliability Collaborative (GRC). Condition Monitoring (CM) is one research area under the 

GRC. It is a method to assess a system’s health, which enables proactive maintenance planning, 

reduces downtime and operations and maintenance costs, and, to some extent, increases safety.

To understand the dynamic responses of wind turbine gearboxes under different loading 

conditions, the GRC tested two identical gearboxes. One was tested on the NWTC’s 2.5 MW 

dynamometer and the other was first tested in the dynamometer, and then field tested in a turbine 

in a nearby wind plant. In the field, the test gearbox experienced two oil loss events that resulted 

in damage to its internal bearings and gears. Since the damage was not catastrophic, the test 

gearbox was removed from the field and retested in the NWTC’s dynamometer before it was 

disassembled. During the dynamometer retest, various condition monitoring systems, e.g.,

vibration and oil debris, collected data along with testing condition information. The vibrationbased condition monitoring system and the test condition data enabled NREL to launch a Wind 

Turbine Gearbox Condition Monitoring Round Robin project, as described in this report. The 

main objective of this project is to evaluate different vibration analysis algorithms used in wind 

turbine CM and determine whether typical practices are effective. With the involvement of both 

academic researchers and industrial partners, the Round Robin provides cutting edge research 

results to industry stakeholders.

Under this project, the collected vibration and testing condition data, along with the test gearbox 

configuration information, were shared with partners who signed memoranda of understanding 

documents with NREL. The partners were given a time window of two months to analyze the 

shared data using whichever algorithms they had or could develop. Partners did not have prior 

knowledge of the extent or location of the damage in the test gearbox. After their diagnostic 

results were submitted to NREL, the actual damage information on the test gearbox was 

disclosed to them so they could further fine tune their results. The project had sixteen partners, 

including seven universities and nine from the private sector. The main body of this report 

discusses detailed analysis algorithms and diagnostic results from eight of the sixteen partners. 

Below is a brief synopsis for this report: 

• In Chapter 1, the background and objectives of this Round Robin project are presented, 

along with the summary of blind study stage diagnostics results from all sixteen project 

partners. 

• In Chapter 2, the test gearbox, dynamometer test facility, one customized vibration data 

acquisition system, test conditions, and actual damage found on the test gearbox through 

its disassembly are presented. 
v

• In Chapter 3, to overcome the inaccuracy incurred by speed variations, a synchronous 

sampling technique is introduced. To accommodate high gear ratios in wind turbine 

gearboxes, a digital domain synchronous re-sampling technique is presented. 

• In Chapter 4, an evaluation is conducted of analysis algorithms originally developed for 

Department of Defense applications, including the results of these algorithms when 

applied to the GRC wind turbine dataset. The algorithms consist of sensor validation, 

bearing fault detection/isolation, and gear fault detection/isolation modules. A joint time 

frequency analysis is also discussed. 

• In Chapter 5, a validation is presented of analysis algorithms that are used in the 

aerospace community for the wind industry. The focus is on two methodologies: 

synchronous analysis of shaft/gear components and non-synchronous analysis of 

bearings. 

• In Chapter 6, various vibration signal processing and feature extraction algorithms are 

evaluated. It details the evaluated methods including frequency domain, cepstrum, 

bearing envelope analysis, spectral kurtosis filtering, time synchronous averaging, and a 

planet separation method. 

• In Chapter 7, sideband pattern analysis is performed on all gears for gear fault diagnosis. 

Data from torque measurements have also been analyzed to facilitate annulus gear 

diagnosis. For the bearing diagnosis, a multi-scale enveloping spectra technique is 

investigated.

• In Chapter 8, analysis of “jerk” data derived from vibration acceleration data of the test 

wind turbine gearbox are discussed. For component failure identification, the correlation 

coefficient analysis and clustering analysis are applied to identify the failure stage of the 

gearbox in the time domain.

• In Chapter 9, the algorithms for bearing diagnostics are presented. They consist of several 

different stages to separate and enhance the bearing signals, and then envelope analysis is 

applied. For parallel stage gear diagnostics, classic synchronously-averaged signatures 

are studied and comparisons are made of spectra and cepstra from the healthy and faulty 

conditions. For individual planet and sun gear diagnostics, the premium current method is

investigated. 

• In Chapter 10, a two stage fault detection framework, with analytical and graphical 

analysis for wind turbine gearbox CM, is proposed. The analytical diagnostics and 

graphical analysis are performed for fault detection and defect severity level evaluation of 

different damage modes based on sideband and kurtosis analyses. 

• In Chapter 11, some recommended practices for data acquisition and data analysis are 

described for use in conducting vibration-based wind turbine drivetrain condition 

monitoring. 

It is worth noting that the synopses detailed for Chapters 3-10 were based on the analysis 

algorithms of the project's partners. Detailed diagnostic results obtained by each partner are 

listed in this report.
vi

The study has demonstrated that the wind industry can improve vibration analysis algorithms for 

drivetrain condition monitoring. Both the presented algorithms and the recommended practices 

can be considered by CM equipment suppliers in their future product releases for the benefit of 

the wind industry.
vii

Table of Contents

Acknowledgements ..................................................................................................................................... i

Nomenclature .............................................................................................................................................. ii

Executive Summary................................................................................................................................... iv

1 Introduction............................................................................................................................................ 1

2 Tests and Actual Gearbox Damage ..................................................................................................... 3

2.1 Test Article ............................................................................................................................... 3

2.2 Dynamometer Test Facility ...................................................................................................... 6

2.3 One Customized Vibration Data Acquisition System............................................................... 7

2.4 Test Conditions ........................................................................................................................ 9

2.5 Actual Gearbox Damage........................................................................................................ 10

3 Analysis Algorithms and Diagnostics Results from General Electric ........................................... 12

3.1 Fundamentals......................................................................................................................... 12

3.2 Round Robin Analysis Results............................................................................................... 19

3.3 Discussions ............................................................................................................................ 32

4 Combining Novel Approaches with Proven Algorithms for Robust Wind Turbine Gearbox Fault 

Detection .................................................................................................................................... 34

4.1 Introduction............................................................................................................................. 34

4.2 Algorithm Overview ................................................................................................................ 34

4.3 Results Summary................................................................................................................... 38

4.4 Lessons Learned and Conclusions........................................................................................ 48

5 Analysis Algorithms and Diagnostics Results from NRG Systems ............................................... 49

5.1 Introduction............................................................................................................................. 49

5.2 Analysis Algorithms................................................................................................................ 49

5.3 Analysis Results ..................................................................................................................... 52

5.4 Discussion.............................................................................................................................. 56

6 Review and Application of Methods and Algorithms in Wind Turbine Gearbox Fault Detection58

6.1 Introduction............................................................................................................................. 58

6.2 Signal Processing and Feature Extraction Methods .............................................................. 58

6.3 Summary of Results............................................................................................................... 80

6.4 Conclusions and Future Work................................................................................................ 82

7 Defect Diagnosis in Wind Turbine Gearbox basd on Sideband Energy and Enveloping Spectral 

Analysis...................................................................................................................................... 83

7.1 Introduction............................................................................................................................. 83

7.2 Algorithms .............................................................................................................................. 83

7.3 Results ................................................................................................................................... 84

7.4 Lessons Learned.................................................................................................................... 90

8 Fault Analysis of a Wind Turbine Gearbox: A Data Driven Approach ........................................... 91

8.1 Introduction............................................................................................................................. 91

8.2 Methodologies ........................................................................................................................ 91

8.3 Results ................................................................................................................................... 93

8.4 Conclusion and Discussion .................................................................................................... 97

9 Techniques for Separation and Enhancement of Various Components in the Analysis of Wind 

Turbine Vibration Signals......................................................................................................... 98

9.1 Introduction............................................................................................................................. 98

9.2 Algorithms .............................................................................................................................. 99

9.3 Results ................................................................................................................................. 105

9.4 Discussion, Conclusions, Lessons Learned ........................................................................ 122

10 A Two Stage Fault Detection Framework for Wind Turbine Gearbox Condition Monitoring..... 124

10.1 Introduction........................................................................................................................... 124

10.2 Vibration Based Condition Monitoring Framework............................................................... 124

10.3 Analytical Diagnostics .......................................................................................................... 126

10.4 Graphical Diagnostics .......................................................................................................... 129

10.5 Results ................................................................................................................................. 130
viii

11 Recommended Practices .................................................................................................................. 132

11.1 Data Acquisition ................................................................................................................... 132

11.2 Data Analysis ....................................................................................................................... 133

Appendix A – Project Partners .............................................................................................................. 135

References............................................................................................................................................... 136

List of Figures

Figure 1.1. Blind study stage diagnostics results comparison ........................................................ 2

Figure 2.1. GRC test turbine ........................................................................................................... 3

Figure 2.2. GRC gearbox internal components view...................................................................... 4

Figure 2.3. GRC gearbox internal nomenclature and abbreviations............................................... 4

Figure 2.4. GRC gearbox layout and bearing nomenclature .......................................................... 5

Figure 2.5. Diagram of NREL 2.5 MW dynamometer test facility ................................................ 7

Figure 2.6. NREL dynamometer test stand with the test article installed....................................... 7

Figure 2.7. Vibration data acquisition system sensor locations...................................................... 8

Figure 2.8. Physical sensor installation........................................................................................... 9

Figure 2.9. Test gearbox high speed stage gear damage............................................................... 11

Figure 3.1. Synchronous sampling – analog approach ................................................................. 13

Figure 3.2. Synchronous sampling– digital approach................................................................... 14

Figure 3.3. Time synchronous averaging...................................................................................... 14

Figure 3.4. Synthesized tachometer generation from speed function........................................... 16

Figure 3.5. Analog devices-based approach ................................................................................. 18

Figure 3.6. Digital processing-based approach............................................................................. 19

Figure 3.7. Gearbox power flow................................................................................................... 19

Figure 3.8. HSGM (22) modulated by HSS (1)............................................................................ 23

Figure 3.9. HSGM X2 (44) modulated by HSS (1)...................................................................... 24

Figure 3.10. HSGM X3 (66) modulated by HSS (1).................................................................... 24

Figure 3.11. HSGM (22) modulated by HSIS (0.25).................................................................... 25

Figure 3.12. HSGM X2 (44) modulated by HSIS (0.25).............................................................. 25

Figure 3.13. HSGM X2 (66) modulated by HSIS (0.25).............................................................. 26

Figure 3.14. ISGM and higher order harmonics........................................................................... 26

Figure 3.15. Planetary gear stage meshing order and harmonics from AN4................................ 27

Figure 3.16. PLTGM X3 modulated by planet passing order (0.037).......................................... 28

Figure 3.17. Planetary gear stage meshing order and harmonics from AN3................................ 28

Figure 3.18. PLTGM X3 and X4 modulated by planet passing order (0.037) ............................. 29

Figure 3.19. Sensor AN3 acceleration enveloping order spectrum .............................................. 29

Figure 3.20. Modulation by LSIS in PLTGM is very small ......................................................... 30

Figure 3.21. Envelope spectrum of AN7 ...................................................................................... 31

Figure 3.22. Zoomed envelope spectrum of AN7......................................................................... 31

Figure 3.23. Possible bearing D BPFI .......................................................................................... 32

Figure 4.1. False alarm caused by faulty sensor........................................................................... 35

Figure 4.2. ImpactEnergy overview.............................................................................................. 36

Figure 4.3. GearMod overview..................................................................................................... 37

Figure 4.4. Example JTFA approach (short time Fourier transform)........................................... 38

Figure 4.5. High speed gear fault evidence, blind results (AN6) ................................................. 40
ix

Figure 4.6. High speed gear fault evidence, blind results (AN7) ................................................. 40

Figure 4.7. Intermediate speed downwind bearing fault evidence, blind results (AN6, 

Data 2b)............................................................................................................................. 41

Figure 4.8. Intermediate speed downwind bearing fault evidence, blind results.......................... 42

Figure 4.9. Sun pinion gear fault evidence, blind results.............................................................. 43

Figure 4.10. JTFA speed gear fault evidence, blind results.......................................................... 44

Figure 4.11. Intermediate speed upwind bearing damage evidence ............................................. 45

Figure 4.12. Intermediate speed upwind bearing fault evidence, post-inspection results ............ 46

Figure 4.13. High speed downwind bearing fault evidence, revisited (Data 2a).......................... 47

Figure 4.14. High speed downwind bearing fault evidence, revisited (Data 2c).......................... 47

Figure 5.1. Generation of the TSA and selected CIs .................................................................... 51

Figure 5.2. Process for generating gear CIs.................................................................................. 52

Figure 5.3. Synthetic tachometer .................................................................................................. 53

Figure 5.4a. HSS TSA/spectrum................................................................................................... 53

Figure 5.4b. HSS gear analysis..................................................................................................... 53

Figure 5.5a. TSA intermediate shaft............................................................................................. 54

Figure 5.5b. Intermediate speed pinion, where the units for the Energy Operator, Narrowband 

and Amplitude Modulation analysis are in G’s, and the Frequency Modulation analysis 

is in radians. ...................................................................................................................... 54

Figure 5.6a. Sun gear .................................................................................................................... 55

Figure 5.6b. Planet gears............................................................................................................... 55

Figure 5.7. Ring gear .................................................................................................................... 55

Figure 5.8a. High speed shaft, downwind side ............................................................................. 56

Figure 5.8b. Intermediate speed shaft downwind side.................................................................. 56

Figure 5.9. Low speed shaft downwind side................................................................................. 56

Figure 6.1. Vibration spectrum - Case C: top plot - AN7 baseline; bottom plot - AN7 degraded 

gearbox.............................................................................................................................. 61

Figure 6.2. Sideband ratio gear features - Case C: (a) Low speed shaft pinion; (b) High speed 

shaft gear; (c) High speed shaft pinion ............................................................................. 63

Figure 6.3. Real cepstrum - Case C: top plot - AN7 baseline; bottom plot - AN7 degraded 

gearbox.............................................................................................................................. 64

Figure 6.4. Cepstrum peak features from Case C: blue – baseline; red - degraded gearbox........ 64

Figure 6.5. Cepstrum health Indicator for Case C calculated for high speed shaft gear and 

pinion ................................................................................................................................ 65

Figure 6.6. Bearing envelope analysis flow chart......................................................................... 66

Figure 6.7. Envelope spectrum - Case C: (a) AN6 - peaks at BPFI for ISS upwind bearing and 

HSS downwind bearing; (b) AN7 - BPFI peak for HSS downwind bearing.................... 67

Figure 6.8. Envelope spectrum accelerometer AN10 - Case C: (a) band-pass filter from 9500 

Hz - 10,500 Hz, peaks at BPFO and 2X BPFO for ISS downwind bearing; (b) band pass 

filter from 4000 Hz - 6000 Hz, peak at BPFO for planet carrier upwind bearing and also 

peak at 2X BPFO for ISS downwind bearing................................................................... 67

Figure 6.9. (a) Wiener filter based on spectral kurtosis; (b) raw and filtered AN4 accelerometer 

signal – Case A ................................................................................................................. 69

Figure 6.10. Filtered AN4 signal showing the periodic repetition based on 2 revolutions of the 

carrier – Case A ................................................................................................................ 69

Figure 6.11. Kurtosis of filtered signal - shown for all 3 cases.................................................... 70
x

Figure 6.12. TSA signal and residual signal from accelerometer AN7 - Case C: top plot - TSA 

signal for high speed shaft pinion; bottom plot - residual signal for high speed shaft 

pinion ................................................................................................................................ 72

Figure 6.13. TSA vibration spectrum for accelerometer AN7 and high speed shaft - Case C..... 72

Figure 6.14. TSA signal and residual signal from accelerometer AN3 - Case C: top plot - TSA 

signal for ring gear; bottom plot - residual signal for ring gear........................................ 73

Figure 6.15. High speed pinion amplitude and phase modulation signal from accelerometer 

AN7 - Case C: top plot - Time Synchronous Average; middle plot - amplitude 

modulation signal; bottom plot - phase modulation signal.............................................. 74

Figure 6.16. Ring gear amplitude and phase modulation signal from accelerometer AN3 - Case 

C: top plot - TSA; middle plot - amplitude modulation signal; bottom plot - phase 

modulation signal.............................................................................................................. 75

Figure 6.17. Flow chart for planet separation algorithm .............................................................. 76

Figure 6.18. Narrow band amplitude modulation signal for determining planet passing –

Case C............................................................................................................................... 77

Figure 6.19. Example Tukey window used for planet separation algorithm - in this study, Nv

was set to 3 to include 3 mesh periods.............................................................................. 77

Figure 6.20. Top - TSA signal for Planet 2; bottom - residual signal for Planet 2 – Case C ....... 78

Figure 6.21. TSA vibration spectrum for Planet 2 – Case C ........................................................ 78

Figure 6.22. Top - TSA signal for sun gear; bottom - residual signal for sun gear – Case C....... 79

Figure 6.23. Planet Gear 2 amplitude and phase modulation signal from accelerometer AN3 – 

Case C: top plot – TSA; middle plot - amplitude modulation signal; bottom plot -

phase modulation signal.................................................................................................... 80

Figure 7.1. Locations of defective components in the gearbox assembly .................................... 84

Figure 7.2. Comparison analysis between test data and reference data for HS_Pinion and 

INT_Pinion ....................................................................................................................... 85

Figure 7.3. Comparison analysis between test data and reference data for Annulus_Gear and 

Sun_Gear........................................................................................................................... 86

Figure 7.4. Time series of torque data under 1200 rpm................................................................ 87

Figure 7.5. The envelope spectrum of torque data under 1200 rpm............................................. 88

Figure 7.6. Wavelet enveloping spectrum of sensor AN3 at 1,800 rpm....................................... 88

Figure 7.7. Wavelet enveloping spectrum of sensor AN6 at 1,800 rpm....................................... 89

Figure 8.1. Run chart of maximum rate of speed ......................................................................... 94

Figure 8.2. Bar char of R .............................................................................................................. 94

Figure 8.3. RMS across 12 sensors - Case 2b............................................................................... 96

Figure 8.4. Crest factor across 12 sensors - Case 2b .................................................................... 97

Figure 8.5. Kurtosis across 12 sensors - Case 2b.......................................................................... 97

Figure 9.1. Signal processing approach pre release of inspection report.................................... 100

Figure 9.2. Reference (speed) signal extraction stages: (a) identifying a separable band; (b) 

extracting the band into a new buffer; (c) inversing the transform signal b into the time 

domain [60]..................................................................................................................... 101

Figure 9.3. HSS estimates: Top - data 2a:5; Bottom - data 2c:5 ................................................ 102

Figure 9.4. Synchronously averaged signals from sensor 3, data 2a:5....................................... 103

Figure 9.5. Synchronously averaged signals from sensor 3, Data 2c:5 ...................................... 104

Figure 9.6. Schematic diagram of the cepstral method for removing selected families of 

harmonics and/or sidebands from time signals [57] ....................................................... 105
xi

Figure 9.7. Squared envelope spectrum for data 2_a_10 sensor 7.............................................. 106

Figure 9.8. Squared envelope spectrum for data 2_c_10 sensor 7.............................................. 106

Figure 9.9. Zoom-in around the BPFI. Harmonic cursors for the ISS........................................ 107

Figure 9.10. Squared envelope spectrum for data 2_a_5 sensor 8 showing the BPFI of bearing 

NU2220........................................................................................................................... 108

Figure 9.11. Squared envelope spectrum for data 2_a_5 sensor 8 showing the FTF harmonics 

of bearing NU2220 ......................................................................................................... 108

Figure 9.12. Squared envelope spectrum of data 2c_5 sensor 6 showing the shaft speed (30.06 

Hz), what appears as 2×BPFO for bearing 32032X and the BPFI for bearing NU2220 109

Figure 9.13. Power spectrum density comparison of the high speed data through sensor 5 ...... 110

Figure 9.14. Residual of signal 2a_5 sensor 5 ............................................................................ 111

Figure 9.15. Squared envelope spectrum of the residual signal shown in Figure 9.14 .............. 111

Figure 9.16. Spectrum comparison using the data from sensor 3............................................... 113

Figure 9.17. Cepstrum comparison using the data from sensor 3............................................... 113

Figure 9.18. Spectrum comparison using the data from sensor 5............................................... 114

Figure 9.19. Cepstrum comparison using the data from sensor 5............................................... 114

Figure 9.20. Spectrum comparison using the data from sensor 6............................................... 115

Figure 9.21. Spectrum comparison using the data from sensor 6............................................... 115

Figure 9.22. Cepstrum comparison using the data from sensor 6............................................... 116

Figure 9.23. Spectrum comparison using the data from sensor 7............................................... 117

Figure 9.24. Time records from the averaged ISS signals: (a) original, including four rotations of 

the HSS; (b) Residual after removal of the HSS average. .............................................. 118

Figure 9.25. Spectra of signals of Figure 9.24: (a) original including four rotations of the HSS; 

(b) residual after removal of the HSS average................................................................ 118

Figure 9.26. Whitened synchronously averaged signals corresponding to the periods of all major 

gear components in the gearbox, which enhance local faults......................................... 119

Figure 9.27. Phase shifts for separated sun gear averages.......................................................... 120

Figure 9.28. Sun Gear – residual of DSTO average data set 2c (high speed, high load) ........... 120

Figure 9.29. Sun Gear – residual of DSTO average data set 2a (low speed, low load).............. 121

Figure 9.30. Residual signals for the three planet gears............................................................. 121

Figure 9.31. Average for the annulus gear.................................................................................. 122

Figure 10.1. Vibration based condition monitoring approach .................................................... 125

Figure 10.2. HSS downwind bearing BPFO – graphical analysis.............................................. 130

List of Tables

Table 2.1. Gear element dimensions and detail .............................................................................. 5

Table 2.2. Bearing type, number, and location............................................................................... 6

Table 2.3. Sensor notations and descriptions.................................................................................. 8

Table 2.4. Test conditions............................................................................................................. 10

Table 2.5. Actual damage on the test gearbox.............................................................................. 10

Table 3.1. Gear damage features................................................................................................... 20

Table 3.2. Bearing damage features.............................................................................................. 21

Table 3.2. Bearing damage features (continued) .......................................................................... 22

Table 4.1. Select gear diagnostic feature definitions.................................................................... 37

Table 4.2. Initial blind results summary ....................................................................................... 39
xii

Table 4.3. Post-inspection results summary ................................................................................. 45

Table 6.1. Summary of evaluated methods – advantages and disadvantages............................... 60

Table 6.2. Frequency domain gear features.................................................................................. 62

Table 6.3. Summary of results for each algorithm with the following notation: L-low 

confidence, M-medium confidence, H-high confidence, NA –not applicable or 

evaluated; black - indicates a method that was evaluated before the failure report, 

blue - indicates a method that was evaluated after the failure report .......................... 81

Table 7.1. Sideband energy comparison between new gearbox and gearbox at the end of service 

life ............................................................................................................................... 87

Table 7.2. Comparison between the analysis result and the actual damage of a tested gearbox.. 89

Table 8.1. Correlation coefficient analysis of the mean of jerk data: Case 2b ............................. 95

Table 8.2. Correlation coefficient analysis of the mean of jerk data: Case 2c ............................. 95

Table 8.3. Clustering based classification..................................................................................... 96

Table 10.1. Procedure for vibration data preprocessing ............................................................. 125

Table 10.2. Sensor and component relationship ......................................................................... 126

Table 10.3. Procedure for analytical diagnostics........................................................................ 126

Table 10.4. Sideband-based severity definition.......................................................................... 127

Table 10.5. Severity factor analysis of sensor AN 6 for Case 2a ............................................... 128

Table 10.6. Vibration-based condition monitoring results ......................................................... 130
1

1 Introduction

Wind energy is currently the fastest growing type of renewable energy resource in the world [1]. 

However, the industry still experiences premature component failures, which increase operation

and maintenance (O&M) costs, and subsequently, the cost of energy (COE) for wind power. As 

turbines increase in size and are installed offshore, these failures will become even more costly.

To make wind power more competitive, there is a need for the industry to improve turbine 

reliability and availability. 

Given that the gearbox is the most costly drivetrain component to maintain throughout the

expected 20-year design life of a wind turbine, the National Renewable Energy Laboratory 

(NREL) organized a consortium called the Gearbox Reliability Collaborative (GRC) to address 

the gearbox reliability and availability challenges. The GRC engages key representatives in the 

wind turbine gearbox supply chain, including turbine owners, operators, gearbox manufacturers, 

bearing manufacturers, lubricant companies, and wind turbine manufacturers. The GRC's goals

are to conduct research that improves gearbox reliability and increases turbine availability. The 

GRC engages a multi-track approach, which includes modeling and analysis, dynamometer 

testing, field testing, condition monitoring (CM), and developing a gearbox failure database [2]. 

CM is a method to assess a system’s health, which enables proactive maintenance planning, 

reduces downtime and operations and maintenance costs, and, to some extent, increases safety

[3]. It will be the main focus of this report. 

The GRC uses two identical test gearboxes: one was tested on NREL’s 2.5 MW dynamometer;

the other was first tested in the dynamometer, and then field tested in a turbine in a nearby wind 

plant. In the field, the test gearbox experienced two oil loss events that resulted in damage to its 

internal bearings and gears. Additional field tests of this gearbox were terminated to prevent 

further damage to the gearbox. From the CM point of view, however, it provided a unique 

opportunity to evaluate different monitoring techniques by retesting the gearbox in NREL’s

dynamometer under controlled testing conditions. The gearbox was removed from the field and 

retested in the NREL’s 2.5 MW dynamometer before it was disassembled. During the 

dynamometer retest, various condition monitoring systems data were collected, e.g., vibration 

and oil debris, along with testing condition information. The vibration-based condition 

monitoring system and the test condition data enabled NREL to launch the Wind Turbine 

Gearbox Condition Monitoring Round Robin (Round Robin) project that involves the analysis of 

the collected vibration data by several independent research partners and then draws 

conclusions from the comparison of their analysis results.

The main objective of the CM Round Robin project was to evaluate different vibration analysis 

algorithms used in wind turbine CM and to determine whether typical practices are effective. 

Another project objective was to assess the capability of vibration-based CM and to establish a 

baseline from which future improvements can be measured. With the involvement of both 

academic researchers and industrial partners, the Round Robin provides cutting edge research 

results to industry stakeholders.

In the project, the collected vibration and testing condition data, along with the test gearbox 

configuration information, were shared with partners who signed memorandum of understanding 
2

documents with NREL. The partners were given a time window of two months to analyze the 

shared data using whichever algorithms they had or could develop. Partners did not have prior 

knowledge of the actual damage within the test gearbox. After their diagnostics results were 

submitted to NREL, the actual damage information within the test gearbox was disclosed to 

them, so they could further fine tune their results. The project had sixteen partners, including 

seven universities and nine from the private sector. The main body of this report discusses 

detailed analysis algorithms and diagnostics results from eight of the sixteen partners. (For a list 

of partners, see Appendix A.)

The project is unique since the initial diagnostic results from the partners were obtained during a

blind study. Also, the test gearbox did not begin with seeded faults, as have been investigated in 

many other studies. Based on the particulars of the actual damage found after the test gearbox 

was disassembled [4], all of the partners agreed that seven damage instances could be detected 

through vibration analysis. These damage instances were chosen as the reference for the partners' 

diagnostics performance evaluation. The evaluation criteria included successful identifications, 

false alarms, and missed detections. A comparison of the results, without the partners' names is 

illustrated in Figure 1.1. The chart depicts the highest ratio of successful identification as five of 

the seven damage instances. Most partners had more missed detections than false alarms. Thus, 

there is room for the industry to improve vibration-based diagnostic algorithms. Most of the

Round Robin study partners agreed that this project was a valuable effort. 

Figure 1.1. Blind study stage diagnostics results comparison

The next chapter of this report describes the test gearbox configuration, its customized data 

acquisition system, test conditions, and actual damage information obtained during the test 

gearbox disassembly. The main body of the report contains a detailed presentation of the analysis 

algorithms and diagnostic results from eight out of the sixteen research partners. Finally, the 

report concludes with some recommended practices for conducting vibration-based wind turbine 

drivetrain CM.
3

2 Tests and Actual Gearbox Damage

The test gearbox, dynamometer test facility, one customized vibration data acquisition system, 

test conditions, and actual damage found on the test gearbox through its disassembly are 

presented in this chapter. 

2.1 Test Article 

The GRC test turbine drivetrain (Figure 2.1) is designed for a stall-controlled, three-bladed,

upwind turbine, with a rated power of 750kW. The turbine generator operates at 1800 rpm and 

1200 rpm nominal, on two different sets of windings, depending on the wind conditions. 

