a comparative study on vibration-based condition monitoring algorithms for wind turbine drive trains

SPECIAL ISSUE PAPER

A comparative study on vibration-based conditionmonitoring algorithms for wind turbine drive trainsDavid Siegel, Wenyu Zhao, Edzel Lapira, Mohamed AbuAli and Jay Lee

Department of Mechanical Engineering, Center for Intelligent Maintenance Systems, University of Cincinnati, PO Box 210072,Cincinnati, Ohio 45221-0072, USA

ABSTRACT

The ability to detect and diagnose incipient gear and bearing degradation can offer substantial improvements in reliabilityand availability of the wind turbine asset. Considering the motivation for improved reliability of the wind turbine drivetrain, numerous research efforts have been conducted using a vast array of vibration-based algorithms. Despite these efforts,the techniques are often evaluated on smaller-scale test-beds, and existing studies do not provide a detailed comparisonbetween the various vibration-based condition monitoring algorithms. This study evaluates a multitude of methods, includingfrequency domain and cepstrum analysis, time synchronous averaging narrowband and residual methods, bearing envelopeanalysis and spectral kurtosis-based methods. A full-scale baseline wind turbine drive train and a drive train with several gearand bearing failures are tested at the National Renewable Energy Laboratory (NREL) dynamometer test cell during the NRELGear Reliability Collaborative Round Robin study. A tabular set of results is presented to highlight the ability of each algorithmto accurately detect the bearing and gear wheel component health. The results highlight that the cepstrum and the narrowbandphase modulation signal were effective methods for diagnosing gear tooth problems, whereas bearing envelope analysis couldconfidently detect most of the bearing-related failures. Copyright © 2013 John Wiley & Sons, Ltd.

KEYWORDS

time synchronous averaging; envelope analysis; cepstrum; planet separation algorithm; wind turbine gearbox condition monitoring

CorrespondenceDavid Siegel, Department of Mechanical Engineering, Center for Intelligent Maintenance Systems, University of Cincinnati, POBox 210072, Cincinnati, Ohio 45221-0072, USA.E-mail: [email protected]

Received 19 March 2012; Revised 7 September 2012; Accepted 25 November 2012

1. INTRODUCTION

In terms of renewable energy sources, wind turbines are one of the fastest growing sources. Despite this recent growth,further improvement in the reliability and maintainability of wind turbines is needed in order to achieve the US Departmentof Energy’s goal of 20% of the total energy by 2030 coming from wind turbines.1 One paramount aspect for obtainingimproved wind turbine reliability is the use of condition monitoring technology.2 The benefits of the condition monitoringtechnology include its capability to provide considerable cost savings, even if the replacement cost for a given component isrelatively low. As noted by a report by General Electric, the cost of replacing a $5000 bearing could end up being over$250,000 because of the additional cost needed for a crane, a service crew, replacement of the gearbox and also the lossof power generation during that downtime period.3 Considering that it is not feasible to monitor every aspect of a windturbine, various studies have focused on subsystems that are critical to the reliability of the wind turbine. The study byLu et al.4 noted that the wind turbine drive train, and in particular the gearbox, is one of the most critical subsystemsregarding maintenance. This study also mentioned that gearbox bearing failures were the most common component failure.

Considering the economic impact along with the need for improved reliability of wind turbine drive train components,various studies have developed algorithms for monitoring the health condition of the wind turbine drive train. A statisticalregression-based algorithm was proposed by Villa et al.5 in order to assess the gearbox condition under multiple speed andloading regimes. In this study, the results showed that it was advantageous to diagnosis the health condition when data frommultiple operating conditions were included as compared with using data from a single operating regime. Although the

WIND ENERGYWind Energ. (2013)

Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/we.1585

Copyright © 2013 John Wiley & Sons, Ltd.