The gearbox under test was one of two units, which were originally taken from the field and 

redesigned, rebuilt and instrumented with more than 125 sensors. The gearbox first finished its 

run-in in the NREL dynamometer test facility and later was sent to a wind plant located near to 

NREL for field tests, where two oil loss events occurred while the turbine was being tested. The 

gearbox has an overall ratio of 1:81.491. It is composed of one low speed (LS) planetary stage 

and two parallel stages, as shown in the expanded view in Figure 2.2. Nomenclature for the 

internal elements is described in Figure 2.3, and the gear dimensions, teeth number, and helix 

angles are listed in Table 2.1.

Figure 2.1. GRC test turbine

Generator

Hub

Main 

Bearing

Main 

Shaft

Brake

Generator 

Shaft

Gearbox

Bed Plate
4

Figure 2.2. GRC gearbox internal components view

Figure 2.3. GRC gearbox internal nomenclature and abbreviations

Annulus

Planet

Sun

Gear

Gear Pinion

Pinion

PLC

Low Speed Stage

LS-ST

High Speed Stage

HS-ST

Intermediate Speed Stage

IMS-ST

Low Speed Shaft

LS-SH

Intermediate Speed 

Shaft

IMS-SH

High Speed Shaft 

HS-SH
5

Table 2.1. Gear element dimensions and detail

Gear Element No. of 

Teeth

Mate 

teeth

Root 

diameter 

(mm)

Helix 

angle

Face 

width 

(mm)

Ratio

Ring gear 99 39 1047 7.5L 230

Planet gear 39 99 372 7.5L 227.5

Sun pinion 21 39 186 7.5R 220 5.71

Intermediate gear 82 23 678 14R 170

Intermediate pinion 23 82 174 14L 186 3.57

HSS gear 88 22 440 14L 110

HSS pinion 22 88 100 14R 120 4.0

Overall: 81.49

Several bearing types are employed in the gearbox, according to the loading conditions and 

gearbox life requirements. The planet carrier is supported by two full-complement cylindrical 

roller bearings (fcCRB) and each planet gear is supported by two identical cylindrical roller 

bearings (CRB). Each parallel shaft in the gearbox is supported by a CRB on the upwind side of 

the assembly, and by two back-to-back mounted, tapered roller bearings (TRB) on the downwind 

side. Table 2.2 provides the location and bearing manufacturer part number of all bearings in the 

gearbox. Location and shaft designations are as noted in Figure 2.4. The letter following the 

abbreviation indicates the position of the bearing according to the component from upwind (A) 

to downwind (B, C). Lubrication oil is another important component in the test gearbox, 

although it is not shown in either Table 2.2 or Figure 2.4. 

Figure 2.4. GRC gearbox layout and bearing nomenclature

PLC-A PLC-B

LSS-A LSS-B LSS-C

PL-A PL-B

ISS-A ISS-B ISS-C

HSS-A HSS-B HSS-C Annulus

Planet

Sun

Gear

Gear Pinion

Pinion
6

Table 2.2. Bearing type, number, and location

Location Location

Designation Type Provider Part Number 

Planet carrier PLC-A fcCRB INA SL 18 1892 E

PLC-B fcCRB INA SL 18 1880 E

Planet PL-A CRB FAG NJ 2232 E.M1.C3

PL-B CRB FAG NJ 2232 E.M1.C3

Low Speed Shaft

LS-SH-A fcCRB INA SL 18 1856E

LS-SH-B TRB SKF 32948

LS-SH-C TRB SKF 32948

Intermediate Speed Shaft

IMS-SH-A CRB FAG NU 2220 E.M1.C3

IMS-SH-B TRB SKF 32032 X

IMS-SH-C TRB SKF 32032 X

High Speed Shaft

HS-SH-A CRB FAG NU 2220 E.M1.C3

HS-SH-B TRB SKF 32222 J2

HS-SH-C TRB SKF 32222 J2

The operating gear mesh and bearing characteristic frequencies can be determined by the project 

partners, based on the data shown in Tables 2.1 and 2.2, along with catalogue information from 

bearing suppliers. 

2.2 Dynamometer Test Facility 

The retest of the damaged gearbox was conducted in the NREL 2.5 MW dynamometer test 

facility (DTF), which conducts performance and reliability tests on wind turbine drivetrain 

prototypes and commercial machines [5,6]. The facility is capable of providing static, highly 

accelerated life and model-in-the-loop tests. The prime movers of the dynamometer are a 2.5

MW induction motor, a three-stage epicyclical reducer, and a variable-frequency drive, with full 

regeneration capacity. The rated torque provided by the dynamometer to a test article can be up 

to 1.4 meganewton meters (MNm), with speeds varying from 0 rpm to 16.7 rpm. Non-torque 

loading actuators, rated up to 440 kilonewtons (kN) for radial load and 156kN for thrust load, 

also can be utilized in the dynamometer to apply thrust, bending, and shear loads similar to those 

typically generated by a wind turbine rotor. Figure 2.5 provides a diagram of the test facility. 

Figure 2.6 is a photo of the test implementation, with the test gearbox installed. The complete 

nacelle and drivetrain was installed in the NREL DTF and hard fixed to the floor, without the 

hub, rotor, yaw bearing, or yaw drives. The actual field controller was used to provide start-up 

and system safety response.
7 

Figure 2.5. Diagram of NREL 2.5 MW dynamometer test facility

Figure 2.6. NREL dynamometer test stand with the test article installed. NREL/PIX #16913.

2.3 One Customized Vibration Data Acquisition System 

During the dynamometer retest of the damaged gearbox, the data for this Round Robin project 

was collected by a vibration data acquisition system (DAS) customized by NREL. It is composed 

of twelve accelerometers. Low speed shaft torque and generator speed were recorded, in addition 

to the accelerometer data. The HSS speed measurement was obtained by an optical encoder. For 
8

simplicity of implementation, data was collected at 40 kHz per channel using a National 

Instruments PXI -4472B high speed DAS. 

The accelerometers mounting locations are illustrated in Figure 2.7, with sensor labels and 

descriptions given in Table 2.3. The mounting locations were chosen to reflect typical sensor 

placement practices seen in commercial wind turbine drivetrain vibration-based condition 

monitoring systems. The physical installation of these accelerometers is shown in Figure 2.8.

Figure 2.7. Vibration data acquisition system sensor locations

Table 2.3. Sensor notations and descriptions 

Sensor Label Description

AN1 Main bearing radial

AN2 Main bearing axial

AN3 Ring gear radial 6 o’clock

AN4 Ring gear radial 12 o’clock

AN5 LSS radial

AN6 ISS radial

AN7 HSS radial

AN8 HSS upwind bearing radial

AN9 HSS downwind bearing radial

AN10 Carrier downwind radial

AN11 Generator drive end radial

AN12 Generator non-drive end axial
9

 a) AN1, AN2, AN3, and AN4 (From left to right, NREL/PIX #19589, 19590, 19588, 19587)

 b) AN5, AN6, AN7, and AN8 (From left to right, NREL/PIX #19591, 19592, 19594, 19593)

 c) AN9, AN10, AN11, and AN12 (From left to right, NREL/PIX #19595, 19598, 19597, 19596)

Figure 2.8. Physical sensor installation

2.4 Test Conditions

The vibration data was collected under the test conditions shown in Table 2.4. The highest test 

load applied was 50% of rated power to reduce the chances of a catastrophic gearbox failure. 

Under each test condition, ten minutes of data was collected and broken into 10 separate files,

each containing one minute of test data. In total, thirty data files from three test conditions were 

shared with the project partners. 
10

Table 2.4. Test conditions 

Test Case LSS Speed

(rpm)

Nominal HSS Speed

(rpm)

Electric Power 

(% of rated)

Duration 

(min)

CM_2a 14.72 1200 25% 10

CM_2b 22.09 1800 25% 10

CM_2c 22.09 1800 50% 10

2.5 Actual Gearbox Damage 

After the dynamometer retest, the gearbox was sent to a rebuild shop, where it was disassembled

and a detailed failure analysis [4] was conducted. A complete list of actual damage found 

through the failure analysis is given in Table 2.5. For example, the high speed stage gear damage

in Figure 2.9 shows clear scuffing marks. 

Table 2.5. Actual damage on the test gearbox

Damage # Instances Mode

1 HSS Gear Set Scuffing 

2 HSS Downwind Bearings Overheating 

3 ISS Gear Set Fretting Corrosion 

Scuffing 

Polishing Wear 

4 ISS Upwind Bearing Assembly damage 

 Plastic deformation 

Scuffing 

False brinelling 

Debris dents 

Contact Corrosion 

5 ISS Downwind Bearings Assembly damage 

Plastic deformation 

Dents 

6 Annulus/Ring Gear, or Sun Pinion Scuffing and polishing 

Fretting Corrosion 

7 Planet Carrier Upwind Bearing Fretting Corrosion 

8 Sun Pinion Thrust Rings Fretting Corrosion

Adhesive Wear

9 Oil Transfer Ring for Planet Carrier Polishing 

10 LSS Seal Plate Scuffing 

11 LSS Downwind Bearings Abrasion 

12 HSS Shaft Misalignment 
11

Figure 2.9. Test gearbox high speed stage gear damage. NREL/PIX #19599.

The root cause of the faults was assembly damage and oil starvation resulting from the two oil 

loss events in the field test. Among the 12 damaged items listed in Table 2.5, the consensus 

reached among the sixteen Round Robin partners was that the first seven should be detectable by 

vibration analysis. Damage 12 could potentially be detected by vibration analysis as well, but 

most partners considered it to be an operational condition and not damage. Therefore, the first 

seven damage instances were used as references for performance evaluations of the partner's

diagnostic results, as discussed in the introduction chapter of this report. The task for the partners 

was to diagnose possible internal component damage of the test gearbox based on the shared 

vibration, rpm, and torque data. As the project progressed, each of the partners recognized that 

some baseline data collected from a healthy test gearbox would be beneficial. Therefore, 

vibration spectrum data collected by several accelerometers mounted on the test gearbox, when it 

was considered healthy, were later shared with the project partners. The following report sections

were submitted by eight out of the sixteen partners who took part in the CM study.
12

3 Analysis Algorithms and Diagnostics Results from General 

Electric 

Huageng Luo*, Charles Hatch, Matthew Kalb, Jesse Hanna, Adam Weiss

General Electric Energy *

Corresponding Author Email: luoh@ge.com

3.1 Fundamentals 

Solutions provided by the General Electric (GE) Energy Team are mainly based on order 

analysis to accommodate the constant speed variations in a wind farm. For gear damage 

detection, the sideband distributions were used to estimate the gear meshing condition and a 

sideband energy ratio was used to qualitatively evaluate the gear damage. For early bearing 

damage detection, the acceleration enveloping detection technique was used.

In the wind farm, the wind speed is not predictable, thus many wind turbines are operated at 

variable speed. As a result, the gearbox operational speed is constantly changing. Due to this 

kind of speed variation, a direct application of the conventional Fast Fourier Transform (FFT) 

will not result in accurate gearbox condition features, especially those features extracted from 

high frequency response, such as acceleration enveloping analysis techniques [7,8]. On the other 

hand, to improve the energy extraction efficiency, the wind turbine rotor speed has to be geared 

up about two orders of magnitude before being used to drive the generator shaft. Because of the 

high gear ratio, a very high-count encoder is needed. For example, in a 1.5 MW wind turbine, 

the ratio between the high-speed gear meshing frequency and the rotor frequency can easily be 

greater than 1500. 

To overcome these difficulties, the GE team utilized a series of signal processing techniques, 

such as synchronous sampling, synchronous analysis, digital domain encoder synthesizing, 

acceleration enveloping analysis, and sideband energy ratio (SER), in the data processing and 

damage feature extractions. 

3.1.1 Synchronous Sampling

For rotating machinery, vibrations may occur at multiples and submultiples of the shaft speed. 

For example, if the shaft is rotating at 3600 rpm, which is 60 Hz, then the vibration response at 

multiples of this frequency, and sometimes fractions of this frequency, can be seen. These 

multiples are called orders (or harmonics in musical terms). The general relationship between the 

order (O), the shaft speed (RPM), and the frequency (f) in Hz is

60

O RPM f × = (1)

If the rotating speed is fixed, a regular FFT analysis can have the desired results. However, if the 

rotor speed changes within the time window of data acquisition, the variation of the rotor speed 

will cause the fundamental order and harmonics in the frequency domain to be smeared into 

multiple frequency bins. On the other hand, the frequency of interest may not always be right at 

a bin, depending on the resolution of the frequency analysis. The signal energy has to be split 

into neighboring bins, in such a case. That is why in rotor dynamics, order analysis is preferred 

over the frequency spectrum analysis. In the order domain, the values of the fundamental order 
13

and the harmonics remain constant with respect to the shaft speed; the first order is always at the 

shaft speed and the second order is always twice the shaft speed, and so on. 

To achieve order analysis in rotating machinery applications with variable running speeds, 

instead of sampling at equal increments of time, a different sampling technique has to be used.

Sampling is conducted at equal increments of shaft rotation position, thus reducing the effect of 

the shaft speed variations. This is called synchronous sampling. The synchronous sampling 

technique is very useful for rotating machinery-related data processing, especially in instances of

varying shaft speed.

Generally, there are two approaches to achieving synchronous sampling - analog and digital 

approaches. One of the analog approaches uses an Analog to Digital (A/D) sampling clock to 

achieve the synchronous sampling. The key to this approach is generating an appropriate 

sampling clock based on shaft rotation conditions. As shown in Figure 3.1, the sampling clock is 

derived from the shaft encoder by an analog ratio generator to meet the desired order analysis 

requirements (such as order resolution and maximum order). In cases where only lower order 

components are of interest, the encoder output can be used as a sampling clock directly. 

In the digital approach, or synthesized synchronous sampling [9], both vibration and encoder 

signals are discretized simultaneously, preferably at high speed. Different signal processing 

techniques can be used to resample the data and convert time domain data into shaft cycle 

domain data, with the help of an encoder signal from the shaft (refer to Figure 3.2). In this 

approach, both the encoder and key phaser can be used as a shaft speed reference. Regardless, 

the availability of the shaft encoder/key phaser is crucial to both analog and digital synchronous 

sampling approaches. 

Figure 3.1. Synchronous sampling – analog approach
14

Figure 3.2. Synchronous sampling– digital approach

With the synchronously sampled data, a common way to enhance the signal components of 

interest is through time synchronous averaging [10]. With a shaft encoder/key phaser, the 

vibration signal detected contains three major components: the synchronous coherent signal 

component, the synchronous, non-coherent component, and random noise. Conventional time 

synchronous averaging can only enhance the synchronous coherent signal component. The 

synchronous, non-coherent component and the random noise will be averaged out with a 

sufficient number of averages. 

Figure 3.3 (a) shows a simulation result with a combination of the shaft response, a ( f t) 0 sin 2π ; its 

second harmonic, b ( f t) 4 0 sin π ; a nonsynchronous coherent signal, c ( f t) 3 0 sin 2π ⋅1. ⋅ ; and a uniform 

random noise. After 250 times of synchronous averaging, the results are shown in Figure 3.3 (b);

the random noise and the nonsynchronous coherent component have been successfully removed.

Figure 3.3. Time synchronous averaging
15

When applying the synchronous sampling technique to diagnose bearing/gear damage, there are 

two issues that need to be resolved. The first is that the bearing damage signatures are usually 

nonsynchronous to the shaft order. In complicated gear sets, such as in the planetary gear, not all 

gear meshing frequencies are integer multipliers of a shaft frequency. So, if the regular time 

domain synchronous averaging technique is applied to the vibration response, the bearing 

damage signatures will be averaged out. Thus, instead of averaging in the time domain, order 

domain averaging should be used in gearbox health feature extractions. The second problem is 

unique to a wind turbine gearbox. For example, in a typical 1.5 MW wind turbine, the order 

span between the main shaft and the third stage gear meshing (the high speed shaft gear meshing 

frequency) can be above 1500. Care must be taken on the order resolution and on the maximum 

order applied during the data acquisition.

3.1.2 Synthesized Synchronous Sampling

With the help of a tachometer, the equal time sampled data can be converted into equal shaft 

angular space data as shown in Figure 3.2. 

In the event that the direct shaft tachometer signal is not available, traditional synchronized 

sampling becomes difficult, if not infeasible. For example, in this Round Robin project, only the 

speed profile is provided. If a synthesized tachometer signal can be generated from the speed 

signal, then the equal circumferential space sampling (synchronous sampling) can be carried out 

following well-established routines. 

The following describes a procedure to synthesize a tachometer from the shaft speed profiles. In

Figure 3.4, assume we have determined that the synthesized tachometer generated a pulse at time 

i t . We need to find out the location of the next pulse timing i +1 t . The time elapsed, from i t to 

i +1 t , i.e., i i t = t − t 1 +1 ∆ , is the instantaneous shaft rotation period. On the other hand, if we have 

determined the i +1 t , since we know the shaft speed as a function of time, the average speed, n , 

between i t and i +1 t can be calculated numerically. Therefore, the shaft instantaneous period can 

also be approximated by the averaged instantaneous shaft speed, i.e., ∆t2 = 60 / n . In theory, by 

equalizing 1 ∆t and 2 ∆t , we can determine i +1 t ; thus, calculating the next pulse location. In 

practice, due to time resolution and speed accuracy, an approximation procedure is used instead 

of solving for an exact solution. The following steps further explain the procedure of the 

synthesized synchrophaser: 

1. Assume a synchrophaser pulse at time zero.

2. Once the ith synchrophaser pulse is located, at i t , assume the (i+1)th pulse be located at 

i +1 t . 

3. Calculate the average shaft speed, n in RPM, which is a function of i +1 t , from i t to i +1 t

( ) ( ) ∫

+

− =

+

+

1

1

1

1 i

i

t

t

i i

i ShaftSpeed t dt

t t

n t (2)

4. Formulate the time elapsed from i t to i +1 t
16

i i t = t − t ∆ 1 +1 (3)

and the time elapsed by one instantaneous rotation

∆t2 = 60 / n (4)

5. Find i +1 t such that 1 2 ∆t − ∆t is minimized. 

The i +1 t then is the approximate location of the ( )

th i +1 synchrophaser pulse. The tachometer 

can be generated from the synchrophaser, say, by equal spacing between the consecutive 

synchrophaser pulses. 

With this method, one of the major error sources is the discretization resolution. The maximum 

error in the shaft period is 2

T , where T the sampling period is. Fortunately, for bearing and gear 

dynamic response analysis, especially acceleration enveloping analysis, the frequency of interest 

is usually much higher than the shaft speed. In other words, the digitization rate is usually 

several orders of magnitude higher than the shaft speed. Thus, the synthesizing error from the 

digitization error is expected to be negligibly small. 

Figure 3.4. Synthesized tachometer generation from speed function

3.1.3 Sideband Energy Ratio

Sideband Energy Ratio (SER) [11] is calculated from high resolution spectrum data. Each 

spectrum is created from time-based waveform data generated by an accelerometer sensor and 

collected by the monitoring system. Several accelerometer sensors were mounted in strategic 

locations on the wind turbine gearbox to monitor each gear mesh. The waveforms from each 

sensor were synchronously sampled so that the sampling frequency tracks change in speed. This 

technique produces narrow spectral lines of speed-dependent frequencies, like gear mesh 

frequencies and associated sidebands, for variable speed machines; they are essential to 
17

accurately calculate SER. Once the spectrum is generated the SER algorithm sums the 

amplitudes of the first six sideband peaks on each side of the center mesh frequency and divides 

by the amplitude of the center mesh frequency. 

SER= ∑ Sideband Amplitudei

6

i=1

Center mesh frequency amplitude (5)

SER is sensitive to the sideband amplitudes relative to the center mesh frequency. In a healthy 

gear mesh, any sidebands have small amplitude compared to the center mesh frequency, or they

may be missing altogether resulting in a low SER. SER is typically less than one for a healthy 

gear mesh. As damage develops on a gear tooth that passes through the gear mesh, the sidebands 

increase in amplitude, as well as in number, and SER will go up. In GE Bently Nevada’s wind 

turbine condition monitoring system, ADAPT.wind, SER is calculated for the fundamental mesh 

frequency and the first two harmonics of each gear mesh.

3.1.4 Acceleration Enveloping

The acceleration enveloping technique was originally called the high frequency resonance 

technique. It was discovered, almost accidentally, from an oscilloscope display [7] in the early 

1970s, through a National Aeronautics and Space Administration (NASA) funded project [8]. 

The acceleration enveloping technique is based on the following assumptions. When a defect 

occurs in a bearing, repetitive impacts occur during rotation. These kinds of impacts are a 

broadband excitation. This broadband excitation stimulates the resonant response of the 

bearing's support system. However, the resonant response levels from the defect impacts, such 

as unbalance, are usually very low compared to the shaft excitation; though, the frequency 

contents of the resonant response are usually much higher. If the dynamic range of the vibration 

sensor and the consequent analyzer is low, the resonant response signals are down in the noise 

level. The key to detecting bearing faults is to capture the low amplitude response caused by 

bearing defect excitation, without including the high amplitude rotational vibration signals and 

system fundamental resonant frequency responses. To accomplish this, a band pass filter is used 

to isolate the signal. Once the high frequency damage response is captured, the signal goes 

through a rectification device and the envelope of the signal is detected from the rectified signal. 

Applying FFT to the envelope signal will reveal the frequency and amplitude, which is uniquely 

associated with the damaged bearing component. 

In theory, any vibration sensor can achieve bearing/gear damage detection through the 

enveloping or demodulation processes, as long as the sensor has the frequency range required. 

Since the bearing/gear damage excited response is known to have high frequency content, the 

accelerometer has an advantage over velocity and displacement sensors.

In the early days, this enveloping detection process was performed using several analog devices. 

As shown in Figure 3.5, the conditioned vibration sensor signal is first passed through an analog 

filter to isolate the impulse response excited by the bearing damage. The filtered response is

then passed through a rectifier to flip the negative half of the oscillation signal to the positive 

side. The rectified signal is fed into an envelope detector to identify the envelope of the signal. 

The envelope signal is then used to identify bearing damage signature through a signal analyzer. 

If necessary, a low-pass filter can be added before the analyzer. 
18

The process shown in Figure 3.5 works well, if all the analog devices are appropriately designed 

for a particular application. However, a different application may require different parameter 

settings of the analog devices. For example, the bearing support system may have a different 

resonant structure; thus, it requires a different cut-off frequency design for the band-pass filter to 

isolate the damage impulse response. For different structural damping, the envelope detector 

needs a different time constant design to match the impulse response decay rate, so that the 

bearing damage-related high frequency and low amplitude vibration signals can be maximized. 

More importantly, the bearing damage detection is usually conducted in a harsh environment. 

An increased number of electronic components involved in the bearing defect detection process 

will usually decrease the overall system reliability.

Figure 3.5. Analog devices-based approach

With the improvement of computer technology and the development of high dynamic range A/D 

converters, the acceleration enveloping-based bearing damage detection becomes much easier to 

implement. Many of the analog devices, as shown in Figure 3.5, can now be replaced by digital 

signal processing techniques, thus improving detection accuracy and system reliability. One 

possible digital signal processing-based realization of acceleration enveloping is shown in Figure 

3.6. The conditioned acceleration signal is first digitized with high speed and high dynamic range 

A/D converter. The high speed and high dynamic range A/D is especially important because it 

ensures that the digitized vibration data contain low amplitude high frequency resonant responses 

excited by the bearing damage impulse. The digitized data are then passed through a digital 

band pass filter to isolate the resonant response excited by the bearing damage. Next, the 

enveloping detection algorithm is used to detect the envelope of the filtered data. In the digital 

domain, this process can be achieved by the Hilbert transform. The digital Hilbert transform is 

related to the FFT and can be easily achieved [12]. If accurate enveloping detection is required, 

a local maximum interpolation technique can provide better results [13]. The bearing damage 

detection is then accomplished by spectrum analysis on the enveloped data.
19

Figure 3.6. Digital processing-based approach

3.2 Round Robin Analysis Results

3.2.1 Bearing and Gear Damage Features

Based on the gear configuration data given by NREL, the gear damage features were calculated 

and listed in Table 3.1. Similarly, the bearing damage features were calculated and listed in 

Table 3.2. In both tables, MS stands for Main Shaft. The bearing notations used in Table 3.2 is

the same as those used in the test gearbox failure analysis report [4] and illustrated in Figure 3.7. 

The numbers of gear mesh teeth count are also marked in Figure 3.7. 

Figure 3.7. Gearbox power flow
20

Table 3.1. Gear damage features

Shaft frequencies Relative freq at 1800 rpm at 1200 rpm 

MS HSS [rpm] [Hz] [rpm] [Hz]

Rotor/carrier 1.00 0.012 22.1 0.37 14.7 0.25

Planets (minus carrier rotation) 2.54 0.031 56.1 0.93 37.4 0.62

Planets 3.54 0.043 78.2 1.30 52.1 0.87

Sun shaft (minus carrier rotation) 4.71 0.058 104.1 1.74 69.4 1.16

Sun shaft 5.71 0.070 126.2 2.10 84.1 1.40

Intermediate shaft 20.37 0.250 450.0 7.50 300.0 5.00

Generator shaft 81.49 1.000 1800.0 30.00 1200.0 20.00

Gear mesh tooth passing freqs

Gear mesh - Planet > Ring 99.00 1.215 3048.2 36.45 2032.1 33.87

Gear mesh - Sun > Planet 99.00 1.215 3048.2 36.45 2032.1 33.87

Gear mesh - Sun shaft > Intermediate 468.57 5.750 10350.0 172.50 6900.0 115.00

Gear mesh - Intermediate > HSS 1792.80 22.000 39600.0 660.00 26400.0 440.00

Single gear tooth fault freqs

HSS gear set pinion (HSS) 81.49 1.000 1800.0 30.00 1200.0 20.00

HSS gear set wheel (intermediate shaft) 20.37 0.250 450.0 7.50 300.0 5.00

Intermediate gear set pinion (intermediate shaft) 20.37 0.250 450.0 7.50 300.0 5.00

Intermediate gear set wheel (sun shaft) 5.71 0.070 126.2 2.10 84.1 1.40

Sun gear 14.14 0.174 312.4 5.21 208.3 3.47

Planet gear 7.08 0.087 156.3 2.61 104.2 1.74

Ring gear 3.00 0.037 66.3 1.10 44.2 0.74
21

Table 3.2. Bearing damage features

Bearings Relative Freq

Main Bearing MS HSS

Main bearing (INP-A) - roller rotation freq 5.22 0.064

Main bearing (INP-A) - cage freq 0.45 0.006

Main bearing (INP-A) - roller defect freq (= 2 x roller rotation freq) 10.44 0.128

Main bearing (INP-A) - outer race defect freq 12.70 0.156

Main bearing (INP-A) - inner race defect freq 15.30 0.188

HSS A1 & A2 Relative freq

HSS-A1 and A2 - roller rotation freq 253.99 3.117

HSS-A1 and A2 - cage freq 34.63 0.425

HSS-A1 and A2 - roller defect freq (= 2 x roller) 507.98 6.234

HSS-A1 and A2 - outer race defect freq 691.89 8.490

HSS-A1 and A2 - inner race defect freq 937.93 11.510

HSS B Relative freq

HSS-B - roller rotation freq 254.78 3.127

HSS-B - cage freq 47.10 0.578

HSS-B- roller defect freq (= 2 x roller) 509.56 6.253

HSS-B- outer race defect freq 584.60 7.174

HSS-B - inner race defect freq 800.74 9.826

ISS C1 &C2 Relative freq

ISS-C1&C2 - roller rotation freq 106.14 1.303

ISS-C1&C2 - cage freq 9.25 0.114

ISS-C1&C2 - roller defect freq (= 2 x roller) 211.88 2.600

ISS-C1&C2 - outer race defect freq 287.25 3.525

ISS-C1&C2 - inner race defect freq 344.30 4.225

ISS D Relative freq

ISS-D - roller rotation freq 63.70 0.782

ISS-D - cage freq 11.78 0.145

ISS-D- roller defect freq (= 2 x roller) 127.39 1.563

ISS-D- outer race defect freq 146.15 1.793

ISS-D - inner race defect freq 200.19 2.457
22

Table 3.2. Bearing damage features (continued)

Bearings Relative Freq

LSS E1&E2 Relative freq

LSS-E1&E2 - roller rotation freq 41.37 0.508

LSS-E1&E2 - cage freq 2.67 0.033

LSS-E1&E2 - roller defect freq (= 2 x roller) 82.86 1.017

LSS-E1&E2 - outer race defect freq 109.71 1.346

LSS-E1&E2 - inner race defect freq 124.57 1.529

Hollow Shaft F Relative freq

HS-F - roller rotation freq 47.20 0.579

HS-F - cage freq 3.03 0.037

HS-F - roller defect freq (= 2 x roller) 94.39 1.158

HS-F - outer race defect freq 139.61 1.713

HS-F - inner race defect freq 157.53 1.933

Carrier G Relative freq

Carrier-G - roller rotation freq 8.59 0.105

Carrier-G - cage freq 0.53 0.006

Carrier-G - roller defect freq (= 2 x roller) 17.17 0.211

Carrier-G - outer race defect freq 25.43 0.312

Carrier-G - inner race defect freq 28.57 0.351

Carrier H Relative freq

Carrier-H - roller rotation freq 8.11 0.100

Carrier-H - cage freq 0.53 0.007

Carrier-H - roller defect freq (= 2 x roller) 16.22 0.199

Carrier-H - outer race defect freq 23.93 0.294

Carrier-H - inner race defect freq 27.07 0.332

Planet 1G&1R Relative freq

Planet-1G&1R - roller rotation freq 8.28 0.102

Planet-1G&1R - cage freq 1.46 0.018

Planet-1G&1R - roller defect freq (= 2 x roller) 16.57 0.203

Planet-1G&1R - outer race defect freq 19.42 0.238

Planet-1G&1R - inner race defect freq 26.27 0.322
23

3.2.2 Tool Development

A MATLAB-based tool was developed for easy data processing operations. The tool 

incorporated regular FFT spectrum analysis, acceleration enveloping analysis, synthesized 

synchronous sampling, and order analysis. 

3.2.3 Damaged Gearbox Data analysis

The main goal of the Round Robin project was to identify the gear and bearing damage 

associated with the gearbox. In our analysis, we categorized the gear damage according to the 

gearbox meshing stages: the high speed gear meshing stage (HSGM), the intermediate gear 

meshing stage (ISGM), and the planetary gear meshing stage (PLTGM). For bearings, we 

categorize the damage according to the shaft, which the bearing is associated with, i.e., the High 

Speed Shaft (HSS), the High Speed Intermediate Shaft (HSIS), the Low Speed Intermediate 

Shaft (LSIS), and the Low Speed Shaft (LSS) or the Main Shaft (MS).

3.2.3.1 HSGM

The sensor AN7 was used to evaluate the HSGM stage health condition. From the order 

spectrum, it can be clearly seen that the fundamental gear meshing order is heavily modulated by 

the HSS speed, as seen in Figure 3.8.The sideband energy ratio (SER) is over three, which 

indicates severe gear damage in the HSGM pinion. The sideband contents in the higher order 

harmonics of HSGM also indicate the pinion damage, as seen in Figure 3.9 and Figure 3.10. 

Post-test examination indicated that the HSP had severe scuffing [4].

Figure 3.8. HSGM (22) modulated by HSS (1)
24

Figure 3.9. HSGM X2 (44) modulated by HSS (1)

Figure 3.10. HSGM X3 (66) modulated by HSS (1)

Similar order analyses also indicated that the HSGM order was modulated by the HSIS shaft

(Figure 3.11). This kind of modulation is visible in the HSGMX2 and HSGMX3 as well (refer 

to Figure 3.12 and Figure 3.13 respectively). Post-test examination indicated that the HSG also 

had severe scuffing [4].
25

Figure 3.11. HSGM (22) modulated by HSIS (0.25)

Figure 3.12. HSGM X2 (44) modulated by HSIS (0.25)
26

Figure 3.13. HSGM X2 (66) modulated by HSIS (0.25)

3.2.3.2 ISGM

Damage signatures related to the ISGM were not shown in the vibration analysis. As seen in 

Figure 3.14 though, the ISGM and higher order harmonics do exist. However, the shaft 

modulations are too small to draw any conclusion regarding the gear damage. The post-test 

examinations revealed fretting corrosion, polishing wear, and scuffing damage in the ISGM 

pinion; however, the damage was imprinted on all teeth because the gear-set had a hunting tooth 

gear ratio, which has potentially smoothed out the damages and reduced vibration responses 

incurred by the damage.

Figure 3.14. ISGM and higher order harmonics
27

3.2.3.3 PLTGM

For planetary gear stage damage detection, sensors AN3 and AN4 were used (refer to Table 2.3

for more information on sensors). The planetary gear set arrangement in this gearbox is a 

simultaneous mesh; thus, there was no cancellation/enhancement around the gear mesh 

frequency and harmonics, as seen in the sequential mesh design. Detailed order spectrum 

analysis indicated that the planetary gear mesh order and its harmonics are present Figure 3.15

for sensor AN4). Sidebands of planet passing are visible around the PLTGM and its harmonics. 

The modulation is significant at the third harmonic of the PLTGM (Figure 3.16). Similar 

information can be extracted from the sensor AN3 and the corresponding order spectra are 

shown in Figure 3.17 and Figure 3.18, respectively. 

The acceleration enveloping analysis of the sensor AN3 (Figure 3.19) indicated that the damage 

is likely associated with the ring gear (0.037 Order), instead of planet gear (0.087 Order) or sun 

gear (0.174 Order). Post-test examination confirmed the ring gear scuffing and polishing 

damage [4].

The post-test also indicated severe fretting corrosion on the sun pinion. Though the sun/plant 

gear meshing is evident in the data analysis, as shown in Figure 3.15 and Figure 3.17, the LSIS 

shaft modulation (0.07 Order) is very small (Figure 3.20); thus, the sun pinion damage is 

inconclusive using current vibration-based analysis. 

Figure 3.15. Planetary gear stage meshing order and harmonics from AN4
28

Figure 3.16. PLTGM X3 modulated by planet passing order (0.037)

Figure 3.17. Planetary gear stage meshing order and harmonics from AN3
29

Figure 3.18. PLTGM X3 and X4 modulated by planet passing order (0.037)

Figure 3.19. Sensor AN3 acceleration enveloping order spectrum
30

Figure 3.20. Modulation by LSIS in PLTGM is very small

3.2.3.4 HSS Bearings

An acceleration enveloping analysis (AEA) on the high speed shaft sensor, AN7, indicated 

possible damage initiation of the HSS downwind bearing inner race. As seen in Figure 3.21, 

there was a fundamental order of 11.48 and its harmonics (22.95 and 34.42) in the envelope 

order spectrum. These orders re modulated by the HSS shaft speed. By referring to Table 3.2, 

we can identify that the order 11.48 is very close to the 11.51, the HSS-A1 and/or HSS-A2 inner 

race defect frequency. These two bearings are identical; therefore, further differentiation is not 

feasible.

The post-test examination revealed that the HSS-A1 bearing had mild overheating, which created 

straw-yellow temper colors near each end of the IR raceway [4]. However, it is not likely the 

overheating caused the BPFI response in the envelope spectrum. Acceleration enveloping 

analysis can be very sensitive to bearing mechanical damage. It is likely that the damage 

response was caused by the minor scratches on the race edge or the small indentations in the 

middle of the raceway.

An acceleration enveloping analysis on the high speed shaft sensor AN7 also indicated possible 

HSS-A1 cage damage. In the envelope spectrum (Figure 3.22), there is a minor but clear tone at 

0.4261 Order and its harmonics at 0.8522 and 1.278 Order. By referring to Table 3.2, we can see 

that this fundamental tone of 0.4261 Order is very close to HSS-A1 cage damage tone of 0.425 

Order. However, HSS-A1 cage damage was not reported in the post-test inspection. 
31

Figure 3.21. Envelope spectrum of AN7

Figure 3.22. Zoomed envelope spectrum of AN7

3.2.3.5 HSIS Bearings

Initial data analysis did not reveal any damage signatures of the bearings on the HSIS shaft. 

However, the post-test examinations indicated moderate assembly damage and mild contact 

corrosions on the bearing D inner race [4].

By careful re-examination of the order spectrum Figure 3.23, we saw that there was a small peak 

at 2.43 Order, which is very close to bearing D BPFI 2.457 Order; however, it was also the 

second harmonic of the planet gear mesh between the ring gear and the planets. Therefore, it 
32

was very difficult to draw a conclusion about the bearing D BPFI damage signature at the current 

stage.

Figure 3.23. Possible bearing D BPFI

3.2.3.6 LSIS Bearings

No damage signatures were identified from post-test inspection or from data analysis.

3.2.3.7 Carrier/ Main Shaft Bearing

Post-test inspection found severe fretting corrosion on the bearing H outer race [4]. However, no 

damage signature was identified from data analysis, because, even though the corrosion was 

severe in this bearing, the outer race surface was still smooth. Thus, it does not incur any 

additional vibrations. In conclusion, this kind of bearing damage cannot be detected by a 

vibration-based condition monitoring system.

3.3 Discussions

This Round Robin project provided a platform for commercial wind turbine condition 

monitoring system suppliers, as well as, academic institutions to exercise different 

methodologies. The GE Bently Nevada team provided a unique set of solutions based on the 

techniques developed and implemented into its commercially available wind turbine drivetrain 

condition monitoring system, ADAPT.wind. 

Compared to the condition monitoring systems for other rotating machinery, condition 

monitoring systems for wind turbines face a few unique challenges including constantly variable 

operating speeds and a high gear-up ratio from the rotor to the high-speed shaft. To overcome 

the inaccuracy incurred by speed variations, synchronous sampling is the preferred data 

acquisition technique. Subsequently, a synchronous analysis technique can be used to extract the 

bearing and gear damage signatures. To accommodate high gear ratios in wind turbine 

gearboxes, a digital domain synchronous re-sampling is very useful for signature extraction. The 

digital synchronous re-sampling utilizes a low count mechanically- or electrically- based 
33

encoder, or a key phaser, and interpolates the data between the pulses, with linear or more 

sophisticated speed variation assumptions.

The data provided by NREL for the Round Robin analysis included accelerometer data and 

speed profile data. To carry out the digital synchronous sampling, without shaft encoder or key 

phaser data, the GE team developed and implemented a so-called synthesized synchronous 

sampling technique. Although the phase information cannot be recovered, the technique 

successfully carried out the synchronous analysis using the shaft speed profile.

The vibration sensing-based method is believed to be the cost effective approach for wind 

turbine condition monitoring. However, any gearbox anomalies that do not incur additional 

vibrations, such as overheating, minor fretting, and smoothed polishing will not be effectively 

detected by vibration sensors. 

Generally speaking, vibration-based wind turbine condition monitoring systems can detect 

damage in the high speed side with higher confidence than that from the low speed side, 

especially planetary gear set-related component damage. This is because accelerometers are 

inherently more sensitive to high frequency vibrations. In addition, the mechanical 

transmissibility from planetary gear components is usually low. Damage detection and condition 

monitoring related to the gearbox low speed side is an area that needs more research attention in 

the future.
34

4 Combining Novel Approaches with Proven Algorithms for 

Robust Wind Turbine Gearbox Fault Detection

Jeremy Sheldon*, Matthew Watson, Genna Mott and Hyungdae Lee

Impact Technologies, A Sikorsky Innovations Company 

*

Corresponding Author Email: jeremy.sheldon@impact-tek.com

4.1 Introduction

Impact Technologies’ analysis efforts focused on applying a number of novel vibration 

diagnostic algorithms to the GRC data set. They have been developed and matured by the team 

in Department of Defense (DOD) applications for more than 10 years. The algorithms and results 

are summarized herein. Generally, the methods employed by the team worked well, once the 

challenges and peculiarities of the data set were realized. In particular, the absence of raw, timedomain data from a healthy system (only FFT plots were provided) made it difficult to baseline 

the system for comparison purposes. Regardless, the results of the automated algorithms were 

corroborated with visual spectral analysis and are provided herein.

4.2 Algorithm Overview

Impact applied several component-specific analysis modules to the GRC data set. Each

algorithm is briefly introduced below. 

4.2.1 FirstCheck: Sensor Validation

Having accurate and validated data is critical to performing effective condition monitoring. Even 

the most durable sensors often become loose, disconnected, or damaged providing corrupted 

system information. Consequently, changes in the dynamics of a vibration signal that are 

characteristic of various sensor faults can be deceptively similar to those of mechanical failures, 

or vice versa, inevitably resulting in false alarms.

For example, Figure 4.1 shows the result of the authors’ previous analysis of a gear pinion failure 

that occurred on the test stand of a high-speed (thousands of RPMs), high-power (tens of 

thousands of horsepower) military fighter aircraft drive train. As seen, several vibration features 

react simultaneously, indicating that a potential fault is present in the system. Information 

gathered solely from this sensor would confidently indicate a fault. However, upon further 

investigation of the raw sensor data (shown in the top plot of the figure), one can see that this 

reaction was caused by faulty (intermittent) data and, therefore, should not be trusted.
35

Figure 4.1. False alarm caused by faulty sensor 

In addition, because many diagnostic feature algorithms are based on higher order statistics and 

energy measures; it is possible for a corrupt signal to generate feature values that are within an 

acceptable range despite the signal containing no periodic frequency content. Rigorous and 

automated analysis of the integrity of accelerometer data is, therefore, critical to providing 

accurate health assessments. To address this potential source of false alarms, the validity of the 

high frequency vibration sensors is first evaluated as an initial step in the analysis, using an 

approach termed FirstCheck. This module looks at a number of signal characteristics (including 

the range, bias, and other proprietary characteristics) to verify the integrity of the vibration signal 

before it is analyzed by the other algorithms. 

4.2.2 ImpactEnergy: Bearing Fault Detection and Isolation

Bearing fault detection and isolation was performed using a set of algorithms termed 

ImpactEnergy. Although bearing characteristic frequencies are easily calculated, they are not 

always easily detected by conventional frequency domain techniques. Incipient bearing damage 

is most often characterized as short-burst impulses in the vibration signature. Vibration 

amplitudes at these frequencies, due to incipient faults (and sometimes more developed faults),

are often indistinguishable from background noise or obscured by much higher amplitude 

vibration from other sources in a running machine, including rotors, blade passing, and gear 

meshes. Similarly, time domain energy features, such as root mean square (RMS) or kurtosis, are 

not significantly affected by such short burst of low intensity vibrations. Traditional time domain 

or frequency domain analyses, therefore, encounter problems in detecting early stages of bearing 

failure.

The ImpactEnergy module (Figure 4.2) integrates traditional spectral analysis techniques with 

high-frequency demodulation and advanced feature extraction algorithms, providing a more 

effective solution. The advantages of using the high frequency response to identify and track 
36

bearing damage is well documented [14,15] and proven to be an effective method. 

Demodulation, or enveloping, allows the broadband energy caused by failure effects to be 

differentiated from the energy due to normal system noise. This approach provides the ability to 

detect defect impulse events much easier than traditional analysis techniques allow. A key 

consideration is selecting the band-pass filter that is centered on the expected carrier frequencies. 

Through proprietary knowledge and field-application experience, the authors have developed a 

process to identify key carrier frequencies.

Figure 4.2. ImpactEnergy overview

For complete characterization of bearing health from incipient fault to failure, the ImpactEnergy 

module includes algorithms to extract an extensive set of time and frequency domain features 

from both the raw, unprocessed, and demodulated vibration signals. Some time domain features 

include traditional statistical measures, such as RMS, kurtosis, and Crest Factor. Frequency 

domain features include the power levels of specific bearing defect frequencies compared against 

known, health baseline thresholds, which can be very useful in diagnosing a fault [16].

4.2.3 GearMod and GearMod-Shaft: Gear and Shaft Fault Detection and Isolation

The GearMod module (Figure 4.3) is used to extract diagnostic features that are used for gear 

fault detection and isolation. This module contains a broad range of statistical methods based on 

the time synchronous averaged (TSA) signal and other processed signals. The time synchronous 

averaging technique is a useful technique to reduce the random noise level, as well as 

disturbances from events unrelated to the gear of interest, and it has been extensively used to preprocess gear vibration signals [17,18]. The fundamental principle of the TSA is that the vibration 

components related to a shaft rotation and the gears on that shaft repeat periodically with the 

shaft rotation. By dividing the vibration signal into contiguous segments, of exactly one shaft 

rotation, and averaging a sufficiently large number of segments, the vibration components that

are synchronous to the shaft rotation, are reinforced. Non-synchronous vibrations are cancelled

out because they are out of phase in consecutive rotations. 
37

Figure 4.3. GearMod overview

GearMod calculates time-domain features, such as RMS, skewness, kurtosis, and Crest Factor, as 

well as features from the spectrum of the averaged signal, including FM0 (the peak-to-peak

amplitude compared to summation of GMF & harmonic magnitudes), Sideband Index (the 

average spectral magnitude from sidebands on the 1st GMF), and Sideband Level Factor (the 

spectral magnitude of sidebands on the 1st GMF, normalized by TSA RMS). The equations for 

some of these features are included in Table 4.1 [19-21].

Table 4.1. Select gear diagnostic feature definitions

Feature Name Equation Symbols

FM0 ∑=

= n

i

i A f

PPA FM

1

( )

0 PPA = peak-to-peak amplitude

A(fi) = GMF & harmonic amplitudes

Sideband Index

2

( ) ( ) 1, min 1 1, min 1 RMC s RMC s

SI

sb

n

sb

ndo ant − + do ant + =

sb

ndo ant RMC1, min −1 and sbndo ant RMC1, min +1

= 1st order sideband amplitudes about 

fundamental GMF

Sideband Level 

Factor

σ

( ) ( ) 1, min 1 1, min 1 RMC s RMC s

SIL

sb

n

sb

ndo ant − + do ant + = σ = standard deviation

Additional features are also calculated using proprietary methods. In addition, GearMod contains 

built-in functionality to extract the TSA signal without a tachometer signal, making it appropriate 

for situations when an accurate or useable tachometer signal does not exist.

4.2.4 Joint Time Frequency Analysis (JTFA) Overview

Gearbox vibration diagnostics are often based on frequency domain analysis, which assumes the 

monitored signal is “stationary” during the analysis period. However, because operating 

conditions are often non-stationary and evolving, this assumption leads to spectral smearing and 

erroneous analysis that creates uncertainty in the health assessment.
38

Spectral smearing, in which energy from an evolving characteristic frequency (i.e., shaft 

frequency, bearing fault frequency, gear mesh frequency) is spread across multiple frequency 

bins, can reduce the efficacy of traditional frequency domain analysis, including Fourier 

transforms. Typically, this is avoided by defining steady-state operating conditions in which to 

perform the analysis. Although this may be acceptable for some systems, most wind turbines 

have constantly varying shaft speeds and loads. In addition, certain component faults and their 

progressions can also lead to non-stationary signals that could be missed by traditional 

techniques. As a result, the authors have developed a novel vibration diagnostics methodology 

that is applicable during non-steady operation through application of joint time-frequency 

analysis (JTFA)[22]. These methods use various techniques to transform the two dimensional 

time domain signal into a three dimensional, time-frequency domain signal to increase feature 

extraction accuracy. An example is shown in Figure 4.4. Various features are then extracted from 

the three dimensional signals for fault detection.

Figure 4.4. Example JTFA approach (short time Fourier transform)

4.3 Results Summary

The results of the analysis performed by Impact are briefly discussed in the following sections. 

Both the blind results, obtained without knowing details on actual gearbox condition, and the 

conclusions that were drawn after learning the actual damage, are discussed separately. It is 

worth noting that FirstCheck was applied to all vibration data and no sensor faults were detected.

4.3.1 “Blind” Results

The results obtained without knowing the actual gearbox faults are summarized in Table 4.2. The 

table includes the suspected damage, location, or component, severity, and the suspected damage 

mode, as identified by Impact’s “blind” analysis. As shown, Impact correctly identified three of 

the seven damage instances and had one false alarm (planet gear fault was called out but not 

correct). Some specific evidence and results are shown in the following sections.

Segment 2

Segment 1

Segment n

Mag

Mag

Time

Extract

Spectrum

Extract

Spectrum

Extract

Spectrum
39

Table 4.2. Initial blind results summary

4.3.1.1 High Speed Shaft Gears

Figures 4.5 and 4.6 show the results of Impact’s GearMod analysis of data sets 2b and 2c for the 

high speed gear/pinion pair. As seen, the analysis showed typical gear fault indicators, especially 

on accelerometers AN6 and AN7. The distinct harmonics (1-4 and some higher) of the high 

speed gear mesh frequency (GMF) combined with the numerous sidebands around each GMF 

indicated teeth scuffing or other distributed wear (Figure 4.5). In addition, the high second order 

GMF, clearly visible in Figure 4.6, indicated potentially misaligned gears/shafts. 
40

Figure 4.5. High speed gear fault evidence, blind results (AN6)

Figure 4.6. High speed gear fault evidence, blind results (AN7)
41

4.3.1.2 Intermediate Shaft Bearings

Impact’s ImpactEnergy analysis of the bearings on the intermediate shaft is summarized by the 

spectral plots in Figure 4.7 and Figure 4.8. For the downwind bearings (IMS-SH B&C, which are 

indistinguishable since they are the same model bearing running at the same speed), the clear 

peaks in the conventional, non-demodulated spectrum (Figure 4.7) at the outer raceway fault 

frequency indicated substantial localize defects. Notice, too, the clear spectral peak at the IMSSH-A inner raceway defect frequency, in both the faulted and baseline (supposed healthy) FFT. 

Because the bearing fault frequency was visible in the baseline FFT data that was provided, 

Impact was not confident in the evidence enough to call out the fault. As such, this fault was not 

called out in the blind analysis (see Section 4.3.2.1 for more details). .

Figure 4.7. Intermediate speed downwind bearing fault evidence, blind results (AN6, Data 2b)

Damage in the IMS-SH B component was also evident by the elevated levels of multiple 

harmonics of the inner raceway fault frequency seen in the demodulated spectrum (Figure 4.8). 
42

Figure 4.8. Intermediate speed downwind bearing fault evidence, blind results

4.3.1.3 Sun Pinion Gear

Focusing on the planetary gear analysis, Impact found evidence of heavy distributed or uniform 

wear on the Sun Pinion Gear, specifically using the AN3 Ring Gear Radial 180° accelerometer. 

In addition to the relatively low GMF harmonics and high sidebands, as shown in Figure 4.9, 

Impact’s analysis showed higher than normal statistical features, including Energy Ratio (ER, 

ratio of spectral energies between Difference and Regular signals), NB4 (time averaged kurtosis 

of the envelope of the TSA signal band-pass filtered around dominant meshing frequency), FM0,

and RMS.
43

Figure 4.9. Sun pinion gear fault evidence, blind results

4.3.1.4 Intermediate and High Speed Gear JTFA Results

As mentioned above, Impact applied a set of JTFA algorithms to this data set. Since these 

algorithms are still under development, the results summarized in Figure 4.10 were enough to 

raise suspicion, but were not enough alone to call out a fault for the intermediate speed gear pairs 

(and were thus missed). However, when combined with the above gear analysis, Impact’s JTFA 

results further confirmed distributed faults in the high speed gear pairs. Interestingly, several of 

the JTFA features exhibited upward trends, normally indicating fault progression, but there was 

no evidence of fault progression provided to Impact to confirm this behavior. Although the 

torque load increased from 2a to 2c in Figure 4.10, the change was a step change and torque 

levels were fairly steady during each segment. Therefore the upward trends of the features within

each segment (most noticeably 2b and 2c) seem to indicate some other evolving/influencing

phenomena.
44

Figure 4.10. JTFA speed gear fault evidence, blind results

4.3.2 Revisited Results

After providing NREL with the above results from the blind analysis, the gearbox inspection 

results were provided to the Round Robin team. Knowing what to look for, Impact revisited the 

analysis to determine if any additional fault/damage signatures were present in the data. The 

results of the subsequent analysis are described below and in Table 4.3. As seen, most of the 

faults not called out in the blind analysis were detected in hindsight, resulting in the detection of 

six of the seven damage instances. Specifically the intermediate speed shaft upwind bearings and 

the high speed shaft downwind bearing damages were detected. These are described in more 

detail in the following sections. Note that Impact didn’t reevaluate the planet carrier bearing fault 

since it was our opinion that this type of fault is not detectable with vibration analysis due to the 

fact that the damage appears on the outside bore of the outer raceway, not in the contact zone of 

the bearing. 
45

Table 4.3. Post-inspection results summary

4.3.2.1 Intermediate Shaft Upwind Bearings

As briefly mentioned previously, Impact’s analysis during the blind portion of this effort 

revealed a high inner race defect frequency magnitude for both the test data and the provided 

baseline data, as shown in Figure 4.11. Initially this decreased the confidence in diagnosing a 

fault in the IMS Upwind bearing (IMS-SH-A). However, the inspection report revealed that the 

damage was due to an assembly error and, therefore, it was also present during the baseline 

testing. 

Figure 4.11. Intermediate speed upwind bearing damage evidence
46

With this information and the results exemplified by Figure 4.12, Impact could correctly identify 

the fault as a progressed or distributed inner raceway fault because there was little modulation 

and clear inner raceway frequency vibration.

Figure 4.12. Intermediate speed upwind bearing fault evidence, post-inspection results

4.3.2.2 High Speed Shaft Downwind Bearings

During the blind portion of this effort, Impact did not diagnose the defect present on the high 

speed shaft downwind bearings (HSS-SH-B/C). Based on the information contained in the 

inspection report, a discrepancy in the bearing part numbers was found. The initially provided 

documentation listed the HSS-SH-B/C bearings as 32222J2 SKF, but the inspection report 

visually confirmed them as 32222A FAG. Although similar in size, these bearings have different 

fault frequencies.

Using the correct fault frequencies, Impact’s analysis clearly showed small, early stage inner 

raceway defects, as evident by the multiple BPFI harmonics (1x-4x) that are dominant in the 

demodulated FFT (for data sets 2a and 2c). Example demodulated spectra and fault frequency 

peaks are shown in Figures 4.13 and 4.14. Although Impact did detect a defect in the bearing, the 

diagnosed fault signature seems unlikely to have been caused by only the cited overheating

event. Instead, Impact believes the evidence points to some additional defect, which may have 

resulted from the overheating.
47

Figure 4.13. High speed downwind bearing fault evidence, revisited (Data 2a)

Figure 4.14. High speed downwind bearing fault evidence, revisited (Data 2c)
48

4.4 Lessons Learned and Conclusions

Impact’s blind analysis successfully detected three of the seven damaged components that were 

present in the gearbox, with a fourth component detected but not called out due to the relative 

immaturity of the approach that detected the damage. Of the remaining three, two were detected 

during the secondary analysis that was performed after the inspection report was provided. These 

two were originally missed due to: 1) the use of incorrect bearing design information that was 

provided in the original analysis, and 2) the presence of the damage during assembly, which 

caused the baseline results that were used for comparison to be higher. It is Impact’s opinion that 

the seventh damaged component is not detectable with vibration analysis since the damage 

appears on the outside bore of the outer raceway, not in the contact zone of the bearing.

In general, this analysis was confounded by the number and severity of the defects, especially the 

obfuscation of bearing and other faults by the widespread gear damage. Impact believes that in 

actual practice the expected diagnostic performance will be better since a smaller and less severe 

set of faults will be present during the early stages of fault evolution. To clarify, this data set 

contains multiple progressed faults that would be better detected as they individually occur over 

time versus diagnosing each one once they have all occurred. Additionally, assessing the fault 

severity was more difficult due to the lack of time-domain baseline data. Although this was 

overcome by using our experience of previous analysis of different machinery, higher fidelity 

results may be produced by comparing like data to like data and allowing the algorithms to be 

baselined against typical, healthy vibration levels and trended over time. Regardless of these 

minor issues, this analysis and effort should enable a good assessment on the state of wind 

turbine diagnostics, as well as an indication of what work remains. 
49

5 Analysis Algorithms and Diagnostics Results from NRG 

Systems

Eric Bechhoefer

NRG Systems

Email: erb@nrgsystems.com

5.1 Introduction 

NRG Systems, as a participant of this Round Robin study, wished to validate the effectiveness of 

analysis algorithms used in the aerospace community, for the wind industry. The aerospace 

industry, specifically vertical flight, developed an extensive toolset for gearbox fault detection as 

a result of helicopter gearbox failures. These algorithms were specifically developed for shaft, 

gear, and bearing fault detection. This is counter to most installed condition monitoring systems,

which have matured out of industrial monitoring of large turbo-machinery (turbo-machinery 

have no gearbox, focusing extensively on shaft misalignment, out of balance, or rub conditions). 

NRG implemented two analysis methodologies: synchronous analysis of shaft/gear components 

and non-synchronous analysis of bearings. Synchronous methods were based on the work of 

McFadden [23], while the bearing analysis was based on the work of Randall [24].

The data set consisted of 10 samples each under three operating conditions, for a total of 30 files. 

The samples were separated by a short time interval. Because these industrial gearboxes are 

designed to run for years versus minutes, we assumed that the analysis would consist of taking a 

snap shot of the current gearbox condition. No attempt was made to trend component condition 

indicators or look at statistical differences between early and late files. It was assumed that over 

the period of the test, there was no appreciable degradation of the gearbox. The analysis 

consisted of viewing the output of various analysis algorithms for each component, and based on 

some nominal experience with aerospace gearboxes, defining the wind turbine gearbox as good, 

bad, or indifferent.