algorithm showed promise, it is difficult to conclude how the method would generalize to a larger system or different faulttypes, considering that the study used a smaller-scale test-bed and limited the faults to shaft unbalance and misalignment.To improve the diagnosis, Lu et al.6 proposed a sensor fusion approach in which time-frequency features extracted from thevibration and acoustic signal are combined using a principal component analysis-based method. The method by Lu et al.6

was validated on an experimental gearbox test-bed with a variable speed profile; the paper did not further evaluate theproposed algorithm with a full-scale wind turbine gearbox. Additional related work in the area of planetary gearboxcondition monitoring, diagnosis and sensor fusion was conducted by Lei et al.7 The results showed that improvedclassification results were obtained when features from multiple accelerometers were used when compared with the resultsobtained using a single accelerometer. A recent study by Barszcz and Randall8 evaluated the use of spectral kurtosis as wellas frequency analysis and time statistics from data from a wind turbine gearbox. This particular gearbox experienced acatastrophic failure due to a cracked ring gear tooth; however, only the spectral kurtosis method could provide an incipientdetection of this gear tooth fault. The study also noted the difficulty in applying synchronous averaging methods for theplanetary stage gearbox due to the low rotational speed and the variable load conditions.

From the prior work, it appears that there is a need for more in-depth evaluation of the various vibration-based gearand bearing health monitoring algorithms on a full-scale wind turbine gearbox. Although various condition monitoringalgorithms provided successful results under experimental settings, the algorithms’ ability to generalize to a more compli-cated drive train configuration with multiple stages and several bearing and gear wheel components were not sufficientlystudied. In addition, a comparison between conventional and more recently developed vibration-based algorithms is lackingin the prior work. Many of the previous studies provide a limited comparison between their method and conventionaltechniques with only one or two conventional algorithms usually included. This study aims to contribute to the area of windturbine condition monitoring by providing a detailed investigation of the most relevant vibration-based signal processingand feature extraction algorithms. The comparison study is conducted on a full-scale wind turbine gearbox, thus providinga more compelling investigation of whether the methods are applicable to a large-scale system.

The paper is organized as follows. In Section 2, a description of the test-bed, measured signals and operating conditionsis provided. Section 3 provides an overview of the signal processing and feature extraction methods evaluated in the study;more specific details and results from each method are provided in each subsection. A tabular summary of the results isprovided in Section 4, in which the algorithm results are compared with the documented failures from the failure report.Lastly, conclusions and suggestions for future work are discussed in Section 5.

2. DESCRIPTION OF TEST-BED

The data source for this study is from the National Renewable Energy Laboratory during the Wind Turbine GearboxCondition Monitoring Round Robin study that took place in 2011. A complete description of the test-bed and instrumen-tation can be found in the National Renewable Energy Lab Gearbox Reliability Collaborative Round Robin document andrelated publications,9,10 and only a brief review of the experimental testing is provided. The rationale for providing the briefreview is to present the nomenclature used for labeling the gearbox components and measured signals that are used in thesubsequent sections.

The drive train consists of a planetary stage gearbox and a parallel stage gearbox, with the latter being on the outputgenerator side. Table I provides the nomenclature used for naming each respective gear along with the number of teethon each gear wheel. In total, there are seven gear wheels and 14 bearings, with three bearings on each shaft of the parallelstage gearbox and four bearings supporting the planet carrier and planet gears, and one main bearing on the rotor shaft.The gear ratio for this drive train configuration is 1:81.5, with the planetary stage and parallel stage providing a speedmultiplication of 5.7 and 14.3, respectively. The test article consisted of a gearbox from a degraded condition in whichthe system experienced two losses of oil prior to its testing in a dynamometer test cell. Many of the internal gear and bearing

Table I. Listing of gears and number of teeth.

Gear Location Number of teeth

Ring gear Planetary gearbox 99Sun gear Planetary gearbox 39Planet gears (3) Planetary gearbox 21ISS gear Parallel stage gearbox 82ISS pinion Parallel stage gearbox 23High-speed shaft gear (HSS gear) Parallel stage gearbox 88High-speed shaft pinion (HSS pinion) Parallel stage gearbox 22

Comparative study on wind turbine drive train health monitoring D. Siegel et al.