5.2 Analysis Algorithms 

5.2.1 Condition Analysis Algorithms - Feature Extraction to Improve Signal to 

Noise

Vibration signatures for machinery faults tend to be small relative to other vibration signatures. 

For example, in the typical gearbox, the energy associated with gear mesh and shaft vibrations 

will be orders of magnitude larger than a fault feature. Spectral analysis or root mean squares 

(RMS) of vibration are not powerful enough analyses to find early faults or defects. Techniques 

to improve the signal to noise are needed to remove frequencies associated with nominal 

components, while preserving the fault signatures.

Gear analysis was based on operations of the time synchronous average [23]. Time synchronous 

averaging (TSA) is a signal processing technique that extracts periodic waveforms from noisy 

data. The TSA is well suited for gearbox analysis, where it allows the vibration signature of the 

gear under analysis to be separated from other gears and noise sources in the gearbox that are not 

synchronous with that gear. Additionally, variations in shaft speed can be corrected, which 

would otherwise result in spreading of spectral energy into adjacent gear mesh bins. To do this, a 

signal is phased-locked with the angular position of a shaft under analysis. 
50

This phase information can be provided through an n per revolution tachometer signal (such as a 

Hall sensor or an optical encoder, where the time at which the tachometer signal crosses from 

low to high is called the zero crossing) or though demodulation of gear mesh signatures [25]. In 

the case of the GRC data set, the phase information was extracted from the generator signal itself 

(e.g., voltage signal capacitively coupled onto the RPM signal).

The model for vibration in a shaft in a gear box was given in [23] as: 

x(t) = Σi=1:K Xi(1+ ai(t))cos(2πi fm(t)+ Φi)+b(t)

where:

Xi is the amplitude of the kth mesh harmonic

fm(t) is the average mesh frequency

ai(t) is the amplitude modulation function of the kth mesh harmonic.

φi(t) is the phase modulation function of the kth mesh harmonic.

Φi is the initial phase of harmonic k, and

b(t) is additive background noise. 

The mesh frequency is a function of the shaft rotational speed: fm = Nf, where N is the number of 

teeth on the gear and f is the shaft speed, with no reduction in the analysis performance. This 

vibration model assumes that f is constant. In most systems, there is some wander in the shaft 

speed due to changes in load or feedback delay in the control system. This change in speed will 

result in smearing of amplitude energy in the frequency domain. The smearing effect, and nonsynchronous noise, is reduced by re-sampling the time domain signal into the angular domain: 

mx(θ) = E[x(θ)] = mx(θ+Θ). The variable Θ is the period of the cycle that the gearbox operation 

is periodic, and E[] is the expectation (e.g., ensemble mean). This results in the assumption that 

mx(θ) is stationary and ergodic. If this assumption is true, then non-synchronous noise is reduced

by 1/sqrt(rev), where rev is the number of cycles measured for the TSA.

5.2.2 TSA Techniques for Condition Indicators

The TSA is an example of angular resampling [23], [25], where the number of data points in one 

shaft revolution (rn) is interpolated into m number of data points, such that:

• For all shaft revolutions n, m is larger than r,

• And m = 2ceiling (log2 (r)) (typical for radix 2 Fast Fourier Transform).

The TSA itself can be used for Condition Indicators (CIs). Typically, a CI is a statistic of a 

waveform (in the case the TSA). Common statistics are RMS, peak to peak, Crest Factor, 

kurtosis and skewness. For the shaft, a shaft order (SO) of 1, 2, and 3 (first, second and third 

shaft rate harmonic) can be used to determine shaft out of balance, bent shaft, and/or shaft 

coupling damage, respectively. Figure 5.1 outlines the process of generating the TSA, and shaft 

CIs.
51

Figure 5.1. Generation of the TSA and selected CIs

5.2.3 Gear Fault Indicators

There are at least six failure modes for gears: surface disturbances, scuffing, deformations, 

surface fatigue, fissures/cracks, and tooth breakage. Each type of failure mode, potentially, can 

generate a different fault signature. Additionally, relative to the energy associated with gear 

mesh tone and other noise sources, the fault signatures are typically small. A number of 

researchers have proposed analysis techniques to identify these different faults [25,26]. 

Typically, these analyses are based on the operation of the TSA. Examples of analysis are:

• Residual Analysis. Shaft order 1, 2, and 3 frequencies, and the gear mesh harmonics, of 

the TSA are removed. Faults such as a soft/broken tooth generate a 1 per rev impact in 

the TSA. In the frequency domain of the TSA, impacts are expressed as multiple 

harmonics of the 1 per rev. The residual analysis removes the shaft order 1, 2, and 3 

frequencies and gear mesh harmonics in the frequency domain, and then the inverse FFT 

is performed. This allows the impact signature to become prominent in the time domain. 

CIs are statistics of this waveform (RMS, peak to peak, Crest Factor, and kurtosis).

• Energy Operator (EO), which is a type of residual of the autocorrelation function. For a 

nominal gear, the predominant vibration is gear mesh. Surface disturbances and scuffing 

generate small higher frequency values, which are not removed by autocorrelation. 

Formally, the EO is: TSA2:n-1 x TSA2:n-1 – TSA1:n-2 x TSA3:n . The bold indicates a vector 

of TSA values. The CIs of the EO are the standard statistics of the EO vector.

• Narrowband Analysis operates the TSA by filtering out all tones except that of the gear 

mesh and with a given bandwidth. It is calculated by zeroing bins in the Fourier 

transform of the TSA, except the gear mesh. The bandwidth is typically 10% of the 

number of teeth on the gear under analysis. For example, a 23-tooth gear analysis would 

retain bins 21, 22, 23, 24, and 25, and their conjugates in the Fourier domain. Then, the 

inverse FFT is taken, and statistics of the waveform are taken. Narrowband analysis can 

capture sideband modulation of the gear mesh tone due to misalignment, or detect a 

cracked/broken tooth.
52

• Amplitude Modulation (AM) analysis is the absolute value of the Hilbert transform of the 

Narrowband signal. For a gear with minimum transmission error, the AM analysis feature 

should be a constant value. Faults will greatly increase the kurtosis of the signal. 

• Frequency Modulation (FM) analysis is the derivative of the angle of the Hilbert 

transform of the narrowband signal. It is a powerful tool capable of detecting changes of 

phase due to uneven tooth loading, a characteristic of a number of fault types.

For a more complete description of these analyses, see [25] or [26]. Figure 5.2 is an example of 

the processing to generate the gear CIs for a spiral bevel gear with surface pitting and scuffing. 

Figure 5.2. Process for generating gear CIs

The cepstrum was also evaluated, although it is difficult to implement in an automated system. 

For bearing analysis, the envelope analysis was used.

5.3 Analysis Results

5.3.1 Synthetic Tachometer Signal

All shaft and gear analysis is based on the TSA, which requires a tachometer signal for a keyphasor. The data set contained an RPM signal, but not a raw tachometer signal. It was noticed 

that the RPM signal carried modulated noise. It was conjectured that this was the convolution of 

60 Hz power, with the 20/30 Hz output of the generator onto the RPM signal (indicating a poor 

ground). By removing the DC value of the RPM signal, then low pass filtering, the generator 20 

Hz signal was isolated and used as a tachometer zero crossing index. This is possible because the 

20 Hz generator signal is synchronous with the high speed shaft, see Figure 5.3.
53

Figure 5.3. Synthetic tachometer

5.3.2 High Speed Shaft/High Speed Pinion

The HSS/HSP showed a large shaft order 1 in the TSA Figure 5.4a (spectrum in G’s) and a large 

vibration in the AM signal (units of G’s) of Figure 5.4b coupled with a large phase change in the 

FM signal (units of radian). This indicates a large eccentricity (the gear was not centered on the 

shaft). Additionally, the energy operator was large and periodic, indicating severe

scuffing/pitting. There was limited evidence of a soft/broken tooth (a broken or soft tooth result 

in a 1/rev impact, which is visible in the residual analysis, the EO signal (units of G’s), and the 

AM and FM analysis). 

Figure 5.4a. HSS TSA/spectrum Figure 5.4b. HSS gear analysis
54

5.3.3 Intermediate Speed Shaft/High Speed Gear and Intermediate Speed Pinion

The ISS/HSG/ISP showed a large shaft order 4 in the TSA (Figures 5.5a and 5.5b). Since there is 

a 4:1 relationship with the HSS, this further confirms the eccentricity of the HSP. Both the HSG 

and ISP showed large (e.g., .05 G’s) energy operator, indicative of sever pitting/scuffing. The 

AM and FM signals did not indicate any missing teeth/soft teeth, but did reflect a high variation 

in loading due to the HSP (Figure 5.5b).

Figure 5.5a. TSA intermediate shaft Figure 5.5b. Intermediate speed pinion, where 

the units for the Energy Operator, 

Narrowband and Amplitude Modulation 

analysis are in G’s, and the Frequency 

Modulation analysis is in radians.

5.3.4 Sun/Planet Gear Analysis

The Sun Gear showed no soft/broken teeth. However the EO values are large. Similarly, the 

planet gears showed large EO values. This suggests that there is pitting/scuffing on these gears 

(Figures 5.6a and 5.6b). Because the accelerometer is in a fixed frame relative to the planet, the 

planet AM analysis should show a sinusoid of three cycles (corresponding to the number of 

plants passing the sensor. Because this is not present, it could indicate that one of the planet 

bearings is worn and the planet is not sharing the load evenly with its two neighboring planets 

(Figure 5.6b AM and FM plots). The bearing analysis could not confirm the presence of a planet 

bearing fault, although this may be due to poor window selection. The units for the Energy 

Operator, Narrowband and Amplitude Modulation analysis is in G’s, and the Frequency 

Modulation analysis is in radians.
55

Figure 5.6a. Sun gear Figure 5.6b. Planet gears

5.3.5 Annulus/Ring Gear

The ring gear shows no cracked tooth/soft tooth. The carrier is not cracked. The large EO 

indicates scuffing/pitting. There is some suggestion that the pitting is larger on the ring gear than 

the planet (Figure 5.7). Note that in the AM analysis, the variation in load is a function of the 

planets passing the fixed sensor. As suggested earlier, because the load is not even across all 

three planets, this may indicate planet bearing error. The units for the Energy Operator, 

Narrowband and Amplitude Modulation analysis is in G’s, and the Frequency Modulation 

analysis is in radians.

Figure 5.7. Ring gear

5.3.6 Bearing Analysis

Bearing analysis was based on the envelop algorithm. The raw data was heterodyned to the base 

band; the carrier frequency is based on the resonance of the bearing structure. The energy 

spectrum (units of G’s) is taken on the base band signal, where the modulation rate is taken as 

the bearing fault frequency [28].
56

Figure 5.8a. High speed shaft, downwind side Figure 5.8b. Intermediate speed shaft 

downwind side

It was found (Figures 5.8a, 5.8b, and 5.9) that most bearings had some level of damage. The 

analysis could not find direct evidence of a fault on the planet bearing. While some attempt was 

made in optimizing the window frequency using spectral kurtosis, it’s likely that the lack of 

performance was due to poor window selection in the envelope analysis.

Figure 5.9. Low speed shaft downwind side

5.4 Discussion

The lack of fleet data forces one into an analysis of individual algorithm waveforms. It is 

desirable to have vibration analysis off of a fleet of gearboxes to compare the test gearbox 

against. Additionally, it is desirable to have at least six months of condition indicator data on a 

gearbox to observe (or capture) degradation. Because of the lack of fleet data or any appreciable 

history, analysis was based on a “by eye” analysis. It is likely that better performance could be 

gained with more experience on this gearbox, or in comparison of waveforms with a known,

good gearbox. The algorithms, based on the TSA, appear to find faults that were consistent with 

[26]. In fact, most analysis did show a response indicative of a wear/fault. Because there seemed 

to be no broken/soft tooth, the residual analysis was nominal on all gears. It was noted that 

0 50 100 150

2

3

4

5

6

7

8

x 10-3

Gs

Freq (Hz)

Cage: 2

Ball: 50

Outer: 85

Gear: 5 Hz Inner: 70

AN6 ISSRadial Bearing: Int Speed Shaft: Downwind
57

cepstrum analysis showed numerous harmonics (indicative of fault), but because the cepstrum is 

not a synchronous analysis, it was difficult to assign a particular frequency with a component. 

In general, the analysis methodology seemed appropriate for wind turbines, and has the 

advantage of being relatively simple to implement in an autonomous manner, e.g., the generation 

of statistics from the analysis waveforms, which could be trended or a threshold set to indicate 

when a maintenance action needs to be performed. This lends credence that aerospace gearbox 

analysis techniques are appropriate for wind turbine gearbox analysis.
58

6 Review and Application of Methods and Algorithms in Wind 

Turbine Gearbox Fault Detection 

David Siegel*, Wenyu Zhao, Edzel Lapira, Mohammed AbuAli, and Jay Lee 

Center for Intelligent Maintenance Systems, University of Cincinnati *

Corresponding Author Email: siegeldn@mail.uc.edu

6.1 Introduction

This chapter contains a description of the method and algorithms used by the research team at the 

University of Cincinnati – Center for Intelligent Maintenance Systems (IMS) for the Round 

Robin study. The outline of this chapter is as follows: Section 6.2 provides an overview of the 

signal processing and feature extraction methods evaluated in the study by the IMS research 

team, followed by more specific details for each method. Section 6.3 provides a summary of the 

results for each evaluated method along with some additional discussion. The final summary 

table in Section 6.3 also provides an indication of which analysis methods were considered prior 

to and after the failure report was released. Lastly, conclusions and suggestions for future work 

are provided in Section 6.4. 

6.2 Signal Processing and Feature Extraction Methods

An overview of the signal processing methods evaluated during this study is provided in Table 

6.1, along with the advantages and disadvantages of each method. Despite its simplicity, the use 

of analyzing the vibration data in the frequency domain does have its merits for detecting gear 

related problems. Gear mesh frequencies and associated sidebands can be identified in the 

vibration spectrum and various vibration indicators or features can be calculated in the frequency 

domain [27]. The real cepstrum is particularly useful for analyzing a family of harmonics, which 

has application for gear related faults [24]. A series of sidebands can be analyzed by calculating 

the cepstrum and comparing them to the baseline condition; the magnitude of the peaks 

compared to that baseline can be used to diagnose the health condition for each gear. The 

calculation of the real cepstrum can also be performed from the frequency spectrum; this was a 

useful asset for this analysis since only a baseline frequency spectrum was provided. 

For bearing condition monitoring, the most established method in the literature is bearing 

envelope analysis, also called the high frequency resonance technique [24]. The general concept 

is that a spall or damage on the bearing race or rolling element causes a series of impacts that 

excite the structural resonances of the mechanical system; this causes an amplitude modulation 

effect in which the carrier frequency is the resonance frequency and the bearing fault frequency 

is the modulation frequency. By filtering around the excited resonance and performing the 

demodulation, the envelope spectrum, along with the calculated fault frequencies, can be used to 

diagnose the bearing condition. A more detailed description of bearing faults, the bearing 

envelope analysis method, and methods for selecting the band-pass filter frequency range are 

provided in [24]. Despite bearing envelope analysis being a very effective technique; the method 

usually requires a high sampling rate since the excited resonance can occur at frequencies above 

10 KHz for many applications. The selection of the band-pass filter is also a crucial aspect in the 

method and a current area of research [24]. The use of spectral kurtosis filtering can be used to 

select the filter band for the bearing envelope analysis method, as well as for calculating 

indicators for the overall health condition of the monitored gearbox [28]. 
59

Time synchronous averaging represents one of the most established signal processing techniques 

for gear condition monitoring. The method is ideally suited for the processing of gear vibration, 

since the synchronous averaging method enhances and separates the periodic gear vibration from 

the cyclostationary vibration of rolling element bearings. Additional processing methods can be 

performed on the time synchronous average signal, including the gear residual signal and the 

amplitude and phase modulation functions [18]. For planetary gearboxes, due to the relative 

motion of the planet gears and the multiple contact points between each planet gear meshing 

with the sun and ring gear, the traditional synchronous averaging algorithm is not able to isolate 

the individual vibration for each planet gear or the sun gear. Specific algorithms for performing 

synchronous averaging for planetary gears are also evaluated in this work; the method suggested 

by McFadden [29] is used in this study. This specific algorithm for planetary gearboxes does 

have some potential drawbacks; in particular, the long data acquisition period needed to perform 

the calculation procedure is a major challenge for implementing this method. 
60

Table 6.1. Summary of evaluated methods – advantages and disadvantages

# Technique Advantages Disadvantages

1 Frequency Domain

Sidebands around gear mesh frequencies 

can be identified and provide a relatively 

simple method for extracting gear 

condition indicators without a tachometer 

signal [27].

Signal to noise ratio is not enhanced by using 

a tachometer signal, which can help reduce the 

vibration from other sources not synchronous 

with the shaft and gear components.

2 Cepstrum

Convenient method for extracting 

information from a family of harmonics; 

ideally suited for extracting gear condition 

indicators due to sidebands and amplitude 

modulation [24].

Family of harmonics could be related to shaft 

problems such as imbalance or misalignment 

and may not be due to a gear related fault; 

requires a baseline for comparing the 

cepstrum and determining whether there is a 

significant change.

3 Bearing Envelope 

Analysis

Most established method for bearing 

diagnosis in the literature [28]; is more 

suited for detecting incipient bearing 

spalls.

Selection of the demodulation band is not 

trivial and still an area of active research [28],

also could require a higher sampling rate 

depending on the excited system resonance.

4 Spectral Kurtosis 

Filtering

Filters signal based on the frequency band 

that is most impulsive [30]; can be used to 

calculate features on the filtered signal and 

to select an appropriate filter in envelope 

analysis.

Extended spalls or faults might not be 

impulsive, and hence, this affects the ability of 

this method to detect these types of faults.

5 Time Synchronous 

Averaging

Enhances vibration synchronous with the 

shaft, residual signal can look for 

abnormalities in the regular meshing 

pattern, demodulation around gear mesh 

frequency can detect a soft tooth by 

analyzing amplitude and phase modulation 

signals [18].

Requires accurate tachometer signal for 

performing the synchronous averaging, might 

require a long acquisition time for low speed 

shafts due to the low rotational speed and 

collecting an ensemble of readings for 

averaging. 

6 Planet Separation 

Method

Specific algorithm designed for 

performing synchronous averaging for 

planetary gearboxes [29], provides a way 

to individually analyze the health condition 

of the multiple planet gears and the sun 

gear.

Requires very long acquisition time, collecting 

enough rotations to perform the averaging; 

also requires a tachometer for aligning the 

data with respect to the carrier rotation.

6.2.1 Frequency Domain Methods

For rotating machinery, gaining an understanding of the time domain and frequency domain 

signature is a typical first approach prior to applying more advanced processing methods. For 

meshing gears in particular, there are signature frequencies related to the gear mesh frequencies 

and sidebands; the use of the Fast Fourier Transform (FFT) and an analysis of the gear mesh 

frequency peaks and sidebands can provide an initial evaluation of the gear wheel health 

condition. Gears in a nominal healthy or degraded condition typically have a similar gear mesh 

frequency peak; however, the magnitude of the sidebands is more useful for assessing the gear 

health condition. In addition, the spacing of the sidebands can indicate which particular shaft 

and associated gear wheel is degraded [27]. An example vibration spectrum from this study is 

provided in Figure 6.1, in this example one can clearly identify the gear mesh frequency peak 

(for the high speed shaft gear and pinion) at 662 Hz in the vibration spectrum for the gearbox in 

the nominal baseline condition. The gear mesh frequency peak is also present in the vibration 

spectrum of the degraded gearbox; however, there are very large sidebands at 631 Hz and 691

Hz for the degraded gearbox. The sidebands are spaced at 30 Hz, which is the high speed shaft 
61

rotational speed; this initial example provides some evidence that the high speed pinion is 

degraded due to the sidebands observed in the vibration spectrum. 

Figure 6.1. Vibration spectrum - Case C: top plot - AN7 baseline;

bottom plot - AN7 degraded gearbox

To further quantify these observations from the vibration spectrum; a set of gear wheel vibration 

features was extracted using the baseline spectrum and the spectrum from the degraded gearbox. 

To quantify the magnitude of the sidebands, the sideband level was calculated using Equation

(6). In this calculation, SBLa stands for the sideband level, Sba1 is the magnitude of the lower 

sideband and SBa2 is the magnitude of the upper sideband. In addition, a sideband ratio was also 

calculated using Equation (7); this normalizes the sideband ratio by the gear mesh frequency 

peak. Prior work by Combet et al. [31] has shown this sideband ratio feature to be an effective 

metric to quantify gear health since it is less susceptible to load fluctuations due to the sideband 

magnitude being divided by the gear mesh frequency peak [31]. Table 6.2 provides a listing of 

the frequency domain gear features; a total of 16 were calculated. For each respective gear, four 

features were calculated. The sideband ratio and sideband level were calculated for the gear 

mesh frequency and the first harmonic of the gear mesh frequency. Also, the frequency domain 

gear features were only calculated for the four gears on the parallel gearbox stage; the analysis of 

the sideband patterns for the planetary gearbox is quite complicated and more advanced 

techniques were evaluated for the planetary gearbox. 
62

Table 6.2. Frequency domain gear features

Signal Feature Name # of Features

AN5 Side Band Ratio and Sideband level for Intermediate 

Speed Shaft Gear 4

AN6 Side Band Ratio and Sideband level for Intermediate 

Speed Shaft Pinion and High Speed Shaft Gear 8

AN7 Side Band Ratio and Sideband level for High Speed Shaft 

Pinion 4

SBLa = SBa1 +SBa 2 (6)

peak

a a

a GMF

SB SB SBR 1 + 2 = (7)

Example results using the frequency domain gear features are provided in Figure 6.2. In this 

example, the sideband ratio for the intermediate speed shaft pinion and the high speed shaft 

pinion are much larger in magnitude for the degraded gearbox when compared to the gearbox at 

the baseline condition. The sideband ratio for the high speed shaft gear is very similar to the 

baseline level and would imply that this particular gear is normal using this frequency domain 

feature. It should be noted in the failure report that the high speed shaft gear set was observed to 

have severe scuffing on both gears. In addition, the failure study reported that the intermediate 

speed shaft gear set had severe fretting corrosion and scuffing for both gears as well. From the 

frequency domain method, there is a strong indication that there is damage on the high speed 

shaft pinion. There also is an indication, but with lower confidence, of damage on the 

intermediate speed shaft pinion. However, there is little evidence from the frequency domain 

gear features of damage on the high speed shaft gear or the intermediate speed shaft gear despite 

the reported damage in the failure report. Other processing algorithms were used to further 

investigate the health condition of the parallel stage gear wheels, as well as the other bearing and 

gear components. If several processing methods provide evidence of a degraded component, this 

can provide an increased level of confidence that the component is damaged. 
63

Figure 6.2. Sideband ratio gear features – Case C: (a) Low speed shaft pinion;

(b) High speed shaft gear; (c) High speed shaft pinion

6.2.2 Cepstrum Processing Method

The real cepstrum provides a processing method that is ideally suited for analyzing a family of 

harmonics, in a much more consolidated way than the frequency domain representation. For 

calculating the real cepstrum, the inverse Fourier Transform is applied to the logarithm of the 

power spectrum, as shown in Equation (8), where Cxx(t) is the real cepstrum and A(f) is the 

frequency spectrum [24]. For mechanical systems and gears in particular, the cepstrum provides 

a convenient way of analyzing a series of sidebands that are spaced at a given shaft speed; 

comparing the cepstrum from a baseline and current state can be used to infer the health 

condition of each gear. The example cepstrum result in Figure 6.3 further illustrates this aspect,

in which the cepstrum from the baseline gearbox is compared to the degraded gearbox. In both 

instances, one can observe a peak in the cepstrum at 0.133s, which corresponds to 7.5 Hz and the 

intermediate speed shaft. This implies that a family of harmonics spaced at 7.5 Hz was always 

present in this gearbox. However, an additional peak at 0.0325s, which corresponds to 30 Hz 

and the high speed shaft, can be seen in the cepstrum of the degraded gearbox. This additional 

set of harmonics spaced at 30 Hz for the degraded gearbox provides evidence that the gear wheel 

on the high speed shaft (high speed shaft pinion) is degraded and is responsible for this 

noticeable change in the cepstrum. 

( ) [2 ln( ( )]] 1 C A f xx

− τ = I (8)
64

Figure 6.3. Real cepstrum - Case C: top plot - AN7 baseline; bottom plot - AN7 degraded gearbox

Figure 6.4. Cepstrum peak features from Case C: blue – baseline; red - degraded gearbox
65

Additional vibration features were extracted from the cepstrum at the corresponding shafts, using 

data from both the baseline gearbox and the degraded gearbox. Example results from the 

cepstrum features are provided in Figure 6.4, in which several peaks in the cepstrum are 

noticeably larger in magnitude when comparing the degraded gearbox to the baseline gearbox. 

The cepstrum peak related to the high speed shaft pinion is highlighted, since this feature was 

dramatically larger in magnitude for the degraded gearbox. This provides an additional set of 

evidence that the high speed shaft pinion is damaged. To further quantify the difference in the 

cepstrum features from the baseline state, and diagnose which gear in a meshing pair had the 

most severe condition, a cepstrum based health indicator using Equation (9) was calculated [32]. 

In this calculation, d(t) is the cepstrum health indicator, Ap(t) is the cepstrum peak for the input 

gear at time t, Ar(t) is the cepstrum peak for the output gear at time t, Ap(0) is the cepstrum 

baseline peak for the input gear, and Ar(0) is the cepstrum baseline peak for the output gear. For 

a monitored system, this health indicator would be zero in the baseline condition, close to -1, if 

the output gear is degraded, and close to 1 if the input gear is degraded. Figure 6.5 provides a 

result from this health indicator calculation, for the high speed shaft gear and pinion meshing 

pair. The health indicator is near -1 for all 10 data samples, which indicates that the high speed 

pinion is the gear with the more severe level of damage, according to this metric. This agrees 

with the previous result from the sideband features in the vibration spectrum, in which there was 

evidence of damage on the high speed shaft pinion, but little evidence of damage on the high 

speed shaft gear. 

( ) / (0) ( ) / (0)

( ) / (0) ( ) / (0) ( )

p p r r

p p r r

A t A A t A

A t A A t A

d t

+

− = (9)

Figure 6.5. Cepstrum health Indicator for Case C calculated for high speed shaft gear and pinion

1 2 3 4 5 6 7 8 9 10

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Sample #

Cepstrum Peak / Ratio

Cepstrum Peak Ratio Plot (HSS/ISS) - Case C

ratio index (d21)

Sum Index

ISS CepPeak

HSS CepPeak
66

6.2.3 Bearing Envelope Analysis

Although the area of bearing condition monitoring has been an area of research for quite some 

time, with new algorithms and methods proposed each year; the bearing envelope analysis 

method remains one of the more effective techniques for bearing condition monitoring [28]. A 

more detailed description of bearing envelope analysis can be found in prior work [28, 33], 

therefore, this study simply provides a brief review of the method and highlights the results for 

this study. A flow chart that shows the steps in this algorithm is provided in Figure 6.6, in which 

the initial step is to band pass filter around an excited natural frequency. The selection of the 

band-pass filter center frequency and bandwidth is an important step and also a current area of 

research [28]. In this study, the filter parameters were selected by inspection of the frequency 

domain spectrum for the respective accelerometers, but alternative methods could also be 

considered. After filtering the signal, the Hilbert Transform is used to extract the envelope 

signal, which is further analyzed in the frequency domain. For a bearing with damage on the 

rolling element or bearing races, the bearing fault frequency peaks are usually much easier to 

distinguish in the envelope spectrum when compared to the frequency spectrum. 

Figure 6.6. Bearing envelope analysis flow chart

For performing envelope analysis in this Round Robin study, a band pass filter centered at 

10,000 Hz, with a bandwidth of 1000 Hz was used, with the exception of accelerometer AN10 in 

which two different frequency bands were evaluated. Sample results from this method are 

provided in Figure 6.7, in which the envelope spectrum is shown for accelerometer AN6 and 

AN7. The envelope spectrum for AN6 shows noticeable peaks at 73 Hz and 345 Hz. The peak 

at 73 Hz corresponds to the ball pass frequency inner race (BPFI) for the intermediate shaft 

upwind bearing. The failure report confirms the inner race damage for this particular 

intermediate shaft bearing. The peak at 345 Hz is very close to the calculated BPFI frequency 

(336 Hz) for the high speed shaft downwind bearing; the failure report confirms that this bearing 

had inner race damage, with overheating as the mode. The envelope spectrum for AN7 also 

clearly shows a peak at the BPFI frequency (345 Hz) for the high speed shaft downwind bearing. 

The envelope spectrum for accelerometer AN10 in Figure 6.8 is provided using two different 

band pass filter ranges; the first one is at a high frequency from 9,500 Hz - 10,500 Hz and the 

later is from a frequency range of 4,000 Hz – 6,000 Hz. The results shown in Figure 6.8 (a) 

clearly show a peak at the BPFO and its first harmonic for the intermediate speed shaft 

downwind bearing; the failure report confirms that there was an outer race damage on this 

Vibration Signal

Band pass filter around excited natural 

frequency

Take Hilbert Transform of band 

pass signal

Take magnitude of analytical signal 

to obtain envelope signal

Take Fast Fourier Transform (FFT) 

of envelope signal

Analyze envelope spectrum at 

bearing fault frequencies
67

bearing. The envelope spectrum in Figure 6.8 (b) shows a peak at the BPFO for the planet 

carrier upwind bearing; this bearing also had outer race damage according to the failure report. 

Using a filter from 9,500 Hz-10,500 Hz would have resulted in a missed detection for the planet 

carrier upwind bearing. Using the frequency band from 4000 Hz - 6000 Hz resulted in a 

detection of an outer race fault on the planet carrier bearing; however, it provided a less clear 

detection for the ISS downwind bearing, in which only the first harmonic of the BPFO could be 

identified.

Figure 6.7. Envelope spectrum - Case C: (a) AN6 - peaks at BPFI for ISS upwind bearing and HSS 

downwind bearing; (b) AN7 - BPFI peak for HSS downwind bearing

Figure 6.8. Envelope spectrum accelerometer AN10 - Case C: (a) band-pass filter from 9500 Hz -

10,500 Hz, peaks at BPFO and 2X BPFO for ISS downwind bearing; (b) band pass filter from 4000

Hz - 6000 Hz, peak at BPFO for planet carrier upwind bearing and also peak at 2X BPFO for ISS 

downwind bearing
68 

6.2.4 Spectral Kurtosis Filtering

For condition monitoring of mechanical systems, the vibration signals for damaged gear and 

bearing components typically display an impulsive signature. Detecting that impulsive signature 

is not a trivial task since the signature could be masked by other sources of vibration. 

Techniques and filtering methods based on spectral kurtosis are aimed at finding the optimal 

frequency band for recovering the impulsive fault signature that could be hidden in the raw 

vibration waveform. A brief review of the calculation procedure and the results of this study are 

provided, and the interested reader is referred to the work by Antoni et al [30] and Combet et al 

[34] for a more detailed discussion on the use of spectral kurtosis for filtering vibration signals. 

The initial step in this algorithm is to calculate the short time Fourier Transform of the vibration 

signal, denoted by H(t,f). Equation (10) indicates that the average value of the fourth power of 

H(t,f) is divided by the mean square value of H(t,f), which provides a kurtosis value as a function 

of frequency. The Wiener filter is constructed using the kurtosis values for each frequency bin, 

as shown in Equation (11); the frequency bin is only included if the kurtosis value is above a 

statistical threshold at a given confidence level [30]. The Wiener filter is then multiplied by the 

frequency domain representation of the original signal, X(f), and the result is transformed back to 

the time domain as indicated in Equation (12). The advantage of this method is that the signal is 

filtered without any a priori knowledge of which frequency band to filter in, and instead is based 

on which frequency band is most impulsive. 

2

),(

),( )( 2 2

4

= −

ftH

ftH

r fK

(10)







 > = 0 Otherwise

)(Kfor )( )( ˆ r α fK sf fW r (11)

{ })()( ˆ )( 1 fXfWty − I= (12)

In this study, the filtering algorithm was used to process data for all 12 accelerometers using a 

block size of 256 data samples and an overlap of 80% when performing the short time Fourier 

Transform calculation. When applying this processing method, only high kurtosis values were 

observed for accelerometers AN3 and AN4; thus, the example results do not include the other 

accelerometers. An example result from the filtering method is provided in Figure 6.9 from 

accelerometer AN4, in which one can observe that the Wiener filter is focused on the high 

frequency content of the signal from approximately 8 KHz - 18 KHz. This implies that although 

the rotational frequencies of the carrier are quite low; structural resonances at a high frequency 

appear to be excited by defects and damage from the internal components within the planetary 

gearbox. Figure 6.9 illustrates how the impulsive signature is masked in the raw time signal, but 

is quite clear in the filtered signal; the raw signal has a kurtosis value of only 3.39 compared to a 

kurtosis value of 169 for the filtered signal. Further examination of the filtered signal shows a 

pattern that repeats for every 2 revolutions of the carrier. This periodic pattern in the filtered 

signal from accelerometer AN4 is shown in Figure 6.10. The high kurtosis value of the filtered 

signal, along with the periodic pattern that is related to the carrier rotation, and the location of the 

accelerometer each point to a problem with the internal components in the planetary gearbox. 

However, it was difficult to determine which gear or bearing component was the cause of this 

problem from the filtered signal and the envelope spectrum; a potential reason is that multiple 
69

faults occurred in the planetary gearbox. The results from the failure report indicate that the ring 

gear and sun pinion both had scuffing and corrosion damage and the planet carrier's upwind 

bearing had damage on the outer race. 

Figure 6.9. (a) Wiener filter based on spectral kurtosis; (b) raw and filtered AN4 accelerometer 

signal – Case A

Figure 6.10. Filtered AN4 signal showing the periodic repetition based on 2 revolutions of the 

carrier – Case A

0 1 2 3 4 5 6 7 8

-100

0

100

Time (s)

Vibration (m/s2)

Filtered AN4 Signal (First 2 Rotations)

0 1 2 3 4 5 6 7 8

-100

0

100

Time (s)

Vibration (m/s2)

Filtered AN4 Signal (Third and Fourth Rotations)

0 1 2 3 4 5 6 7 8

-100

0

100

Time (s)

Vibration (m/s2)

Filtered AN4 Signal (Fifth and Sixth Rotations)
70

The results in Figures 6.9 and 6.10 and were from an example data file from Case A. The same 

filtering method was also applied to the remaining data files and the kurtosis feature from the 

filtered signal was stored. The results of the filtered kurtosis value are provided in Figure 6.11 

and provide an interesting point for discussion. The kurtosis values were very large for files 

from Case A, with values above 50. It is also worth noting that the kurtosis values show a 

decreasing trend for the data files in Case A, in which each file was collected in sequential order. 

For Case B and Case C, the kurtosis values are quite low and in a normal range between 2 and 4. 

This implies that the fault signature was not present for accelerometer AN3 and AN4 for the 

operating conditions in Case B and Case C. This could imply that the operating conditions for 

Case A are more conducive for detecting this type of problem in the planetary gearbox. 

However, it is also worth noting that the data was collected in sequential order from Case A to 

Case C; this could imply that the vibration signature became less impulsive with the running 

time of the gearbox. Despite these discussion points for potential reasons as to why the signature 

was not present in all three operating conditions, the spectral kurtosis filtering method provided a 

very clear detection of a problem in the planetary gearbox for Case A, based on the very high 

kurtosis values. This provided enough confidence and evidence to believe that the internal 

components in the planetary gearbox stage were degraded. 

Figure 6.11. Kurtosis of filtered signal - shown for all 3 cases

6.2.5 Time Synchronous Averaging

This section discusses the results using time synchronous averaging for the parallel stage gears 

and the ring gear. The rationale for excluding the results for the planet and sun gears in this 

section is that a specific algorithm is needed for extracting the synchronous average signals for 

the individual planet and sun gears. The synchronous averaging algorithm and results for the 

plant and sun gears are provided in section 6.2.6. For all gears, the results from the residual 

signal, amplitude modulation signal, and the phase modulation signal are extracted and analyzed 

for determining the health condition of each gear. 

0 5 10 15 20 25 30

0

50

100

150

200

250

Sample #

Kurtosis of Filtered Signal - AN4

Kurtosis of Filtered Signal - AN4 - All Cases

Case A

Case B

Case C
71

The additional processing methods for the residual signal (section 6.2.5.1) and the amplitude and 

phase modulation signals (section 6.2.5.2), first require the extraction of the time synchronous 

average signal for each shaft. The time synchronous averaging algorithm requires a reference 

pulse train for aligning the data with respect to a given shaft, and ensemble averaging the signal 

over several rotations. In this study, a tachometer signal was not provided, but an alternative 

method was used for extracting a reference signal. The provided speed signal had a clear tone at 

the generator shaft speed (20 Hz or 30 Hz); band pass filtering in a range between 15 Hz – 35 Hz 

provided a way of extracting a pulse train from the speed signal. The filtered speed signal was 

used as a surrogate for the tachometer signal; alternative methods that use the gear mesh 

frequency peak for estimating a synthetic tachometer signal could also have been used [35]. 

With the necessary reference signal, the vibration signals could be aligned and ensemble 

averaged with respect to the carrier, low speed shaft, intermediate speed shaft, and the high speed 

shaft, using the established synchronous averaging methods. More specific details on the 

synchronous averaging method including the different interpolation methods; the frequency 

domain implementation can be found in [36]. In this study, a time domain interpolation method 

was used. From the provided vibration signals, accelerometer AN3 was used for calculating the 

time synchronous average signal for the carrier shaft, AN5 was used for the low speed shaft, 

AN6 was used for the intermediate speed shaft, and AN7 was used for the high speed shaft.

6.2.5.1 Gear Residual Signal

The extraction of the periodic vibration waveform using time synchronous averaging allows one 

to further analyze the vibration signature and meshing pattern for each gear. Departures of the 

regular meshing pattern could be indicative of a fault in the gear; the residual signal aims to 

remove the regular meshing pattern from the synchronous signal to further examine this aspect. 

The residual signal for a gear can be calculated by removing the shaft harmonics and the gear 

mesh frequency and harmonics from the time synchronous average signal [18]. Considering that 

the time synchronous average signal of the gear is aligned with the shaft, the signal is periodic 

and the filtering can be conveniently performed in the frequency domain and transformed back to 

the time domain. It is common to remove the first five shaft harmonics, the gear mesh 

frequency, and all of the gear mesh frequency harmonics when calculating the residual signal. 

Prior works from seeded fault studies have also shown the residual signal to be effective for 

detecting gear tooth pitting faults [37]. 

The time synchronous average signal and the residual signal are shown in Figure 6.12 for the 

high speed shaft pinion. The kurtosis value of the residual signal for this gear is quite low (2.34),

and there appear to be no abnormalities that can be seen in the time averaged signal or the 

residual signal. However, previous results from the cepstrum and frequency domain methods 

indicated large sidebands and a significant problem with this high speed shaft pinion; these were 

also confirmed in the failure report study. Large sidebands are noticed in the frequency domain 

representation of the time synchronous average signal for the high speed shaft, which is provided 

in Figure 6.13. The gear mesh frequency peak (order 22) is lower in magnitude then a peak at 

one of the sidebands (order 23). The inability for the residual signal to detect this fault on the 

high speed shaft pinion highlights the importance of extracting multiple gear vibration features to 

have better coverage for the different failure modes. 
72

Figure 6.12. TSA signal and residual signal from accelerometer AN7 - Case C: top plot - TSA signal 

for high speed shaft pinion; bottom plot - residual signal for high speed shaft pinion

Figure 6.13. TSA vibration spectrum for accelerometer AN7 and high speed shaft – Case C

Another example residual signal is shown for the ring gear in Figure 6.14. The kurtosis value of 

the ring gear is also in a normal range (3.36), and there appears to be no abnormal patterns or an 

0 50 100 150 200 250 300 350 400

-4

-2

0

2

4

High Speed Shaft Angle (degree)

Vibration (m/s2)

Time Synchronous Signal HSS Pinion

0 50 100 150 200 250 300 350 400

-4

-2

0

2

4

High Speed Shaft Angle (degree)

Vibration (m/s2)

Residual Signal HSS Pinion

Kurtosis Value of 2.3433

0 50 100 150

0

0.2

0.4

0.6

0.8

1

1.2

X= 23

Y= 0.35919

Orders of High Speed Shaft

Vibration (m/s2)

TSA Spectrum High Speed Shaft AN7
73

indication of a fault in the time synchronous average signal or the residual signal for the ring 

gear. This is in sharp contrast to the results from the phase modulation function provided in the 

subsequent section, in which there is a clear indication of damage on the ring gear. The residual 

signal for the other parallel shaft gears also offers no indication of damage. This highlights that 

the residual signal was not the most appropriate algorithm for detecting the failure modes that 

were occurring on the parallel shaft gears and the ring gear. 

Figure 6.14. TSA signal and residual signal from accelerometer AN3 - Case C: top plot - TSA signal 

for ring gear; bottom plot - residual signal for ring gear

6.2.5.2 Amplitude and Phase Modulation

For detecting local defects, such as a fatigue crack in a gear wheel, the prior work done by 

McFadden [38] suggested an analysis of the amplitude and phase modulation function of the 

gear vibration. For performing this analysis, the synchronous average signal for a given shaft is 

performed. A band pass filter around a dominant gear mesh frequency is used and typically 

includes a number of sidebands around the gear mesh frequency peak. The Hilbert Transform is 

then performed on the filtered signal. The modulus and phase of the analytical signal provide the 

envelope and phase modulation functions, respectively. The amplitude and phase modulation 

functions were calculated for each gear wheel in this study. In addition, the kurtosis of the 

amplitude modulation function and the kurtosis of the derivative of the phase modulation 

function were also calculated to quantify the health condition of each gear. For the parallel shaft 

gears, the band pass filter included four sidebands, while the band pass filter for the ring gear 

included six sidebands. The accelerometer AN3 was also effectively down sampled to 200 Hz 

prior to extracting the synchronous average for the ring gear. Sample results for this method are 

provided in Figure 6.15, in which the amplitude and phase modulation functions are plotted for 

0 50 100 150 200 250 300 350 400

-0.15

-0.1

-0.05

0

0.05

Carrier Angle (degree)

Vibration (m/s2)

Time Synchronous Signal Ring Gear

0 50 100 150 200 250 300 350 400

-0.1

-0.05

0

0.05

0.1

Carrier Angle (degree)

Vibration (m/s2)

Residual Signal Ring Gear

Kurtosis Value of 3.3604
74

the high speed shaft pinion. As one can observe, there are significant jumps in the phase 

modulation function for this gear and a high kurtosis value at 12.8. This would be an indication 

of a damage on the high speed shaft pinion. In addition, the amplitude modulation function is 

close to zero when these significant changes in phase occur. The phase modulation function for 

the high speed shaft gear had a moderate indication of a gear problem, with a kurtosis value of 

5.2. However, there was no indication of a problem for the intermediate speed shaft gear or 

pinion. Another example is provided in Figure 6.16, in which the amplitude and phase 

modulation for the ring gear is provided. There appears to be a clear indication of a problem 

with the ring gear through visual observation of the amplitude and phase modulation signals. 

The phase modulation function, in particular, has a high kurtosis value and two noticeable shifts 

in phase, which indicate a damaged gear. In summary, the amplitude and phase modulation 

functions provide a strong indication of a problem with the ring gear and high speed shaft pinion, 

and a moderate indication for the high speed shaft gear; however, there was no indication of a 

problem for the other gear wheels. 

Figure 6.15. High speed pinion amplitude and phase modulation signal from accelerometer AN7 -

Case C: top plot - Time Synchronous Average; middle plot - amplitude modulation signal;

bottom plot - phase modulation signal

0 50 100 150 200 250 300 350 400

-5

0

5

High Speed Shaft Angle (degree)

Vibration (m/s2)

Time Synchronous Signal HSS Pinion

Kurtosis Value of 2.8923

0 50 100 150 200 250 300 350 400

0

0.5

1

1.5

High Speed Shaft Angle (degree)

 Envleope (AM) (m/s2)

AM and PM Modulation Signal HSS Pinion

Kurtosis Value of 2.5465

0 50 100 150 200 250 300 350 400

-20

-10

0

10

High Speed Shaft Angle (degree)

Phase Modulation (Rad)

Kurtosis Value of 12.8058
75

Figure 6.16. Ring gear amplitude and phase modulation signal from accelerometer AN3 - Case C:

top plot – TSA; middle plot - amplitude modulation signal; bottom plot - phase modulation signal

6.2.6 Planet Separation Algorithm – Time Synchronous Averaging

Considering the relative motion of the planet gears and the multiple mesh points that occur 

because the planet gears mesh with the ring gear and sun gear simultaneously, it is necessary to 

use a specific algorithm for extracting the time synchronous average signal for the individual 

planet and sun gears. The algorithm considered in this study follows the algorithm proposed by 

McFadden et al [29]. There are variations of this algorithm, including the method proposed by 

researchers at the Defence Science and Technology Organisation (Australia) (DSTO) [39], as 

well as a version that uses multiple accelerometers on the planetary gearbox housing [40]. A 

flow chart of the algorithm is provided in Figure 6.17 and highlights the algorithm processing 

steps. The initial step is to calculate the time synchronous average signal with respect to the 

carrier rotation. The central idea in this method is to capture a meshing period of each tooth 

when the planet gear is in very close proximity to the fixed accelerometer on the gearbox 

housing. To accomplish this, it is necessary to know when the planet gear is passing by the fixed 

accelerometer. Considering the amplitude modulation effect from the increased vibration level,

as each planet passes the fixed accelerometer; the narrow band envelope signal can be used to 

determine the number of planet passing instances. A window function is applied to the 

synchronous average signal when each planet gear passes for a short period of time; the short 

period of time is typically one to three gear mesh periods. Based on the number of teeth for each 

respective gear, a lookup table can be used to determine which tooth was meshing during that 

captured time signal. Then, it is stored in the proper location in the array. This capture of the 

windowed data is repeated for each tooth and requires several rotations of the carrier; the number 

0 50 100 150 200 250 300 350 400

-0.1

0

0.1

Carrier Angle (degree)

Vibration (m/s2)

Time Synchronous Signal Ring Gear

Kurtosis Value of 3.3138

0 50 100 150 200 250 300 350 400

0

0.005

0.01

Carrier Angle (degree)

Envleope (AM) (m/s2)

AM and PM Modulation Signal Ring Gear

Kurtosis Value of 4.1418

0 50 100 150 200 250 300 350 400

-10

-5

0

5

Carrier Angle (degree)

Phase Modulation (Rad)

Kurtosis Value of 33.0163
76

of rotations is equal to the reset time for the planet or sun gear. The result is an assembled 

vibration signal for each gear tooth. This process is repeated until several assembled signals can 

be constructed. Lastly, the constructed waveforms are ensemble averaged and this completes the 

process for extracting the time synchronous average

Figure 6.17. Flow chart for planet separation algorithm

For implementing this method, accelerometer AN3 was initially down sampled to a 200 Hz 

sampling rate. Considering the number of carrier rotations and time period needed by this 

algorithm, five files from Case C were concatenated and combined prior to applying the 

algorithm. A narrow band filter that included four sidebands around the gear mesh frequency 

was applied to the time synchronous average signal for the carrier. The envelope signal of the 

filtered signal is provided in Figure 6.18 and one can clearly observe noticeable peaks that are 

related to the planet passing the fixed accelerometer. The angular spacing of the peaks is 

approximately 120 degrees, which again confirms that these peaks correspond to the passing of 

the three planet gears. For capturing the meshing vibration during the planet passing, a Tukey 

window is used. An example Tukey window is shown in Figure 6.19, in which Nv was set to 

three to capture the vibration for three mesh periods. Using these parameters for the planet 

separation algorithm, the synchronous average signal was extracted for each planet gear and the 

sun gear; the number of averages was eight for the planet gears and 15 for the sun gear. The 

residual signals and amplitude and phase modulation signals were also calculated to further 

analyze the health condition of the gear wheels. For the amplitude and phase modulation signals, 

a band pass filter that included three sidebands was used. 

Vibration Signal

Perform TSA with respect to carrier

Determine planet passing by narrow 

band demodulation

Apply window function for a tooth mesh 

period during planet passing

Store windowed data according to tooth 

number 

Assemble signal from each tooth

Repeat Steps 1-6 and take the average 

of the ensemble

1.

2.

3.

4.

5.

6.

7.
77

Figure 6.18. Narrow band amplitude modulation signal for determining planet passing - Case C

Figure 6.19. Example Tukey window used for planet separation algorithm - in this study,

Nv was set to 3 to include 3 mesh periods

Sample results from the synchronous averaging signal and the residual signal are provided in 

Figure 6.20, in which the result is shown for one of the planet gears. In this example, the time 

synchronous average signal and the residual signal show no abnormal behavior for the planet 

gear; the failure report found no defects on any of the planet gears. The spectrum for the time 

0 0.5 1 1.5 2 2.5 3 3.5 4

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Tooth Mesh Period

Window Magnitude

Example Tukey Window

Tv=NvTm
78

synchronous average signal for this planet gear is shown in Figure 6.21, and one can observe a 

clear gear mesh frequency peak at the 39th order. The sidebands are not large in magnitude in the 

spectrum and the planet gear appears to be in a health state from these data processing results. 

The other two planet gears were also considered to be in a normal condition based on similar 

results that were observed in their time synchronous average signal and residual signal. 

Figure 6.20. Top - TSA signal for Planet 2; bottom - residual signal for Planet 2 – Case C

Figure 6.21. TSA vibration spectrum for Planet 2 – Case C

0 5 10 15 20 25 30 35 40

-0.2

-0.1

0

0.1

0.2

Planet Tooth

Vibration (m/s2)

Time Synchronous Signal Planet 2

0 5 10 15 20 25 30 35 40

-0.1

-0.05

0

0.05

0.1

Planet Tooth

Vibration (m/s2)

Residual Signal Planet 2

Kurtosis Value of 3.287

0 50 100 150

0

0.005

0.01

0.015

0.02

0.025

0.03

X= 39

Y= 0.028945

Orders for Planet 2

Vibration (m/s2)

TSA Planet 2 Spectrum
79

The time synchronous average signal and the residual signal analysis were also performed for the 

sun gear, with the results provided in Figure 6.22. In this example, the residual signal is 

providing a moderate indication of damage on the sun gear, with a kurtosis value of 5.36. The 

failure report confirms scuffing and fretting corrosion on the sun pinion. Additional narrowband 

amplitude modulation and phase modulation analysis was also performed on the time 

synchronous average signals for the planet gears and the sun gear. Although the residual signal 

provided an indication of damage on the sun gear, the amplitude and phase modulation signals 

did not provide any indication of damage on the sun gear. A sample result from one of the planet 

gears is provided in Figure 6.23. Both the amplitude and phase modulation signals do not 

indicate damage on this particular planet gear. The other two planet gears also did not have any 

indication of damage from the narrowband amplitude and phase modulation analysis; this is 

encouraging since the failure report did not find any damage on any of the three planet gears. 

For the sun gear, the residual signal provided a moderate indication of damage, but no damage 

was indicated from the amplitude and phase modulation signals.

Figure 6.22. Top - TSA signal for sun gear; bottom - residual signal for sun gear – Case C

0 2 4 6 8 10 12 14 16 18 20

-0.15

-0.1

-0.05

0

0.05

Planet Tooth

Vibration (m/s2)

Time Synchronous Signal Sun Gear

0 2 4 6 8 10 12 14 16 18 20

-0.1

-0.05

0

0.05

0.1

Planet Tooth

Vibration (m/s2)

Residual Signal Sun Gear

Kurtosis Value of 5.3562
80

Figure 6.23. Planet Gear 2 amplitude and phase modulation signal from accelerometer AN3 –

Case C: top plot – TSA; middle plot - amplitude modulation signal;

bottom plot - phase modulation signal

6.3 Summary of Results

For each data processing method, a qualitative metric was assigned based on its ability to detect 

each failed component in the gearbox used in this study; the results are provided in Table 6.3. 

For each failed component and algorithm, a ranking of three levels is assigned for low, medium, 

and high confidence; the rankings are based on examining the output plots and the calculated 

features. An example of a high confidence rating is the amplitude and phase modulation results 

for the high speed pinion, in which the output plots and large kurtosis values are clear indications 

of damage. In certain instances, an algorithm was not evaluated for detecting a failed component 

or the algorithm is not designed or suited for that task. In this case, the label of NA (not 

applicable) was assigned. An example of the NA ranking is a bearing envelope analysis for 

detecting damage on any of the gear wheels. The spectral kurtosis method was only applied to 

the planetary gearbox (signals AN3 and AN4) and could only provide an indication of 

degradation to the planetary stage, but not which specific gear was degraded. This is reflected in 

the table with the additional notation of “stage” for the spectral kurtosis technique. Lastly, the 

rankings are given a black color if the method was applied prior to the release of the failure 

report and a blue color if the method was applied after the failure report was provided. Bearing 

envelope analysis, time synchronous averaging, and the planet separation algorithm were all 

performed after the failure report was released. 

From the tabular results in Table 6.3, one can observe that the high speed pinion had high 

indications of damage from several techniques, including the vibration spectrum, cepstrum 

processing, and narrowband analysis from the phase modulation signal. Only the residual signal 

0 5 10 15 20 25 30 35 40

-0.2

0

0.2

Planet 2 Tooth

Vibration (m/s2)

Time Synchronous Signal Planet Gear

Kurtosis Value of 3.3138

0 5 10 15 20 25 30 35 40

0.02

0.03

0.04

Planet2 Tooth

Envleope (AM) (m/s2)

AM and PM Modulation Signal Planet2 Gear

Kurtosis Value of 2.8756

0 5 10 15 20 25 30 35 40

-4

-3

-2

Planet2 Tooth

Phase Modulation (Rad)

Kurtosis Value of 2.1986
81

did not provide an indication of a fault for the high speed pinion. The residual signal in general 

did not detect damage on the gear wheels for this study, with only a moderate indication of 

damage on the sun gear. The intermediate speed shaft pinion had a moderate indication of 

damage from both frequency domain analysis and the cepstrum features; however, there was no 

indication of damage by the narrow band analysis. Bearing envelope analysis provided high 

confident indications for three of the bearing failures that were on the intermediate and high 

speed shafts. The bearing damage on the planet carrier upwind bearing had only a moderate 

detection; the peak was less noticeable and a different band pass filter range had to be used to 

detect this fault. For the planetary gearbox, the ring gear appeared to be the easiest to detect, 

with a high confidence indication of damage from the narrowband phase modulation signal. It 

should be noted that none of the planet gears had damage according to the failure report; this 

agrees with the results from the data processing, in which none of the algorithms detected any 

abnormality or damage with the planet gears. In summary, many of the failed components could 

be detected using the evaluated algorithms. However, for gear components, in particular, 

multiple algorithms appear necessary since many of the algorithms are only tuned to one failure 

mode. 

Table 6.3. Summary of results for each algorithm with the following notation: L-low confidence, M-medium 

confidence, H-high confidence, NA –not applicable or evaluated; black - indicates a method that was 

evaluated before the failure report, blue - indicates a method that was evaluated after the failure report

Failed Component Frequency 

Domain Cepstrum Spectral Kurtosis

Bearing 

Envelope

Analysis

TSA –

Residua

l Signal

TSA –

Amplitude / 

Phase 

Modulation

HSS Pinion H H NA NA L H

HSS Gear L L NA NA L M

ISS Pinion M M NA NA L L

ISS Gear L M NA NA L L

Ring Gear NA NA H - stage NA L H

Sun Pinion NA NA H - stage NA M L

ISS Upwind 

Bearing NA NA NA H NA NA

ISS Downwind 

Bearings NA NA NA H NA NA

HSS Downwind 

Bearings NA NA NA H NA NA

Planet Carrier 

Upwind Bearing NA NA NA M NA NA
82

6.4 Conclusions and Future Work

This chapter provides an evaluation of vibration signal processing and feature extraction 

algorithms used by the research team at the Center for Intelligent Maintenance Systems (IMS) 

for the Condition Monitoring Round Robin study. As one can observe from the summary results

table, most of the failed components could be detected by one or more of the processing 

methods. This is encouraging and highlights that vibration-based condition monitoring can be 

used to assess and diagnose which components are in a failed condition. For gear wheels in 

particular, the use of multiple algorithms appears necessary, considering the different number of 

gear failure modes that are possible. The residual signal, in particular, did not seem suited for 

the failure modes exhibited by the damaged gear wheels on the parallel stage shaft, while the 

other algorithms provided more confident detections. The detection results for each algorithm do 

not account for the additional hardware or on-board processing requirements. The planet 

separation algorithm, in particular, is difficult to implement given the time period required to 

accumulate enough rotations of the carrier shaft. 