Wind Energ. (2013) © 2013 John Wiley & Sons, Ltd.DOI: 10.1002/we

components were damaged during these losses of oil events. A list of the different faults that occurred on the gearbox isprovided in Table II, and a more detailed description with pictures of the damaged components can be found in the failurereport by Errichello and Muller.11

The objective was to evaluate the algorithms on the basis of their ability to detect which of the gear and bearingcomponents were in a degraded or fault condition. An additional set of vibration spectrum was also provided from the samegearbox in a baseline condition. In total, 30 data files were provided from the degraded gearbox, with each file containing1min of recorded data. The measured signals included 12 accelerometers at different locations on the gearbox; torque andspeed signals were also provided. The nomenclature and location of the accelerometer signals are provided in Table III. Fora more detailed description of the sensor locations including schematics, the interested reader is referred to the work ofSheng et al.10 A sampling rate of 40 kHz was used for the data collection of the 30 data files from the degraded gearbox;a lower sampling rate was used for acquiring the baseline spectrum. The gearbox was tested under three different operatingconditions regarding the rotational speed and output power as shown in Table IV.

Table II. Listing of degraded components and failure modes.

Damage # Component/location Failure mode

1 HSS gear set Scuffing2 HSS downwind bearings Overheating3 ISS gear set Fretting corrosion

ScuffingPolishing wear

4 ISS upwind bearing Assembly damagePlastic deformationScuffingFalse brinellingDebris dentsContact corrosion

5 ISS downwind bearings Assembly damagePlastic deformationDents

6 Annulus/ring gear, or sun pinion Scuffing and polishingFretting corrosion

7 Planet carrier upwind bearing Fretting corrosion8 Sun pinion thrust rings Fretting corrosion

Adhesive wear9 Oil transfer ring for planet carrier Polishing10 Low-speed shaft (LSS) seal plate Scuffing11 LSS downwind bearings Abrasion12 HSS Misalignment

Table III. Sensor location and description.

Sensor nomenclature Location

AN1 Main bearing radialAN2 Main bearing axialAN3 Ring gear radial (6 o’clock)AN4 Ring gear radial (12 o’clock)AN5 LSS radialAN6 ISS radialAN7 HSS radialAN8 HSS upwind bearing radialAN9 HSS downwind bearing radialAN10 Carrier downwind radialAN11 Generator upwind radialAN12 Generator downwind axialSpeed Encoder on HSSLSS torque Strain gauges on LSS

Comparative study on wind turbine drive train health monitoringD. Siegel et al.


3. VIBRATION-BASED SIGNAL PROCESSING AND FEATURE EXTRACTIONMETHODS—ALGORITHMS AND RESULTS

An overview of the signal processing methods evaluated during this study is provided in Table V, along with theadvantages and disadvantages of each method. Despites its simplicity, analyzing the vibration data in the frequency domaindoes have its merits for detecting gear-related problems. Gear mesh frequencies and associated sidebands can be identifiedin the vibration spectrum, and various vibration indicators or features can be calculated from the frequency domain signal.12

The real cepstrum is particularly useful for analyzing a family of harmonics, which has application for gear-related faults.13

A series of sidebands can be analyzed by calculating the cepstrum; the magnitude of the peaks compared with a baselinecondition can be used to diagnose the health condition for each gear wheel. The calculation of the real cepstrum can alsobe performed from the frequency spectrum; this was a useful asset for this study since only a baseline frequency spectrumwas provided.