Although the results from this study were encouraging, there are some aspects that could have 

aided the study or should be considered for future work. This study could have been aided by 

time domain waveforms instead of frequency spectrums provided for the baseline data. Many of 

the more advanced algorithms require the raw time waveform and they could not be evaluated 

based on the baseline data set. In addition, alternative methods were used for acquiring a 

reference signal for performing synchronous averaging. Further experimental studies should 

acquire and save a tachometer pulse train to avoid this issue. Considering that the gearbox was 

already in a severely damaged condition, the algorithms were evaluated on the basis of their 

ability to detect the health state of the various bearing and gear components. Unfortunately, this 

does not allow one to evaluate the algorithms ability to provide an early detection of a problem 

or whether the extracted vibration features are monotonic with the damage level. Both early 

detection and severity estimation are additional aspects worth evaluating for vibration-based 

condition monitoring techniques for wind turbine drivetrains. Continuous monitoring of a wind 

turbine drivetrain from a baseline condition until failure could provide a way to further evaluate 

the merits of the vibration-based condition monitoring algorithms. 
83

7 Defect Diagnosis in Wind Turbine Gearbox based on Sideband 

Energy and Enveloping Spectral Analysis

Robert X. Gao*1, Jinjiang Wang1, and Ruqiang Yan2

1

Department of Mechanical Engineering, University of Connecticut, Storrs, CT, USA

2

School of Instrument Science and Engineering, Southeast University, Nanjing, China *

Corresponding Author Email: rgao@engr.uconn.edu

7.1 Introduction

To improve cost-effectiveness of wind energy, wind turbines must operate in a highly reliable 

fashion, given the significant cost associated with system repair, maintenance, and unexpected 

failure. Accordingly, techniques for the condition monitoring and fault diagnosis of wind turbine 

structures and components have been gaining increasing attention [41]. 

Of the various components in a wind turbine, the gearbox is a major component that is costly and 

vulnerable to failure. Accordingly, signal processing for gearbox defect identification and 

diagnosis has been an active research area. There are two major components in a gearbox: gears

and bearings. For gear diagnosis, sideband analysis, amplitude, and phase modulation [42], 

wavelet transform [43], and spectral kurtosis [44] have been investigated. Typically, diagnosis is 

achieved through comparisons between a defective gear and a healthy gear. As for the bearing 

diagnosis, a band pass resonant signal processing technique has been reported. Choosing an 

appropriate bandwidth remains an important issue, given its effect on the diagnosis result. 

As part of the CM Round Robin study, three sets of vibration data measured by NREL on a wind 

turbine gearbox (of unknown damaged condition) were analyzed at three different operating 

speeds. For gear fault diagnosis, sideband pattern analysis was performed on all gears. Data from 

torque measurements were also analyzed to facilitate annulus gear diagnosis; whereas for bearing 

diagnosis, the multi-scale enveloping spectra technique [45] has been investigated. The result of 

the analysis was compared with that of a spectral analysis of a healthy gearbox that was provided 

by NREL as a reference base.

7.2 Algorithms

Vibration of a gearbox can be caused by various sources, such as gear meshing, interaction 

between the rolling elements and raceways in bearings, and shaft rotation. Structural defects on 

gear’s surface also constitute a source of vibrations that are carried by gear meshing frequencies. 

Research reported in the literature has shown that the energy associated with frequency 

components at the sidebands around the gear meshing frequency will increase as the health 

condition of the gear deteriorates, in comparison to a healthy gear. Accordingly, sideband 

analysis has been performed for gear analysis in this study. 

For bearing defect diagnosis, the multi-scale enveloping spectra technique has been investigated 

[45], which makes use of the time, scale, and frequency information contained in the bearing 

vibration signal. The algorithm first decomposes the bearing vibration signal into a series of 

wavelet basis functions, through variations of the scales and time shifts of the wavelet function. 

The envelope of each decomposed wavelet function is then extracted from the modulus of the 

wavelet coefficients. Next, spectral analysis is performed repeatedly on the envelope signal, 

resulting in an envelope spectrum of the original signal at the various scales. The integration of 
84

the wavelet transform, using post-spectral analysis, reveals the defect characteristic more clearly, 

enhancing its effectiveness in bearing defect diagnosis. 

7.3 Results

Vibration data measured by NREL on a wind turbine gearbox was analyzed for gear and bearing 

defect diagnosis, respectively. Figure 7.1 illustrates the physical system analyzed for this study, 

with the locations of the specific bearings, shaft, and gears identified. 

Bearing H HS_Shaft

Annulus Gear INT_Pinion

Sun Gear HS Pinion Bearing A1

Bearing C1/C2 Bearing D

Figure 7.1. Locations of defective components in the gearbox assembly

7.3.1 Gear Diagnosis Results

Gear test data at 1,800 rpm measured by vibration sensor AN7, was analyzed by means of 

sideband analysis, and the result is presented in this chapter. Figure 7.2 (a) and Figure 7.2 (b) 

show the spectra of gear vibrations under healthy and deteriorated (at the end of service life) 

conditions, at the locations of HS_Pinion and INT_Pinion, respectively. From the figures, the 

gear meshing frequencies of the HS_Pinion and INT_Pinion can be clearly seen. A zoom-in view 

around the INT_Pinion and HS_Pinion gear meshing frequencies are shown in Figure 7.2 (c) to

Figure 7.2 (f). Comparing the result of the gearbox under healthy and deteriorated conditions, the 

increase in energy content of the sideband frequencies can be identified, for both the HS_Pinion 

and INT_Pinion. This indicates that the tested gear is defective. The same trend is observed from 

the sideband analysis of Annulus_Gear and Sun_Gear, in Figure 7.3, which indicates that the 

Annulus_Gear and Sun_Gear are also defective. In Table 7.1, the sideband energy ratios 

(defined as the first order sideband energy over the energy at the gear meshing frequency) of 

these four gears are summarized. It is seen that for all the four gears, there is a consistent 

increase in the sideband energy ratio (e.g., from 29.4% to 107.7% for the INT_Pinion).
85

120 130 140 150 160 170 180 190 200 210 220 0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

AN7__HSSRadial

Frequency (Hz)

Amplitude (mW)

0 200 400 600 800 1000 1200 1400 1600 1800 2000 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

AN7__HSSRadial

Frequency (Hz)

Amplitude (mW)

120 130 140 150 160 170 180 190 200 210 220 0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

Frequency (Hz)

Amplitude (mW)

AN7

0 200 400 600 800 1000 1200 1400 1600 1800 2000 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Frequency (Hz)

Amplitude (mW)

AN7

600 650 700 750 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

AN7__HSSRadial

Frequency (Hz)

Amplitude (mW)

fHS_Mesh

fHS_Mesh

fHS_Mesh

fHS_Mesh+f2

fHS_Mesh-f2

fHS_Mesh-f1

fHS_Mesh+f1

fHS_Mesh

fHS_Mesh+f2

fHS_Mesh+f1

fHS_Mesh-f2

2*fHS_Mesh

2*fHS_Mesh

fINT_Mesh

fINT_Mesh fINT_Mesh+f2 fINT_Mesh

fINT_Mesh+f2

fINT_Mesh

600 650 700 750 0

0.01

0.02

0.03

0.04

0.05

0.06

Frequency (Hz)

Amplitude (mW)

AN7

(a) (b)

(c) (d)

(e) (f) fHS_Mesh

fHS_Mesh-f2

fHS_Mesh+f2

fINT_Mesh-f2

AN7_New AN7_Defective

AN7_New AN7_Defective

AN7_New AN7_Defective

Figure 7.2. Comparison analysis between test data and reference data for HS_Pinion and 

INT_Pinion
86

0 10 20 30 40 50 60 70 80 90 100 0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Frequency (Hz)

Amplitude (mW)

AN7

0 10 20 30 40 50 60 70 80 90 100 0

0.05

0.1

0.15

0.2

0.25

AN7__HSSRadial

Frequency (Hz)

Amplitude (mW)

15 20 25 30 35 40 45 50 55 0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

AN7__HSSRadial

Frequency (Hz)

Amplitude (mW)

32 34 36 38 40 42 44 46 48 50 52 0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

AN7__HSSRadial

Frequency (Hz)

Amplitude (mW)

32 34 36 38 40 42 44 46 48 50 52 0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Frequency (Hz)

Amplitude (mW)

AN7

15 20 25 30 35 40 45 50 55 0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Frequency (Hz)

Amplitude (mW)

AN7

fAnnulus_Mesh

fSun_Mesh+f3

fSun_Mesh-f3

fAnnulus_Mesh

2*fAnnulus_Mesh

fAnnulus_Mesh

fAnnulus_Mesh-f4

fAnnulus_Mesh

fSun_Mesh

fAnnulus_Mesh+f4

fSun_Mesh

(a) (b)

(c) (d)

(e) (f)

AN7_New AN7_Defective

AN7_New AN7_Defective

AN7_New AN7_Defective

Figure 7.3. Comparison analysis between test data and reference data for Annulus_Gear and 

Sun_Gear
87 

Table 7.1. Sideband energy comparison between new gearbox and gearbox at the end of service life

Components Healthy Gearbox Gearbox at End of Service Life

Meshing 

energy 

(mw)

1st sideband 

energy (mw)

Sideband 

Energy ratio 

Meshing 

energy 

(mw)

1st sideband 

energy (mw)

Sideband 

Energy ratio 

HS_Pinion 0.051 0.016 31.4% 0.051 0.114 223.5%

INT_Pinion 0.017 0.005 29.4% 0.13 0.14 107.7%

Sun_Gear 0.0002 0.0004 200% 0.008 0.019 237.5%

Annulus_Gear 0.035 0.014 40% 0.135 0.059 43.7%

The increase in the sideband energy ratio related to the annulus gear is not as significant as that 

of the other three gears (relative increase is 9.3%). Considering that the annulus gear runs at low 

speed under high torque conditions resulting from the gearbox transmission mechanism, the 

torque measurement may be more effective for low speed gear diagnosis, due to its sensitivity to 

angular vibrations of the gear. Based on this consideration, data obtained from torque 

measurements of the gearbox have been analyzed. Figure 7.4 shows the waveform of the torque 

data under 1,200 RPM. The interval between the peaks is approximately 4.03s, corresponding to 

the rolling-over period of the annulus gear. Figure 7.5 shows the result of envelope spectrum 

analysis of torque data. A peak at frequency of 0.248 Hz, which corresponds to the roll-over 

period of the annulus gear, is identified. This indicates a structural defect on the annulus gear.

0 10 20 30 40 50 60

95

100

105

110

115

120

125

Time (Sec)

Amplitude

1200RPM

Peaks corresponding to defect in annulus gear

Figure 7.4. Time series of torque data under 1200 rpm
88

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

0.5

1

Frequency (Hz)

Enveloping Spectrum (mW)

0.248 Hz

0.496 Hz

Figure 7.5. The envelope spectrum of torque data under 1200 rpm

7.3.2 Bearing Diagnosis Results 

Using the wavelet enveloping technique [45], vibration data of the tested gearbox was analyzed. 

In Figure 7.6, wavelet enveloping spectrum of data measured by sensor AN3 (close to bearing H)

under rotational speed 1,800 rpm is presented. Given the high peak related to the frequency 

component fBPFO , bearing H is considered defective. Furthermore, from the energy concentration 

at the HSS_Shaft rotating frequency (1,000 mw) and its harmonics, it can be concluded that the 

HSS_Shaft has imbalance or misalignment. 

0 10 20 30 40 50 60 70 80 90 100

0

500

1000

1500

2000

2500

3000

Frequency (Hz)

Spectrum (mW)

Bearing H

fBPFO

HSS_Shaft

imbalance fu

HSS_Shaft 

2*fu

HSS_Shaft 

3*fu

Figure 7.6. Wavelet enveloping spectrum of sensor AN3 at 1,800 rpm
89

Figure 7.7 shows the wavelet enveloping spectrum of data measured by sensor AN6 (adjacent to 

bearing D) at the running speed of 1,800 rpm. Defect frequency, fBPFI, of bearing D can be 

identified, although its amplitude is not as significant due to masking from the high energy 

component, fu, which is related to imbalance of the HSS_Shaft.

Bearing D fBPFI

HSS_Shaft imbalance fu

HSS_Shaft 2*fu HSS_Shaft 6*fu

Figure 7.7. Wavelet enveloping spectrum of sensor AN6 at 1,800 rpm

7.3.3 Comparison with Inspection Result

The analyses results have been compared with physical damages identified in the gearbox when 

it was disassembled for visual inspection. As shown in Table 7.2, all gear defects were 

successfully identified. Also, two of the four bearings were identified as defective. 

Table 7.2. Comparison between the analysis result and the actual damage of a tested gearbox

Damage Component Damage mode Severity Rationale

1 HS gear set Scuffing Severe Sideband

2 Intermediate gear set Fretting corrosion and scuffing Severe Sideband

3 Annulus gear Scuffing/polishing Moderate Sideband

4 Sun pinion Fretting corrosion Severe Sideband

5 Bearing H Fretting corrosion Severe Wavelet envelope

6 Bearing D Assembly damage Moderate Wavelet envelope

7 Bearing C1/C2 Assembly damage on spacer Severe Not identified

8 Bearing A1 Overheating Severe Not identified
90

7.4 Lessons Learned

The diagnosis results have demonstrated that sideband analysis provides an effective and 

computationally efficient approach to gear defect diagnosis. Considering that the energy content 

associated with a structural defect may not be significant at the defect incipient stage, 

complementing sideband analysis with other advanced techniques should be considered. 

As for the bearing diagnosis, defects in bearing H and D have been identified by means of 

wavelet enveloping. Because of the low signal-to-noise ratio and interference caused by gear 

meshing frequencies, diagnosis of bearing D was more challenging than that of bearing H. This 

indicates the need for separating the signal related to gear meshing from that of the bearing 

vibration before performing the bearing diagnosis. Because the nature of the damage to Bearing 

A1 is related to overheating, instead of a surface defect, and damage on bearing C1/C2 is not on 

the roller raceway, but on the spacer, defects from bearings C1/C2 and A1 could not be identified 

by the vibration data analysis conducted herein. This leads to the consideration that, besides 

vibration sensing, other sensing techniques (e.g., temperature sensing) should be considered as 

well to enable fusion of diverse sensing modalities for improved gearbox diagnosis. Research is 

needed to address this issue. 
91

8 Fault Analysis of a Wind Turbine Gearbox: A Data Driven 

Approach

Zijun Zhang*, Anoop Verma, Andrew Kusiak

Department of Mechanical and Industrial Engineering, The University of Iowa *

Corresponding Author Email: zijun-zhang@uiowa.edu

8.1 Introduction 

The wind industry has been affected by failures of wind turbine components, such as main 

bearings, gearboxes, and generators. The high cost of replacing failed components impacts the 

energy cost. Therefore, research in fault identification and condition monitoring is warranted. 

Fault identification is concerned with a fault that has occurred and its labeling. In condition 

monitoring, parameters reflecting the component conditions are identified and their changes are 

analyzed to detect an emerging failure. In this chapter, the fault identification analysis is studied 

in the time domain based on the vibration data of an impaired gearbox tested by NREL, which is 

different from the traditional fault analysis from the frequency domain [46-51].

8.2 Methodologies

This section describes the data processing and analysis methods applied to the detection of the 

gearbox faults. 

8.2.1 Change Rate of Vibration Acceleration

To analyze the gearbox vibration in the time domain, jerk is utilized. Jerk describes the rate of 

acceleration change, and it is often used to indicate the excitement of vibration. For the highfrequency vibration acceleration data in Section 2.4, the jerk is approximated in Equation (13).

t tT a a J

T

− − ≈

   (13)

The expression in Equation (13) is derived in Equation (14).

0 lim , and ( ) ( )

t tT t tT

t tT t

da a aa aa J a a a t t tT

dt t t t T T

− −

− ∆ →

∆ − − = = ≈ = ∆ = − ∆= − −

∆ −−

       (14)

where J



is jerk, a



is acceleration, t is the time index, and T represents the sampling interval, 

1/40000 s.

8.2.2 Root Mean Square, Crest Factor and Kurtosis

Besides jerk, the root mean square (RMS), crest factor (CF), and kurtosis are estimated based on 

the acceleration data and utilized in time domain analysis.

RMS is the simplest method for measuring abnormalities in the time domain. The RMS value 

can be used to detect unbalanced rotating elements. It is a statistical measure of the magnitude 

with varying quantity, and it is expressed in Equation (15).

( )

2

1

1 N

i

i

RMS s

N =

= ∑ (15)

The crest factor (CF) is a measure used to detecting changes in the signal pattern due to 

impulsive vibration sources, such as tooth breakage. It can be useful in detecting high peaks in 

the signal at higher magnitudes of the peak and for smaller numbers of peaks. A small value of 
92

RMS and high peak value implies a higher crest factor. A CF with values in the range 2-6 

represents normal operations; whereas, a value higher than six represents a defective component. 

The crest factor is computed by dividing the peak level of the signal average by the standard 

deviation (RMS) of the signal average, as shown in Equation (16).

Peak level CF

RMS = (16)

Kurtosis is defined as the fourth statistical moment of an array of values about the mean. It 

indicates the existence of major peaks. A kurtosis value of less than three represents a component

in a normal health condition; whereas, a value greater than three represents abnormality. The 

greater the number of peaks in the signal, the larger is the kurtosis. The kurtosis is expressed in

Equation (17).

( )

( )

4

1

2

2

1

.

N

i

i

N

i

i

N ss

K

s s

=

=

−

=

  −    

∑

∑

(17)

8.2.3 Correlation Coefficient

The correlation coefficient is a quantity that measures the linear relationship between two 

parameters ranges from -1 to 1. The value of the correlation coefficient equal to 1 (-1) indicates a 

strong positive (negative) relationship between two parameters. A value of the correlation 

coefficient close to zero means there is a weak linear relationship. The formulation of correlation 

coefficient can be written as Equation (18).

2 22 2

( )( )

( )( ) ( )( )

n xy x y

r

nx xny y

− = − −

∑ ∑∑

∑∑ ∑∑

(18)

where r is the correlation coefficient, and x and y are two different parameters.

8.2.4 Clustering

Clustering analysis is an unsupervised method of data analysis. Clustering algorithms group 

observations into clusters by evaluating similarities among the observed data. A k-means 

algorithm [52] is modified in this study to establish clusters. In the original version of the kmeans algorithm, the number of clusters, k, should be arbitrarily set by the analyst. In this study, 

a clustering cost function is introduced to evaluate the cluster quality with k. The clustering cost 

function is formulated as Equation (19) and used in a 10-fold, cross-validation scheme [53,54].

2

1

1

1 (,,)

j i

k

k j i

i C

i

i

d k

m = ∈

=

  =   −

  ∑ ∑

∑ x

x c x c

(19)

where d is the clustering cost, k is the number of clusters, m is the number of observations 

(sensors) contained in each cluster, x is a vector of parameters used in this research, c presents 

the centroid of each cluster, j is the index of each data point, and Ci represents cluster i.

The modified k-means algorithm involves the following steps:
93

Step 1. Set the initial value of k to 2

Step 2. Divide the data set into 10 subsets of equal size. 

Step 3. Repeat 10 times.

Step 3.1. Randomly select nine subsets for training and use the 10th subset for testing. 

Step 3.2. Initialize k centroids.

Step 3.3. Repeat the following two steps until the centroids do not change.

Step 3.3.1. Assign data point to the closest cluster by *

* { : , 1,2, , } t tt

i j ji j i C = −≤ − = xxc xc i k  .

Step 3.3.2. Update the values of the centroids by

/

j i

i j

C

n ∈

= ∑xc x

, where n is the total number of 

observations.

Step 3.4. Compute the clustering cost, d.

Step 4. Estimate the average of clustering cost d in 10-fold cross-validation.

Step 5. Stop the algorithm if d(k,x,c) – d(k – 1,x,c) ≤ ξ or k = 12; otherwise, go back to Step 1.

To implement the modified k-means algorithm, the parameter, ξ, is set to 0.05.

8.3 Results

8.3.1 Data Process and Description

Acceleration data are sampled at 40,000 Hz and recorded for 10 minute intervals. The data set is 

large. As the sensors are used to recording acceleration, the data is transformed based on (1) to 

obtain the jerk values. Acceleration data for all three test cases (2a, 2b, and 2c) at 10 minute

intervals are transformed. Each data set is divided into 40 data subsets of equal size (or equal 

length, 15 seconds) for the further investigation.

Since the sampling frequency of the acceleration data is high, 40,000 Hz, viewing and data 

analysis of the high frequency data directly in the run-chart form is not feasible. Therefore, four 

statistical metrics, the mean, standard deviation, maximum, and minimum, are utilized to 

compute the Jerk value for each data subset discussed in Section 8.2.1. The values of the mean, 

standard deviation, maximum, and the jerk for all 40 data subsets are used to develop three new 

data sets for analysis discussed in Section 8.3.2, 8.3.3, and 8.3.4. The minimum Jerk value is 

always zero and, therefore, it is excluded from this research. 

8.3.2 Detection of Ring Gear Fault

Figure 8.1 displays the time series speed data for 10 minutes. As shown, it is obvious that the 

speed experiences significant change at the third minute. The maximum rate of change is about 

500 rpm/15s and at the same time the change of LSS Torque suddenly increases to 15 kNm/15 s. 

These two phenomena point to a fault. To analyze the faulty component and its location, the 

maximum jerk data from 12 accelerometers, at each 15 second interval, is utilized. The 
94

maximum and minimum of the maximum jerk data of each accelerometer are estimated. Then, 

the ratio, R, is estimated based on the maximum and minimum values of the maximal jerk based 

on Equation (20).

R = (Max{maximum jerk} – Min{maximum jerk}) / Max{maximum jerk} (20)

Figure 8.2 shows the R for each accelerometer. As shown, the Ratio 1 of sensors AN3 and AN4 

is much higher than the R of other sensors. Therefore, the location and component that AN3 and 

AN4 monitored are considered as the possible location where the fault occurred. From the 

specification provided by NREL, the component monitored by AN3 and AN4 is a ring gear and 

the location is in the low speed stage (LSS-T) of the gearbox. 

Figure 8.1. Run chart of maximum rate of speed

Figure 8.2. Bar char of R

8.3.3 Detection of Faults in Intermediate and High Speed Stages

The suspected faults in intermediate and high speed stages manifest themselves by significant 

vibration observed at the high speed stage (HS-ST) and intermediate speed stage (IS-ST) of 

gearbox in testing case 2b and 2c. As HS-ST is connected with IS-ST, there are three possible 

causes: HS-ST damaged, IS-ST damaged, or both are damaged. One possible root cause of high 

vibration in HS-ST and IS-ST is the oil leakage and gear wear at the two stages.

In this section, a correlation coefficient analysis is performed based on a data set containing the 

mean jerk described in Section 8.3.1. Table 8.1 and Table 8.2 present the results of correlation 

coefficient analysis based on cases 2b and 2c. As shown in Table 8.1 and Table 8.2, sensors, 

0

100

200

300

400

500

600

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39

Maximal rate of speed (rpm/15-s)

Time (15 s intervals)

Speed of encoder on HSS

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

AN1 AN2 AN3 AN4 AN5 AN6 AN7 AN8 AN9 AN10AN11AN12

Percentage

Index of sensors

Ratio 1
95

AN5, AN6, AN7, AN8, AN9, AN11, and AN12, are highly correlated. Since the component 

monitored by AN1 and AN2 is considered healthy, results in Table 8.1 and Table 8.2 indicate 

that significant vibration originates at one of the areas AN5, AN6, AN7, AN8, and AN9 

monitored (HS-ST and IS-ST), and it impacts the generator monitored by AN11 and AN12.

Table 8.1. Correlation coefficient analysis of the mean of jerk data: Case 2b

Sensor AN1 AN2 AN3 AN4 AN5 AN6 AN7 AN8 AN9 AN10 AN11 AN12

AN1 1.00 0.98 0.53 0.20 0.02 0.14 0.00 -0.11 0.16 0.16 0.16 0.03

AN2 0.98 1.00 0.59 0.06 0.18 0.30 0.17 0.05 0.32 0.25 0.33 0.19

AN3 0.53 0.59 1.00 0.09 0.31 0.53 0.41 0.19 0.62 0.77 0.48 0.32

AN4 0.20 0.06 0.09 1.00 -0.88 -0.78 -0.85 -0.94 -0.70 -0.11 -0.76 -0.89

AN5 0.02 0.18 0.31 -0.88 1.00 0.94 0.97 0.97 0.90 0.50 0.92 0.97

AN6 0.14 0.30 0.53 -0.78 0.94 1.00 0.98 0.93 0.99 0.60 0.95 0.96

AN7 0.00 0.17 0.41 -0.85 0.97 0.98 1.00 0.97 0.96 0.56 0.94 0.97

AN8 -0.11 0.05 0.19 -0.94 0.97 0.93 0.97 1.00 0.88 0.39 0.90 0.98

AN9 0.16 0.32 0.62 -0.70 0.90 0.99 0.96 0.88 1.00 0.67 0.92 0.93

AN10 0.16 0.25 0.77 -0.11 0.50 0.60 0.56 0.39 0.67 1.00 0.59 0.42

AN11 0.16 0.33 0.48 -0.76 0.92 0.95 0.94 0.90 0.92 0.59 1.00 0.92

AN12 0.03 0.19 0.32 -0.89 0.97 0.96 0.97 0.98 0.93 0.42 0.92 1.00

Table 8.2. Correlation coefficient analysis of the mean of jerk data: Case 2c

Sensor AN1 AN2 AN3 AN4 AN5 AN6 AN7 AN8 AN9 AN10 AN11 AN12

AN1 1.00 0.83 0.32 -0.73 0.50 0.56 0.49 0.67 0.49 0.48 0.64 0.56

AN2 0.83 1.00 0.76 -0.91 0.88 0.90 0.87 0.92 0.87 0.86 0.91 0.91

AN3 0.32 0.76 1.00 -0.67 0.94 0.92 0.95 0.78 0.96 0.95 0.80 0.90

AN4 -0.73 -0.91 -0.67 1.00 -0.85 -0.90 -0.84 -0.97 -0.83 -0.80 -0.94 -0.91

AN5 0.50 0.88 0.94 -0.85 1.00 0.99 0.99 0.92 0.99 0.98 0.92 0.98

AN6 0.56 0.90 0.92 -0.90 0.99 1.00 0.99 0.95 0.98 0.97 0.95 0.99

AN7 0.49 0.87 0.95 -0.84 0.99 0.99 1.00 0.91 0.99 0.98 0.92 0.98

AN8 0.67 0.92 0.78 -0.97 0.92 0.95 0.91 1.00 0.91 0.88 0.96 0.96

AN9 0.49 0.87 0.96 -0.83 0.99 0.98 0.99 0.91 1.00 0.98 0.90 0.98

AN10 0.48 0.86 0.95 -0.80 0.98 0.97 0.98 0.88 0.98 1.00 0.88 0.96

AN11 0.64 0.91 0.80 -0.94 0.92 0.95 0.92 0.96 0.90 0.88 1.00 0.96

AN12 0.56 0.91 0.90 -0.91 0.98 0.99 0.98 0.96 0.98 0.96 0.96 1.00

Besides correlation coefficient analysis, the k-means clustering algorithm is utilized to examine 

the relationship among sensors. Since the k-means algorithm groups parameters into clusters by 

examining their similarity, it is capable of evaluating the relationship among sensors. Table 8.3 

shows the clustering result of both case 2b and 2c. In Table 8.3, AN6, AN7, AN8, AN9 and 

AN12 are grouped into one cluster while other sensors are grouped into another cluster. This 
96

result points to the same pattern as the correlation coefficient analysis, which indicates the faulty 

location of HS-ST and IS-ST.

Table 8.3. Clustering based classification 

Case 2b Case 2c

Index of AN Final classification Index of AN Final classification

1 2 1 2

2 2 2 2

3 2 3 2

4 2 4 2

5 2 5 2

6 1 6 1

7 1 7 1

8 1 8 1

9 1 9 1

10 2 10 2

11 2 11 2

12 1 12 1

The results of RMS, CF, and kurtosis also show an agreement with the correlation and clustering 

analysis. Figure 8.3 presents the RMS values of 2b, averaged over a 1 minute interval. The case 

2b reveals a pattern; whereas, the low RMS values of sensors AN1 and AN2 cause a high crest 

factor. The increase in RMS of AN8 may indicate that a fault is in progress in the gearbox. It 

could be due to the oil leakage.

Figure 8.3. RMS across 12 sensors - Case 2b

Figure 8.4 displays the crest factor of 2b across 12 sensors. In Figure 8.4, it can be observed that 

the main bearing is affected in test case 2b. It can be assumed that the significant amount of crest 

factor near AN1 is contributed by the vibrations of other components.
97

Figure 8.4. Crest factor across 12 sensors - Case 2b

Figure 8.5 represents the kurtosis of three test cases across 12 sensors. In case of CM_2b, 

kurtosis across all 12 sensors shows increasing patterns. This could indicate a gradual wear.

Figure 8.5. Kurtosis across 12 sensors - Case 2b

8.4 Conclusion and Discussion

Analysis of jerk data derived from vibration acceleration data of the test wind turbine gearbox 

was discussed in this chapter. In the analysis of the component failure identification, the 

correlation coefficient analysis and clustering analysis were applied to identify the failure stage 

of the gearbox in the time domain. Some faults of the intermediate and high-speed stages of the 

gearbox were correctly identified by the approaches discussed in this chapter. Some root causes 

could be inferred based on the data patterns of some specific sensors. Since the drivetrain was 

fixed to the floor, other factors (e.g., force from the wind and tower) that could impact the 

vibration excitement were not presented. In the future research, gearbox vibration acceleration 

data collected from field operated wind turbines, as well as data such as wind speed, generator 

torque and tower vibration, is needed to validate applicability of the proposed approach in fault 

identification.
98

9 Techniques for Separation and Enhancement of Various 

Components in the Analysis of Wind Turbine Vibration Signals

Nader Sawalhi1, Robert B. Randall2*, and David Forrester3

1

College of Engineering, Prince Mohammad Bin Fahd University, The Kingdom of Saudi 

Arabia. 2

School of Mechanical and Manufacturing Engineering, The University of New South Wales, 

Australia

3

Defence Science and Technology Organisation, Australia *

Corresponding Author Email: b.randall@unsw.edu.au

9.1 Introduction

This chapter provides a summary of the handling and processing of wind turbine data provided 

by NREL for the CM Round Robin study. The University of New South Wales took an active 

role in this study through Dr. Nader Sawalhi and Professor Bob Randall.

NREL provided three sets of data (taken from a number of accelerometers on the planetary 

gearbox) at different speeds and load conditions. The data was for a faulty condition only. The 

data was first analyzed blindly, in the sense that there was originally no information given as to 

the type and location of faults in the gearbox. Our group concentrated on the search for bearing 

faults, because it is our opinion that to be sure of detecting gear faults, it is necessary to make 

comparisons with signals from the gears in healthy condition. We did, however, look for 

indications of local faults on the gears, as these might show up clearly as local impulsive 

responses in the gear signatures.

Later, after receiving the inspection report, and spectra from the gearbox in good condition, we 

made a further analysis, in particular of the gear signals, and were able to detect other indicators 

of the actual faults. Most of these could have been detected in the original blind analysis, if we 

had had the signals for good condition. 

Our group had already had a certain amount of experience in analyzing signals from wind 

turbine transmissions, and was aware that the main differences, with respect to other similar 

gearboxes, were because the load can vary considerably over relatively short periods, at least 

with respect to the low speed input sections of the transmission. The vibration signal from gears 

is affected greatly by the load, and so some means has to be found to distinguish such variations 

from changes in condition. We have considerable experience with the diagnoses of helicopter 

gearboxes, which are somewhat similar. However, these operate at perhaps ten times higher 

speeds, and it is possible to obtain reasonably long signals with an approximately constant load. 

In contrast to gear fault signals, bearing signals are not so sensitive to torque load (although in 

gearboxes, radial load depends on torque load), and there is usually a dramatic difference in the 

signals in the presence of faults, which often allows them to be diagnosed without necessarily 

having access to historical data. This is because of the development of spectral kurtosis (SK) 

techniques in recent years by our group and colleagues, in particular Professor Jerome Antoni, 

now of INSA Lyon, in France [55]. The techniques we have used for analyzing the signals for 

gear and bearing faults are described in more detail below. Those bearing diagnosis are primarily 

based on a semi-automated procedure, with several different stages to separate and enhance the 
99

bearing signals. Then envelope analysis is applied (spectrum analysis of squared envelope 

signals) to diagnose the fault repetition frequencies and their modulations by lower frequencies 

[56]. We also applied a recently developed cepstral pre-whitening technique, which can 

circumvent some of the stages in the earlier procedure [57]. For gear diagnosis we applied 

classic techniques based on obtaining a synchronously averaged signature for each gear, and then 

looking for localized impulses characteristic of local faults. This requires the signals to be “order 

tracked,” or re-sampled in the angular domain, with equal numbers of samples in each 

revolution. This normally requires a tachometer or shaft encoder signal for synchronization. The 

supplied speed signal was not suitable for this so we extracted a “pseudo-encoder” signal from 

the vibration signal to use for order tracking. For obtaining signatures of the individual planet 

gears and sun gear in the planetary part of the gearbox, the premium current method is one 

patented by DSTO (Defence Science and Technology Organisation), of the Australian Defence

Department. We engaged Dr. David Forrester of DSTO, the inventor of the technique, to obtain 

these signatures for us for the latest results presented at the Wind Turbine Condition Monitoring 

Workshop in Broomfield, CO, in September 2011. Those results are included here. It should be 

mentioned that Dr. Forrester was surprised by the design of the planetary section of the gearbox, 

as the choice of tooth numbers was far from a hunting tooth design, normally considered good 

practice, and as a result of this, groups of teeth always mesh in the same way and repeat 

frequently. The effects of this are discussed below. It is also somewhat unusual that the ratio of 

the high speed section was exactly 4:1 (88:22) meaning that the 22 teeth on the pinion always 

mesh in exactly the same way with four groups of 22 teeth on the intermediate shaft wheel. 

Therefore, a fault on one tooth transfers to individual teeth on the mating gear, and is not 

smeared out as it is in a hunting tooth design.

After receiving spectra for the gearbox in good condition, we were also able to make spectrum

comparisons to detect changes in modulation sideband patterns, often indicative of faults, and 

also cepstrum analysis to concentrate the information in the sideband patterns.

9.2 Algorithms 

Our general approach is to separate the signals, into the components coming from the gears and 

bearings, and analyze them separately. The separation is based on the assumption that the gear 

signals are deterministic (with respect to rotation angle), and the bearing signals are stochastic,

because of the minor random slip between the components and the random positioning of the 

rolling elements in the clearance of the cage. These two effects give an approximately 1-2% 

deviation of the mean value of the actual bearing fault frequencies, with the same order of 

random variation around the mean from those frequencies and calculated on the basis of no slip 

and perfectly uniform spacing. The signals can then be classified as approximately second order 

cyclostationary, which allows their separation from the deterministic gear components [58]. 

There are a number of methods for achieving this separation [28], but the one initially used in 

this research was to first isolate and then remove the deterministic components corresponding to 

each gear in the system, by synchronous averaging, leaving a residual stochastic signal, which 

should be dominated by bearing faults in some frequency bands. The optimum frequency bands 

are found using some sort of kurtogram to find the frequency band with maximum SK. In this 

case, a wavelet kurtogram [59] was used. An alternative preprocessing technique used in this 

case was cepstrum pre-whitening [57]. By this means, the signal spectrum amplitude is set to a 

constant value (whitened) and the original phase used to generate a time signal. This 

simultaneously nullifies the effect of both discrete frequencies and resonances, so that a 
100

frequency band containing an impulsive signal will tend to dominate the time signal. SK can be 

used to further isolate the impulsive band. 

9.2.1 Summary of Processing Algorithm

The five basic steps in the processing algorithm used during the first stage of analysis are listed 

in Figure 9.1.

Figure 9.1. Signal processing approach pre release of inspection report

The first stage involves extracting a pseudo tachometer/encoder (tacho) signal from the measured 

vibration signal; it was found that the speed signal provided by NREL was only useful for giving 

an arithmetic mean estimate of the speed of the high speed shaft (generator rotor) and could not 

be used for re-sampling purposes. The extracted tacho signal was used to resample the signal of 

interest and extract the synchronous average for the intermediate shaft. The residual signal was 

pre-whitened as a first step. The squared envelope spectrum was then obtained using the Hilbert 

transform and scanned for bearing defect frequencies, which had been calculated for each 

bearing in the gearbox. Pre-whitening was achieved using the newly proposed approach based on 

the cepstrum (Cepstrum-pre-whitening). This squared enveloped signal was extracted and 

inspected for bearing faults. 

9.2.2 Pseudo Encoder Extraction and Speed Estimate

The process of extracting a reference speed signal is described schematically in Figure 9.2 [60]. 

In the first step, Figure 9.2 (a), the spectrum of the signal is visually examined to identify a 

proper HSS (high speed shaft) gear mesh harmonic (and a suitable band around it). Highest 

separable harmonics are preferable due to the more evident effect of smearing and will give more 

accurate results. In the second step, Figure 9.2 (b), a buffer (filled with zeros) of a size equal to 

the FFT size is created. The complex spectrum of interest (band) is transferred to this buffer 

(placed in the same lines as in the original spectrum). Note that the presentation in Figure 9.2 (b) 

only shows the amplitude of the spectrum; however, it is the complex spectrum that has been 

transferred to this buffer and the phase information is thus preserved. Finally the buffer is inverse 

transformed to the time domain to obtain the reference signal, Figure 9.2 (c). As the buffer is 

1. Tacho signal extraction

2. Successive signal re-sampling to obtain a synchronously averaged 

signal for each shaft in the gearbox

3. Synchronously averaged signals are examined for gear faults. 

4. Synchronously averaged signals subtracted from re-sampled signal 

(at each stage) to find a residual signal.

5. Residual signal examined for bearing faults:

Pre-whitened (AR)- MED- Squared Envelope spectrum

Basic Processing Algorithm
101

filled with zeros up to the sampling frequency - negative frequencies were set to zero - the 

inverse transform signal is analytic (complex), and it is the real part that will then represent the 

reference signal. Note that zero crossings represent 180° increments in rotation phase, and this is 

unaffected by amplitude modulation by any positive modulating function.

Figure 9.2. Reference (speed) signal extraction stages: (a) identifying a separable band; (b) 

extracting the band into a new buffer; (c) inversing the transform signal b into the time domain

[60]

The signal obtained in 2.c is a sinusoidal-type signal whose periods represent the speed for each 

shaft rotation. The speed variation in this signal (a reflection of the speed variation of the shaft 

under investigation) can be traced using the zero crossings of the consecutive periods, which can 

be achieved by detecting the zero crossings (an interpolation between the samples on either side). 

This signal can also be used to order track the signal. Note, however, that this process may have 

to be repeated progressively to order track the signal to higher harmonics and achieve better 

results. This means that after each stage, a higher harmonic will be made available due to the 

reduction of speed fluctuations and the analyst can select bands around the gear mesh harmonics 

to improve the quality of order tracking and gain more accuracy.

The approach illustrated in Figure 9.2 was used to extract a tachometer and speed signal for the 

High Speed shaft (HSS) of the gearbox. The speed extraction was based on the gear mesh 

frequency of the high speed stage (22 × HSS). For this purpose, sensor 7 was selected for 

extracting the gear mesh signal for the HSS, although this can also be achieved using other 

650 700 750 800 850 900 950 1000 1050 1100

-200

0

200

400

600

800

1000

1200

(a) Step 1: Identifying the band 

of interest. The plot shows the 

amplitude of the spectrum. 

Frequency axis scaled in lines

rather than Hz

0

100

200

300

400

500

600

700

800

NFFT

(b) Step 2: Band of interest

moved into a buffer filled with 

zeros

0 1 2 3 4 5 6 7 8

x 105

-8

-6

-4

-2

0

2

4

6

8 x 10-3

(c) Step 3: real part of the 

IFFT (Inverse Fast Fourier 

Transform) of the buffer

obtained in step 2.

 700 Frequency (line no.) 1000

0 Frequency (line no.)

800

Amp

0

800

Amp

0

0 Time (sample no.) NFFT

Zoom spectrum
102

sensors in close proximity to the high speed shaft. The zero crossings for the signal in Figure 9.2

(c) were used to estimate the speed of the HSS. Examples of estimates at two speeds based on 

this procedure (scaled in rpm) from data set a and data set c are presented in Figure 9.3. It is 

noted that the speed is relatively constant.

Figure 9.3. HSS estimates: Top - data 2a:5; Bottom - data 2c:5

9.2.3 Successive Re-sampling and Synchronous Average Extraction 

A separation algorithm (gear/bearing signal separation) [61,62], which is based on successive resampling of the signal under analysis has been adopted to obtain synchronously averaged signals 

for each shaft and to completely remove the shaft harmonics, without much disruption of the 

vibration signal.

The algorithm works by re-sampling the order-tracked signal to obtain an integer number of 

samples per revolution for a specific shaft. The removal of the harmonics of that specific shaft 

can be achieved by one of two methods. The first is by finding the synchronous average and 

subtracting it (repeated periodically) from the signal. The second is by truncating the signal to an 

integer number of revolutions (preferably a power of 2) and setting the lines corresponding to the 

harmonics of that shaft (after FFT analysis) to √2 times the mean (complex) value of the adjacent 

frequencies (the multiplication by √2 is to make the amplitude statistically the mean of the two 

amplitudes). To avoid treating the negative frequency components, it is recommended that they 

be set to zero after the FFT step, and double the positive frequency components, then take the 

real part of the resulting analytic signal in the time domain. Both methods arrive at the same 

result, as was presented in [62]. 

The extracted tacho signal was used to resample the signal of interest and extract the 

synchronous average for the intermediate shaft. As the HSS and the intermediate speed shaft 

(ISS) have a ratio of four, the removal of the harmonics of HSS was included at this stage. The 

end result of this stage was four synchronously averaged signals for the ISS, Low Speed shaft 

0 0.5 1 1.5 2 2.5 3 3.5 4

x 104

1802

1802.5

1803

1803.5

1804

2c: 5

Rotaional speed of high speed shaft (rpm)

0 0.5 1 1.5 2 2.5

x 104

1205

1205.5

1206

1206.5

2a: 5

 Gear mesh Periods
103

(LSS), the planet carrier shaft, and the planetary gears (a composite of all the planetary gears;

this was later updated to extract an average for each planetary gear). Typical results for the four 

synchronously averaged signals are presented in Figure 9.4 and Figure 9.5 for sensor three

(planetary stage and low speed shaft) for both data set a and data set c.

Figure 9.4. Synchronously averaged signals from sensor 3, data 2a:5

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

-5

0

5

2a:5 sensor 3

Intermediate Shaft

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

-0.5

0

0.5

Low Speed Shaft

Acceleration (m.s2

)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

-1

0

1

Planet carrier

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

-0.5

0

0.5

Planet gear

Time (s)
104

Figure 9.5. Synchronously averaged signals from sensor 3, Data 2c:5

9.2.4 Residual Signal Processing for Bearing Fault Detection

After the removal of the synchronously averaged signals, a residual signal is obtained. This 

should contain non-stationary and second order cyclostationary components. As a first step to 

enhance the residual signal and maximize the impulsiveness, the residual signal was prewhitened. Pre-whitening was attempted using a newly proposed approach based on the cepstrum 

(cepstrum-editing). The approach is described in Figure 9.6. The extreme case of this approach is 

where the real cepstrum is set to zero (spectrum amplitude set to one, i.e. whitened). Both 

discrete frequencies and resonances are thus removed. Uniform spectrum weighting means that 

impulsive frequency bands dominate the time signals.

The whitening stage can, in fact, be used on the raw signals giving an enhancement of the 

bearing related signature. The advantage of pre-whitening is that all frequency components in 

this signal are equally weighted and, thus, the potential to detect faults is enhanced. 

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

-0.5

0

0.5

Intermediate Shaft

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

-0.5

0

0.5

Low Speed Shaft

Acceleration (m.s2

)

0 0.5 1 1.5 2 2.5 3

-1

-0.5

0

0.5

Planet carrier

0 0.2 0.4 0.6 0.8 1 1.2 1.4

-0.5

0

0.5

Planet gear

Time (s)
105

Figure 9.6. Schematic diagram of the cepstral method for removing selected families of harmonics 

and/or sidebands from time signals [57]

The squared envelope spectra for the pre-whitened residual signals were obtained using Hilbert 

Transform techniques (simply by inverse transforming one-sided spectra, shifted to zero 

frequency, and taking the modulus of the resulting complex numbers). 

9.3 Results

9.3.1 Bearings 

9.3.1.1 Initial Bearing Diagnosis Results

Through the inspection of the squared envelope spectra of the residual signals obtained from 

section 9.2.4, two defective bearings were identified. These are FAG 3222 and NU 2220 ECM. 

The diagnosis indicated an inner race fault on bearing FAG 3222 and an inner race fault and 

roller/cage defect on the NU 2220 bearing. 

The inner race fault (localized spalling) of the FAG thrust bearing (3222) was mainly detected 

through signals from sensors seven and nine. The envelope spectra from these sensors contained 

the ball pass frequency of the inner race (BPFI), and its harmonics were clearly modulated by the 

high speed shaft speed. An example from the low speed data (set a) and the high speed data (set 

c) is shown in Figure 9.7 and Figure 9.8 respectively. In Figure 9.7, the high speed shaft 

frequency (20.1 Hz) and its second harmonic are clearly visible. The 230.7 Hz component

(suspected BPFI) and its second harmonic are modulated by the frequency of the high speed 

shaft. The calculated BPFI for the FAG bearing (3222) at an inner race shaft speed of 20.1 Hz is 

around 218.5 Hz. The difference between the observed BPFI in the figure and the calculated one 

is around 5.5%, which can be due to slippage and an incorrect estimation of load angle. This rate 

of slippage is also observed for the high speed data (set c) in Figure 9.8, where the BPFI of 345.3

Hz and its second harmonic are observed. The 345.3 Hz component has around a 5% difference 

from the calculated BPFI, which is in agreement with the low speed data observation of Figure 

9.7. 
106

Figure 9.7. Squared envelope spectrum for data 2_a_10 sensor 7

Figure 9.8. Squared envelope spectrum for data 2_c_10 sensor 7

0 100 200 300 400 500 600

0

0.5

1

1.5

2

2.5

3

3.5

4 x 10-7

X: 461.4

Y: 2.537e-008

X: 20.1

Y: 3.364e-007

X: 230.7

Y: 1.697e-007

Carrier Frequency at : 230.987 Hz, Sideband Spacing at : 20.0878 Hz

0 100 200 300 400 500 600 700 800 900 1000

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

Harmonic Spacing at : 345.3 Hz

Frequency (Hz) 

Frequency (Hz) 
107

Figure 9.9 shows that the suspected BPFI of 345.3 Hz is close to one of the harmonics of the 

intermediate shaft (46th harmonic), but is not in fact a harmonic of the intermediate shaft.

Figure 9.9. Zoom-in around the BPFI. Harmonic cursors for the ISS

The second bearing fault diagnosis indicated the presence of an inner race fault and possible 

roller/cage pitting in the SKF HSS upwind bearing (NU 2220 ECM). This was detected mainly 

through sensor eight and was confirmed by testing data from set a through the presence of the 

BPFI, its harmonics, and the modulation of these harmonics by the high speed shaft speed. There 

are also indications of modulations by the fundamental train frequency (FTF), which can come 

from variations between rollers.

In Figure 9.10, the BPFI at 198.08 Hz modulated by a shaft speed of 20.091 Hz is observed. This 

matches very closely the calculated BPFI of bearing NU 2220 ECM at a shaft speed of about 

20.1 Hz. The FTF harmonics (12.8 Hz) are at the same speed for the NU 2220 bearing, as shown 

in Figure 9.11.

330 335 340 345 350 355 0

0.01

0.02

0.03

0.04

0.05

0.06

Harmonic Spacing at : 7.51772 Hz

X: 345.3

Y: 0.06

Frequency (Hz) 
108

Figure 9.10. Squared envelope spectrum for data 2_a_5 sensor 8 showing the BPFI of bearing 

NU2220

Figure 9.11. Squared envelope spectrum for data 2_a_5 sensor 8 showing the FTF harmonics of 

bearing NU2220

140 160 180 200 220 240 260 -2

0

2

4

6

8

10

12

14 x 10-4 Carrier Frequency at : 198.082 Hz, Sideband Spacing at : 20.0906 Hz

0 10 20 30 40 50 60 70 80 90 100 0

0.01

0.02

0.03

0.04

0.05

0.06

X: 22.54

Y: 0.01013

Harmonic Spacing at : 12.8097 Hz

Frequency (Hz) 

Frequency (Hz) 
109

9.3.1.2 Actual Findings and Missed Detection

In the test gearbox failure analysis report [4], it was shown that the IR raceway and rollers of 

bearing 3222 had straw-yellow temper colors. The color implies that the temperature reached 

about 400°F. The root cause of the overheating was probably lubricant starvation. Even though 

no spalls were detected, it is likely there was geometric distortion from the overheating. The IR 

of bearing NU 2220 ECM had assembly damage at the roller spacing caused by cocking of the 

rollers during blind assembly. Debris dents and lines of false brinelling were also observed. The 

IR of bearing NU 2220 ECM had corrosion at roller spacing. 

The spacer for bearing 32032X outer race had assembly damage at the roller spacing caused by 

interference with the bearing rollers during assembly. This damage was missed in our initial (and 

later) diagnosis. The ball-pass frequency of the outer race (BPFO), when the HSS speed is 30 

Hz is estimated at 105. 9 Hz. Figure 9.12 shows the squared envelope analysis for data c_5, 

sensor 6, where the HSS is 30.06 Hz and is present. A frequency at 210.4 Hz appears clearly in 

this figure. This is close to 7×HSS, but it is also close to 2×BPFO. This main evidence seems to 

indicate the presence of the fault in the 32032X, but it was not considered strong enough for us 

to call the fault. Note also the presence of the 345.1 Hz, which is the BPFI of the NU 2220 

bearing. Also, upon inspection of the spectrum comparison of sensor five (Figure 9.13), there is a

strong presence of 210 Hz and a change around this frequency, in particular.

Figure 9.12. Squared envelope spectrum of data 2c_5 sensor 6 showing the shaft speed (30.06 

Hz), what appears as 2×BPFO for bearing 32032X and the BPFI for bearing NU 2220

0 100 200 300 400 500 600 700 800 900 1000 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

x 10-4

X: 210.4

Y: 7.143e-005

X: 30.06

Y: 0.0001195

X: 345.1

Y: 4.035e-005

Frequency (Hz) 
110

Figure 9.13. Power spectrum density comparison of the high speed data through sensor 5

9.3.2 Gears

9.3.2.1 Initial Diagnosis

Initial diagnosis indicated the possibility of severe damage in the planetary stage of the gearbox. 

The main indications came through sensors three and four and were observed more in the low 

speed data (set a). It was noticed that the impact pattern came in pairs (roughly separated by 10-

12 teeth on the planetary gear). This was clearly observed in data 2_a, but not very clearly in 

2_c. The residual signal from sensor five for data 2a_5 is shown in Figure 9.14, where the 

impacts are seen clearly. The analysis of the squared envelope spectrum of the signal, Figure 

9.14, is shown in Figure 9.15. The carrier speed (around 0.25 Hz), the spin frequency of the 

planetary gear (PGSF) at around 0.625 Hz, and 3×PGSF are very clear in Figure 9.15. It was 

indicated at the time of this diagnosis that to confirm this, further analysis would be required to 

obtain the synchronous average with respect to each planet.

Frequency (Hz) 

Frequency (Hz) 
111

Figure 9.14. Residual of signal 2a_5 sensor 5

Figure 9.15. Squared envelope spectrum of the residual signal shown in Figure 9.14

1 2 3 4 5 6 7

x 105

-6

-4

-2

0

2

4

6

Time (Samples)

0 2 4 6 8 10 12 14 16 18 20

0.5

1

1.5

2

2.5

3

3.5

x 10-5

X: 0.2504

Y: 9.977e-006

Frequency (Hz)

X: 0.626

Y: 1.351e-005

X: 1.878

Y: 1.747e-005
112

9.3.2.2 Revised Diagnosis

The revised diagnoses included using the healthy set of data and comparing it with the faulty 

one, in both the frequency domain (using power spectrum density) and the cepstrum domain. The 

revised analysis also included the removal of shaft related components from the synchronously

averaged signals through pre-whitening. Finally synchronous averages were extracted for the sun 

gear and each planet using an algorithm earlier developed by DSTO.

9.3.2.2.1 Power spectrum and cepstrum comparisons (healthy and faulty signals)

The scaling for the healthy spectra was given in g's, while the time domain was reported in ms-2

. 

The resolution of the healthy spectra was determined and used to find the equivalent FFT 

transform size to use with the faulty data. When scaling both in dB, reference level 1e-6 was used 

for the faulty data and 1e-7 for the healthy data to compensate for the units. Comparisons show 

increases at the gear mesh frequencies and sideband families. This is shown clearly for all 

sensors (AN3, AN5, AN6 and AN7). Harmonic and sideband cursors show dominant 

components and modulations.

Cepstra were generated from the corresponding spectra to give more information on sideband 

patterns. The cepstra represent the amplitude of the analytic cepstrum (from the one-sided log 

spectrum). This version can also be used on zoom spectra [24].

Figure 9.16 shows the spectrum comparison using the data from sensor three, in the low speed 

section of the gearbox. There is a noticeable increase (more than 20 dB) in the HSS, the epicyclic 

mesh frequency, and its sidebands. Most noticeable are the sidebands at the planet pass 

frequency around the epicyclic mesh frequency in the fault case. This is evident in the cepstrum 

comparison presented in Figure 9.17. Note the second rahmonic in the healthy case, 

corresponding to 11⁄2 times the carrier speed, which is unexplained. It is possible that it has 

something to do with the “far from hunting tooth” design of the planetary section and means that 

the particular tooth combinations occur much more frequently than usual.

In Figure 9.18 and Figure 9.19, the spectrum and cepstrum comparisons based on the data from 

sensor five, with generator speed 30 Hz, are presented. The fact that the cepstrum does not 

change appreciably shows that modulation at ISS (which would come from local faults) did not 

occur, and the corresponding lack of sidebands in the faulty spectrum confirms that the faults are 

distributed. 

The distributed wear of the intermediate shaft pinion, ascribed in the inspection report to the 

hunting tooth ratio, is shown in Figure 9.20 in the growth of the harmonics of the IS gear mesh.

Figure 9.21 shows the same spectra, but concentrates on the growth of sidebands around the HS 

gear mesh harmonics, and they are spaced at the HS shaft speed. The corresponding cepstra of 

Figure 9.22 shows that the local faults causing the sideband generation have grown from nothing 

in the healthy condition; whereas, the increased peak corresponding to the ISS probably indicates 

some growth of harmonics at this shaft speed since the sidebands were not in evidence. Both the 

high speed pinion and gear had localized scuffing, which would explain the strong modulation at 

HSS speed.

Data from sensor seven in Figure 9.23 shows the same story as Figure 9.21.
113

Figure 9.16. Spectrum comparison using the data from sensor 3

Figure 9.17. Cepstrum comparison using the data from sensor 3

0 0.5 1 1.5 2 2.5 3 3.5 4

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2 2.5 3 3.5 4

0

0.2

0.4

0.6

0.8

1

Rahmonics of planet pass quefrency

Quefrency (seconds)

0 10 20 30 40 50 60 70 80 90 100 20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90 100 20

30

40

50

60

70

80

90

100

Harmonics at epicyclic gear mesh, sidebands at 

planet pass frequency (3X carrier)

HSS

Frequency (Hz) 

Frequency (Hz) 

Carrier

2

nd

rahmonic unexplained (11⁄2 × carrier speed) 
114

Figure 9.18. Spectrum comparison using the data from sensor 5

Figure 9.19. Cepstrum comparison using the data from sensor 5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.1

0.2

0.3

0.4

0.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.1

0.2

0.3

0.4

0.5

0 50 100 150 200 250 300 350 400 450 500

20

40

60

80

100

0 50 100 150 200 250 300 350 400 450 500

20

40

60

80

100

Harmonics at HSS

Frequency (Hz) 

Frequency (Hz) 

Rahmonics of ISS

Quefrency (seconds)
115

Figure 9.20. Spectrum comparison using the data from sensor 6

Figure 9.21. Spectrum comparison using the data from sensor 6

0 200 400 600 800 1000 1200 1400 1600 1800 2000 40

50

60

70

80

90

100

110

120

0 200 400 600 800 1000 1200 1400 1600 1800 2000 40

50

60

70

80

90

100

110

120

Harmonics at IS gearmesh

Faulty

Healthy

Frequency (Hz) 

Frequency (Hz) 
116

Figure 9.22. Cepstrum comparison using the data from sensor 6

0 0.05 0.1 0.15 0.2 0.25

0

0.2

0.4

0.6

0.8

1

0 0.05 0.1 0.15 0.2 0.25

0

0.2

0.4

0.6

0.8

1

HSS ISS

Quefrency (seconds)
117

Figure 9.23. Spectrum comparison using the data from sensor 7

9.3.2.2.2 AN6 ISS signal processed to remove effects of HSS

Because the ratio is exactly 4:1, the ISS record was divided into four sections, which were 

averaged, recombined, and subtracted. The residual record should contain only information from 

the ISS, for example, the shaft harmonics that are not divisible by four and the IS gear mesh

frequency (23X). Time signals and spectra are shown in Figures 9.24 and 9.25.

The HS gear mesh is strongly modulated by the HSS, because damage is more localized. The IS 

gear mesh is much distorted, with many harmonics, but it is not modulated. This is compatible 

with the distributed damage attributed to the hunting tooth design.
118

Figure 9.24. Time records from the averaged ISS signals: (a) original, including four rotations of 

the HSS; (b) Residual after removal of the HSS average.

Figure 9.25. Spectra of signals of Figure 9.24: (a) original including four rotations of the HSS;

(b) residual after removal of the HSS average.

9.3.2.2.3 Synchronously averaged signals pre-whitened

The pre-whitened synchronous averages presented in Figure 9.26 show impact events of the 

damaged gears (not just a single impact). Such impacts appear clearly in all stages (AN3). Note 

that the denomination “Planet Carrier” really refers to an average over the annulus gear, since 

one revolution of the planet carrier corresponds to meshing with all teeth on the annulus. Local 

faults were found on the HS gear of the intermediate shaft, on the sun gear (and spline) of the 

0 1000 2000 3000 4000 5000 6000 7000 8000

-10

-5

0

5

10

0 1000 2000 3000 4000 5000 6000 7000 8000

-10

-5

0

5

10

0 20 40 60 80 100 120 140 160 180 200

100

102

104

0 20 40 60 80 100 120 140 160 180 200

100

102

104

(a)

(b)

(a)

(b)

Time (sample no.). One rotation of IS

Time (sample no.). One rotation of IS

Harmonics of ISS

Harmonics of ISS
119

low speed shaft, and on the annulus gear. No faults were reported on the planet gears, but this is 

discussed in the next section.

Figure 9.26. Whitened synchronously averaged signals corresponding to the periods of all major 

gear components in the gearbox, which enhance local faults

Note that the “Planet gear” result is a composite of all planets, and shows a similar result to the 

individual planets in the next section. 

9.3.2.2.4 Planet, sun, and annulus gear signatures extracted by Dr. David Forrester using 

patented DSTO software#

Signatures for each planet and the sun gear were extracted by shifted and weighted averages of 

signals taken as the various planets pass the measurement point [63]. Note that the signature for 

each planet tooth is actually a composite of the two teeth meshing simultaneously with the 

annulus and sun gears (opposite flanks). This is an important observation since no faults were 

reported on the planet gears, even though virtually all Round Robin partners detected apparent 

faults corresponding to the planet gear rotation period. This is discussed further below.

The DSTO patented method described in [63] and illustrated below produces average time 

signals for each individual planet gear and the sun gear using shifted weighted signals from 

passage of each planet past the transducer, with correction for the phase offset of individual teeth 

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 -0.2

0

0.2

Intermediate Shaft

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -0.2

0

0.2

Low Speed Shaft

Acceleration (m.s2

)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 -1

-0.5

0

0.5

1

Planet carrier

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 -0.4

-0.2

0

0.2

0.4

Planet gear

Time (s)
120

for each passage. Note that the average for the sun gear can include the contact of individual 

teeth with all planet gears. 

Figure 9.27. Phase shifts for separated sun gear averages

The residual mentioned in some figures is the result of removing the regular tooth mesh signal so 

as to highlight local faults on a gear. 

Figure 9.28. Sun Gear – residual of DSTO average data set 2c (high speed, high load)

Figure 9.28 shows the residual signal for the sun gear at high speed and load. This result is 

compatible with the observation of the inspection report that the sun gear had localized fretting 

corrosion.
121

Figure 9.29. Sun Gear – residual of DSTO average data set 2a (low speed, low load)

Even at a very different speed and load, in Figure 9.29, the sun gear signature is almost identical 

(though displaced because there is no common phase reference). The same was found for the 

individual planet gear signatures discussed below, in Figure 9.30.

Figure 9.30. Residual signals for the three planet gears

Several Round Robin partners found evidence of faults on the planet gears, even though none 

were reported in the inspection report, but the above figure implies that the fault patterns are the 

same on all three planets. This could be caused by the “far from hunting tooth” design of the 

planetary section. Individual pairs of teeth on the annulus and sun gears, both of which had 

Planet 1

Planet 2

Planet 3

Revolutions
122

faults, could mesh simultaneously on opposite sides of a given planet gear relatively frequently. 

It would be natural for this to occur identically for all three planets, since all tooth numbers are 

divisible by three. This potential explanation should be confirmed by more detailed analysis of 

the kinematics of this particular configuration.

Figure 9.31. Average for the annulus gear

Figure 9.31 shows a typical average signal for the annulus gear. The residual in this case did not 

clarify the local faults to any great extent. However, the visible variations are compatible with 

the results of the inspection report, which found a distributed fault pattern from a local area of 

scuffing. Because of the numbers of teeth of all planetary components being divisible by three, 

the damage tended to imprint on every third tooth, and many examples this pattern over groups 

of three teeth can be seen in the above figure.

9.4 Discussion, Conclusions, Lessons Learned 

This research showed that our methods for analyzing gear and bearing faults in wind turbine 

transmissions are basically sound, and picked up most faults that could be expected to change the 

vibration patterns. In the initial blind analysis, we correctly detected faults in two of the three 

bearings with faults, usually in data from both low and high speed operation. We did, however,

miss a fault in the ISS bearing, which should have been detectable, and are at a loss to explain 

why. There is a possibility that there was not good transmission to any of the measurement 

points. We did find indications of local faults on a gear on the IS shaft (initially not separated 

from the HS shaft because of the exact 4:1 ratio), the sun gear, and the annulus gear. There was 

also an indication of local faults on one or more of the planet gears. 

When spectra were received for the gearbox in healthy condition, at about the same time as 

receiving the inspection report, considerably more detailed analysis could be done as to the 

details of the faults on each gear. An exception was the indication of faults on the planet gears, 

which were not found on inspection. Much of this analysis could have been done blind, with the 

availability of a healthy data for comparison from the outset. 
123

Much more detailed analysis was later performed by Dr David Forrester, of DSTO in Australia, 

using patented algorithms that allowed for the production of separate averages for the individual 

planet gears and sun gear. These corresponded well with the detected faults on most gears, but 

once again indicated faults on the planet gears. Other Round Robin partners found the same. It 

now seems likely that the misdiagnosis was due to the “far from hunting tooth” design of the 

planetary section, which could mean that faulty teeth on the sun and annulus gears could mesh 

simultaneously with a healthy planet gear relatively frequently, and thus give an indication of a 

fault on the planet gear. The fact that the three planets had the same fault pattern lends credence 

to this interpretation, as the meshing patterns would likely be the same for all three planets (with 

all tooth numbers divisible by three). This hypothesis needs to be further investigated before it 

can be confirmed.

This highlighted the fact that gear diagnostics is made easier by the adoption of designs as close 

as possible to “hunting tooth” designs, considered good design practice in any case. The exact 

4:1 ratio between the IS and HS shafts also made it difficult to separate the faults on gears on 

these two shafts, although luckily the second mesh on the ISS was a hunting tooth design.

For the relatively modest speed variations in the test data, it was possible to extract information 

on instantaneous speed from the signals themselves in the form of a “pseudo-encoder” signal. 

The signal, typically based on a high speed gear mesh component, can be used for order tracking 

and, thus, synchronous averaging of gear signals throughout the gear train. For larger speed 

variations, which are not uncommon with pitch controlled wind turbines, it would be necessary 

to start with a lower order harmonic of the shaft speed; however, in principle, the process can be 

done iteratively to improve the speed correction. This should be tested in the future.
124

10 A Two Stage Fault Detection Framework for Wind Turbine 

Gearbox Condition Monitoring

Pingfeng Wang* and Prasanna Tamilselvan

Department of Industrial and Manufacturing Engineering, Wichita State University *

Corresponding Author Email: pingfeng.wang@wichita.edu

10.1 Introduction

Maintaining wind turbines in top operating condition ensures not only a continuous revenue 

generation but a reduction in electric power drawn from non-renewable and more polluting 

sources. Despite the large capital for establishing a wind farm, the maintenance activities of wind 

turbines are the primary contributors for the wind energy costs [64-66]. The need for reduction in 

O&M costs are likely to increase due to the rising competition in today’s global economy. 

Effective health diagnosis of wind turbines provides various benefits, such as improved 

reliability and reduced costs for operation and maintenance (O&M). Research on real-time 

diagnostics and prognostics, which interpret data acquired by smart sensors and distributed 

sensor networks, and utilization of these data streams to make critical O&M decisions offers 

significant advancements in creating early awareness of wind turbine health condition before 

unexpected failures. The unexpected breakdowns can be prohibitively expensive since they 

immediately result in lost production [67-70]. To reduce, and possibly eliminate such problems, 

real time condition monitoring is required to avoid sudden catastrophic system failures. 

Vibration analysis is the most vastly used mechanism of condition monitoring in wind turbines. 

It is mainly applied to identify the current condition of rotating components, such as gearbox, 

generator, and main bearing, by installing mechanical sensors on the components. The defects of 

the components are estimated based on the vibrations produced by these components during 

operation. This chapter presents the vibration based condition monitoring framework with 

analytical defect detection method and graphical analysis developed for the CM Round Robin 

study. 

10.2 Vibration Based Condition Monitoring Framework

The framework for the proposed vibration-based condition monitoring is shown in Figure 10.1. 

The two major stages included in the vibration based condition monitoring framework are 

analytical diagnostics and graphical analysis of frequency domain signals. The raw time domain 

vibration data is pre-processed and converted into frequency domain data. The sideband and 

kurtosis-based online defect detection method is employed to process the frequency data 

analytically. The results from the analytical diagnosis are used as inputs to the graphical 

verification process. The failure modes and their severity levels are determined by graphical 

verification from the multi-dimensional vibration-based sensory signals.
125

Figure 10.1. Vibration based condition monitoring approach

The pre-processing of vibration data involves three steps, as shown in Table 10.1. The primary 

step of the vibration analysis is the calculation of gear and bearing frequencies. The gear 

meshing frequencies of all the gears, bearing frequencies such as Ball Passing Frequency Outer 

(BPFO), Ball Passing Frequency Inner (BPFI), and Ball Spinning Frequency (BSF) of all the 

bearings were determined for both speeds 1200 rpm and 1800 rpm. The next step involves the 

identification of the relationship between the sensor and the components. The final step in the 

pre-processing is to develop the frequency spectrum from the raw time domain vibration signal 

using the fast Fourier transformation (FFT) process for the desired sensors.

Table 10.1. Procedure for vibration data preprocessing

Step 1 Calculate Gear Meshing Frequency (GMF) for gears and bearing frequencies

Step 2 Determine relationship between sensors and components

Step 3 Develop FFT plot for desired sensors in each case

The Round Robin study involves three speed stages: low speed (LS), intermediate speed (IS) and 

high speed (HS). In this research, the high frequency rotating components such as intermediate 

and high speed stages of the gearbox are only considered for damage detection. Among the total 

of 10 sensor values from the Round Robin gearbox, the desired sensors for the IS and HS are AN 

5 to AN 9. The relationships between these sensors and the components are determined based on 

the location and proximity to the rotating components, as listed in Table 10.2.
126

Table 10.2. Sensor and component relationship

Sensor Sensor 

Name GMF SRF Bearing Damage

AN5 LSS radial IS gear LSS LSS upwind and 

downwind bearing

LSS bearings defect and ISS 

gear defect

AN6 ISS radial IS pinion and 

HS gear ISS ISS ISS bearings defect, IS pinion defect, HS gear defect

AN7 HSS radial HS pinion HSS HSS HSS bearings defect, HS pinion 

defect

AN8 HSS front 

radial HS pinion HSS HSS upwind bearing

HS pinion defect, HSS upwind 

bearing defect

AN9 HSS rear 

radial HS pinion HSS HSS downwind bearing

HS pinion defect, HSS 

downwind bearing defect

The raw vibration signals from the sensors are time domain signals. The defects from the 

bearings and gears can be identified from their corresponding desired frequency amplitudes in 

the frequency spectrum. The FFT converts the time domain signal into a frequency domain 

signal and helps in analyzing each desired frequency based on its amplitude and its harmonics.

10.3 Analytical Diagnostics

The sideband and kurtosis based online defect detection method is employed to process the 

frequency data analytically and the stepwise procedure is shown in Table 10.3. The maximum 

amplitude of the desired frequency, the sidebands, and the kurtosis values for the sidebands are 

determined to calculate the severity factors to formulate the defect severity matrix. The failure 

modes and their severity levels are determined by the defect severity matrix from the vibrationbased sensory signals.

Table 10.3. Procedure for analytical diagnostics

Step 1 Determine maximum amplitude values for sidebands and desired frequency

Step 2 Determine kurtosis values for sidebands

Step 3 Calculate severity factor 1, 2 and 3

Step 4 Formulate defect severity matrix

10.3.1 Sideband and Kurtosis Analysis

The sidebands are indicators of the failure modes in the frequency spectrum of the rotating 

components based on their spread on both the sides of the desired frequency. The rising and 

inequality of the sidebands correspond to component defects, and moreover, the severity of the 

defect can be identified based on the frequency sideband features, as listed in Table 10.4 [71].

The height and sharpness of the peak amplitudes in the frequency spectrum are measured by 

kurtosis. The spread of the sidebands on either side of the desired frequency can be analyzed 
127

using the kurtosis values. The differences in the kurtosis values of both sidebands denote the 

inequality in the sidebands. The kurtosis ratio KR, is the ratio of the left side of j

th, the desired 

frequency is KLj , to the right side of j

th, the desired frequency KRj is as shown in Equation (21). 

Similarly, the ratio of maximum amplitude of the sideband on left and right sides of the j

th

frequency is determined as AR shown in Equation (21).

; Lj Lj

Rj Rj

K A

KR AR

K A = = (21)

Table 10.4. Sideband-based severity definition

Frequency Sideband Feature Severity Level

Rising of sidebands around desired frequency Low

Unequal sidebands on both sides Medium

High sideband amplitude than frequency amplitude High

10.3.2 Severity Factors

The different failure modes and their severity levels are determined from the converted 

frequency domain signal through analytical sideband and kurtosis analysis. 

Table 10.4 shows the different severity levels based on the frequency sideband features. The 

severity factor analysis resulted in three severity factor metrics for online defect detection. The 

severity factor 1 (SF1) ensures equal spread of the sidebands using the kurtosis ratio metric, as 

shown in Equation (22). The threshold kurtosis ratio, KRT, is considered to be 0.6. The value of 

SF1<1 denotes the unequal spread of sidebands and vice versa. The severity factor 2 (SF2) 

ensures equal maximum amplitude of sidebands on both sides of the desired frequency, as shown 

in Equation (23). The threshold amplitude ratio, AT, is considered to be 0.9. The value of SF2< 1

denotes the unequal frequency amplitudes on both sides of the sidebands and vice versa.

1

1

Min ( , ) j j

T

KR KR

SF

KR

−

= (22)

1

2

Min ( , ) j j

T

AR AR

SF

A

−

= (23)

The severity factor 3 (SF3) ensures that the maximum desired frequency amplitude is higher than 

the maximum amplitude of the sideband Amax, as shown in Equation (24), where AF is the

maximum amplitude at the desired frequency. The value of SF3< 1 denotes the frequency 

amplitude of the sideband, Amax, which is higher compared to the desired frequency, Amax.

3 Max ( , )

F

Lj Rj

A SF

A A = (24)
128

Table 10.5. Severity factor analysis of sensor AN 6 for Case 2a

Component Desired 

Frequency SF1 SF2 SF3 Low Medium High

ISS gear and ISS 

pinion GMF 0.49 0.97 0.46 0 0 1

ISS upwind 

bearing BPFI 0.98 0.73 2.85 0 1 0

ISS downwind 

bearing BPFO 0.86 0.42 2.94 0 1 0

HSS upwind 

bearing BPFO 0.58 1.06 0.23 0 0 1

HSS downwind 

bearing BPFI 0.72 0.58 1.67 0 1 0

The conditions SF1 ≤ 1, SF2> 1, and SF3> 1 show that the component has a low severity defect. 

The severity factor characteristics of the medium severity defect are SF1 ≤ 1, SF2 ≤ 1, and SF3> 

1 and SF1> 1, SF2 ≤ 1, and SF3> 1. Similarly, the high severity defect conditions are SF1 ≤ 1, 

SF2 ≤ 1, and SF3 ≤ 1; SF1> 1, SF2 ≤ 1, and SF3 ≤ 1; SF1 ≤ 1, SF2> 1, SF3 ≤ 1, and SF1> 1, 

SF2> 1, SF3≤ 1. Based on these rules, the severity levels and the failure modes of the 

components are identified based on the each sensor. The severity factor analysis of sensor AN 6 

for 2a case is listed in Table 10.5.

10.3.3 Severity Defect Matrix

The failure modes and their severity levels of the rotating components based on the each sensor 

are identified with different severity metrics. However, the same defect of the rotating 

components can be identified by different sensors in and around the component location. 

Therefore, there is a need for developing a unified metric to make decisions on the failure mode 

and its severity level. This, in turn, will lead to the development of a defect severity matrix, 

combining the results of all the components from the different sensors. The desired component 

matrix U is shown in the Equation (25).

ISS Gear and ISS Pinion

HSS Gear and HSS Pinion

LSS upwind bearing

LSS downwind bearing

ISS upwind bearing

ISS downwind bearing

HSS upwind bearing

HSS downwind bearing

U

   

=

 

(25)
129

The desired component matrix and the severity factor levels of all the components are utilized 

for developing a defect severity matrix. The severity ratio of component u at severity level g, Sug

is represented as Equation (26), where g represents the different severity levels, such as low, 

medium, and high, and Sugm represents the severity level of component u at level g through 

sensor m.

1

3

1 1

M

ugm

m ug M

ugm

g m

S

S

S

=

= =

=

∑

∑∑

(26)

The defect severity matrix, DS, represents the defect component and its severity level in the 

matrix format as shown in Equation (27), where rows of the matrix represent each desired 

component and columns represent the severity level of the components, such as low, medium 

and high. 

11 12 13

UU U 123

SSS

DS

SSS

    =  

 



(27)

The unified DS matrix of the Round Robin study is determined and shown in the Equation (28). 

The analytical diagnostics results indicated that there is no defect in the LSS upwind and 

downwind bearings. The IS gear and pinion each have a high severity defect and the HS gear and 

pinion each have a medium severity defect. The analytical results are further fine-tuned using the 

graphical verification process.

0.33 0.50 0 0 0.67 0.50 0.50 0.60

0.34 0.50 0 0 0.33 0.50 0.33 0.40

0.33 0.00 0 0 0.00 0.00 0.17 0.00

T

DS

    =

 

(28)

10.4 Graphical Diagnostics

The unified defect severity matrix results provide the initial insights about the component defects 

and their severity levels. There is the possibility of false identifications in the analytical 

methodology due to the overlap of different frequencies and their harmonic levels. Therefore, 

there is a need for verification of identified component defects graphically. The frequency 

spectrum of the predetermined component defects are verified graphically based on the sideband 

amplitudes and their spread. The second harmonic of the BPFO (172 Hz) of HSS downwind 

bearing at (344 Hz) in AN 6 ISS is the radial sensor value shown in Figure 10.2. The Amax of 

right sideband is almost two times the Amax of left sideband and moreover, the high amplitude of 

the right sideband is almost eight times the high amplitude of the desired frequency. These 

inferences from the figure prove that there is a high severity failure in the outer raceway. Since 

the sideband amplitudes are found in the second harmonic, there is a chance of misalignment of 

the bearing. Similarly, component defects are identified graphically and the results are discussed 

in the next section.
130

Figure 10.2. HSS downwind bearing BPFO – graphical analysis

10.5 Results

The results from the online analytical defect detection method are used as inputs to the graphical 

verification. The failure modes and their severity levels from the multi-dimensional vibrationbased sensory signals are verified graphically, and the results are unified to the component level,

with their corresponding severity levels, as shown in Table 10.6.

Table 10.6. Vibration-based condition monitoring results

Damage Component Mode Severity

1 HSS pinion Gear tooth failure of HSS pinion High

2 HSS downwind bearing OR failure and bearing misalignment High

3 ISS gear Early stages of gear failure Low

4 ISS upwind bearing IR failure and bearing misalignment Medium

5 ISS downwind bearing OR failure High

The tabulated results were identified before the receiving knowledge of the actual failure modes. 

The possible number of failures that can be identified from the vibration analysis for this Round 

Robin study is about seven. The proposed condition monitoring approach identified five failures 

and their severity levels. Moreover, the failures identified by the proposed vibration analysis 

approach do not have any false identification. The accuracy of the condition monitoring 

approach is due to its two fold analysis process, i.e. the analytical identification and the graphical 

verification. The preliminary results from the analytical identification are further fine-tuned 

using the graphical verification to avoid false identifications. 

330 335 340 345 350 355 360

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Frequency (Hz)

|Y(f)|

2a 10 AN6 ISS Radial
131

As a summary, this research showed that the developed vibration based two stage fault detection 

framework that integrates both analytical diagnostics and graphical diagnostics is quite effective 

for analyzing gear and bearing faults in wind turbine transmissions, as proved by the CM Round 

Robin study results. With successful studies and lessons learned on the drivetrain CM, the 

research can be extended to a probabilistic complex system design framework that potentially 

can quantify the functionality, reliability, uncertainty, and cost/benefits of condition monitoring 

techniques. It can integrate them into a system-level wind turbine design practice, as a 

fundamental solution of enhancing reliability and reducing life cycle cost.
132

11 Recommended Practices 

Based on the comparison of diagnostics results provided by sixteen partners during the blind 

study stage, as presented in Chapter 1, and the detailed results from eight of the sixteen partners, 

as presented in Chapters 3-10, it is clear that there is still room for the industry to improve 

vibration analysis algorithms. Some algorithms presented in this report have not been widely 

adopted in commercialized vibration-based condition monitoring (CM) systems. If adopted, they 

can lead to increased accuracy of vibration-based wind turbine drivetrain condition monitoring.

They may potentially help increase the cost effectiveness of wind turbine condition monitoring 

techniques. In addition, based on the lessons learned in this study, some recommended practices 

were provided by several partners, especially Impact Technologies, National Instruments, and 

STC Consultants. They will be discussed in this chapter. It is hoped that these recommended 

practices can be considered in future research and development efforts within the wind turbine 

condition monitoring community. 

11.1 Data Acquisition 

To meet the dynamometer retest schedule of the damaged GRC gearbox, the vibration CM data 

acquisition system used in this study was put together within an extremely tight time window. 

However, efforts were made, as much as possible, to represent a typical commercialized 

vibration CM system and meet the guidelines recommended by Germanischer Lloyd (GL) [72]. 

For example, anti-aliasing filters and 24 bit ADC were adopted for all sensor channels. 

This study, however, was challenged by poor speed measurements. As pointed out by almost all 

of the project partners, there was no once per revolution signal, which is valuable for time 

synchronous averaging for gear health condition diagnostics. The measured high speed shaft rpm 

also showed oscillations, which could be worked around but was a challenge. A once per 

revolution signal could have been generated based on the raw encoder readings throughout the 

test and provided to all Round Robin project partners. It was not attempted so the project 

partners could have enough time to conduct the blind stage data analysis. However, it is 

recommended that a once per revolution signal be provided in gear health monitoring since

tachometer signal acquisition requires converting pulse trains into a series of timestamps and 

speeds. In general, to isolate mechanical vibration frequencies from one another, accurate speeds

and angular positions of the shaft's rotation are critical. The GL guidelines [72] call for high 

resolution speed measurements as part of an instrumentation system in the field. Further, to track 

vibration frequencies with respect to speed, both vibration and speed measurements should be 

made simultaneously or clocked from the same base clock. In the Round Robin project, speed 

information came from the high speed shaft. Adding a tachometer to monitor the input rotor shaft 

might provide a more accurate result for the lower speed components. 

This Round Robin study focuses on the gearbox, as it is the only component with disassembled 

information. If the main bearing is considered for study, accelerometers, with a measurement 

frequency range down to 0.1 Hz, are recommended. Alternatively, new sensing techniques, such 

as acoustic emission [73], can be investigated. This recommendation may also be applicable to 

the ring gear. In addition, for some bearing locations and types inside the gearbox, it may be 

worth evaluating axial-mounted accelerometers.
133

In this study, only the frequency domain baseline data was provided. Also, the test data was 

collected from one test gearbox for a short period of time. Diagnostics results could have been 

further improved by providing the baseline data in the time domain from a bigger population of 

gearboxes of the same model, and a longer data acquisition window of months or years. 

The data acquisition system developed for this study was put together to facilitate the Round 

Robin research. Its main emphasis was to collect high resolution raw time series data, which can 

be provided to vibration analysts for diagnosis of the monitored gearbox condition. When 

deploying a condition monitoring system in the field, it is important to balance the amount of 

data, communications, and timing of the data acquisition. Communications may be expensive 

when using a cellular modem, or slow using a 900 MHz radio. The amount of data storage onboard an embedded data acquisition system may be limited. For this balancing task, a machine 

with a check trigger state containing continuous acquisition and analysis of incoming sensory 

data can be investigated. When the monitored wind turbine is operating, and measured values 

have changed by a specific percentage or delta, then both pre-trigger and post-trigger sensory 

data is stored to a binary file with a complete descriptive set including enterprise, wind farm, and 

wind turbine. By combining both periodic data recordings with data change driver recordings, a 

complete picture of the wind turbine is possible, using just the right amount of data. 

11.2 Data Analysis 

Once data is collected, the challenge lies in how to interpret the data and derive useful 

information. The diagnostic tasks in the Round Robin project are more challenging because the

drivetrain damage was more complex than in a typical operational wind turbine. Therefore, the 

diagnostics techniques presented in this report could potentially perform better when deployed in 

the field. For this project, NREL is fortunate to have the support from vibration analysts across 

the world. Main recommended practices mentioned by the project partners for vibration data 

analysis are discussed below. 

Though no sensor faults were present in the test data sets shared by NREL for this study, it is 

generally recommended to perform sensor validation before using vibration data for condition 

monitoring of rotating components. GL uses a similar guideline. [72] This will help reduce 

ambiguity between sensor and mechanical faults and reduce false alarms. 

The GRC test turbine operates at two relatively constant speeds. For variable speed wind 

turbines, the GL guidelines call for order tracking using measured speed [72]. 

Due to the complexity in gearbox design and the dynamic operating conditions, an integrated 

approach must be taken that uses diagnostic information from all components (gears, bearings, 

and shafts) as a whole. In other words, the analysis needs to integrate all available diagnostic 

information to confidently detect and isolate problems via a high level reasoning / classifier 

method. In addition, vast differences in speed/torque could cause dramatic differences in results 

of vibration analysis. The accuracy can be increased by comparing results from similar steady 

state operating conditions, e.g., the operational-category concept [74], by applying techniques 

that are less sensitive to the effects, or by normalizing results. Conventional gear diagnostic 

features are limited for planetary gear component fault detection because of the changing 

transmission path, moving fault location, and modulation. As such, special consideration should 

be given to fault detection of these components. For example, multiple cycles of the hunting 
134

tooth ratio should be recorded for each planetary component. In addition, diagnostic approaches 

that are specifically designed for planetary gear fault detection should be used.

Enveloping or demodulation has proven to be an effective approach for bearing diagnostics. 

However, proper selection of various filters used by this approach is critical to diagnostic 

performance, in particular for the incipient fault detection capabilities. These filters should also 

be optimized for each sensor location [75]. Note, too, that these resonant frequencies may likely 

change with operating conditions as well. Enveloping or demodulation at higher frequencies is 

desirable to avoid higher order gear mesh harmonics that obfuscate bearing fault frequencies. 

Ideally, both the sensor and data acquisition system would provide data above 20 kHz. However, 

an increase in only the sampling rate has been shown to increase diagnostic performance. 

Another factor to consider is how much additional cost is needed for collecting data above 20 

kHz. 

Fusing vibration results with those from other sensors would help complete the diagnostic 

coverage. In particular, oil debris, oil temperature, and casing temperature [72,76] would provide 

additional evidence of impending failures. Modeling/simulation of expected vibration at different 

operating and fault conditions is useful and a good compliment to seeded fault and accelerated 

life testing.
135

Appendix A – Project Partners

Brüel & Kjær Vibro A/S

Colorado School of Mines

GE Bently Nevada

Impact Technologies

IVC Technologies

National Instruments

NRG Systems Inc.

Purdue University

Schenck Corporation

Sentient Corporation

STC Consultants (SKF)

University of Cincinnati

University of Connecticut

University of Iowa

University of New South Wales in Australia

Wichita State University
136

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