Time synchronous averaging represents one of the most established signal processing techniques for gear conditionmonitoring. The method is ideally suited for the processing of gear vibration, since the synchronous averaging methodenhances and separates the periodic gear vibration from the cyclostationary vibration from rolling element bearings. Inaddition, additional processing methods can be performed on the time synchronous average signal, including the gearresidual signal and the amplitude and phase modulation functions.14 For planetary gearboxes, because of the relativemotion 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 would not be able to isolate the individual vibration for each planet gearor the sun gear. Specific algorithms for performing synchronous averaging for planetary gearboxes are also evaluated in

Table IV. Gearbox operating conditions.

Test case Input speed (rpm) Output speed (rpm) Electric power (% of rated) Duration (min)

CM_2a 14.72 1200 25 10CM_2b 22.09 1800 25 10CM_2c 22.09 1800 50 10

Table V. Summary of evaluated methods—advantages and disadvantages.

# Technique Advantages Disadvantages

1. Frequency domain Sidebands around gear mesh frequencies canbe identified and provides a relatively simplemethod for extracting gear condition indicatorswithout a tachometer signal12

Signal-to-noise ratio is not enhanced byusing a tachometer signal, which can helpreduce the vibration from other sourcesnot synchronous with the shaft and gearcomponents

2. Cepstrum Convenient method for extracting informationfrom a family of harmonics; ideally suited forextracting gear condition indicators because ofsidebands and amplitude modulation13

Family of harmonics could be related toshaft problems such as unbalance ormisalignment and may not be due to agear-related fault

3. Bearing envelope analysis Most established method for bearing diagnosisin the literature16; is more suited for detectingincipient bearing spalls

Selection of the demodulation band is nottrivial and still an active area of research16,could also require a higher sampling ratedepending on the excited system resonance

4. Spectral kurtosis filtering Filters signal based on the frequency band thatis most impulsive17; can be used to calculatefeatures on the filtered signal and to select anappropriate filter in envelope analysis

Extended spalls or faults might not beimpulsive, and hence this affects the abilityof thismethod to detect these types of faults

5. Time synchronous averaging Enhances vibration synchronous with the shaft,residual signal can look for abnormalities in theregular meshing pattern, demodulation aroundgear mesh frequency can detect a damagedgear tooth by analyzing amplitude and phasemodulation signals14

Requires accurate tachometer signal forperforming the synchronous averaging,might require a long acquisition time forLSSs because of the low rotational speedand collecting an ensemble of readingsfor averaging

6 Planet separation method Specific algorithm for performing synchronousaveraging for individual planet and sun gears16

Requires very long acquisition time forcollecting enough rotations for performingthe averaging



this work; the method suggested by McFadden15 is used in this study. This specific algorithm for planetary gearboxes doeshave some potential drawbacks; in particular, the long data acquisition period needed to perform the calculation procedureis a major challenge for implementing this method.

For bearing condition monitoring, the most established method in the literature is bearing envelope analysis, also calledthe high-frequency resonance technique.13 The general concept is that a spall or damage on a bearing race or rollingelement would cause a series of impacts that excite the structural resonances of the mechanical system. This causes anamplitude modulation effect in which the carrier frequency is the resonance frequency and the modulation frequency isthe bearing fault frequency. By filtering around the excited resonance and performing the demodulation, the envelopespectrum along with the calculated fault frequencies can be used to diagnose the bearing condition. A more detaileddescription of bearing faults, the bearing envelope analysis method and methods for selecting the band-pass filter frequencyrange are provided in the work of Randall and Antoni.16 Despite bearing envelope analysis being a very effectivetechnique, the method usually requires a high sampling rate since the excited resonance can occur at frequencies above10 kHz for many applications. The selection of the band-pass filter is also a crucial aspect in the method and a current areaof research.16 The use of spectral kurtosis filtering can be used for selecting the filter band for the bearing envelope analysismethod as well as for calculating indicators for the overall health condition of the monitored gearbox.17

3.1. Frequency domain methods

For rotating machinery, an initial understanding of the time domain and frequency domain signature is a typical firstapproach prior to applying more advanced processing methods. For meshing gears in particular, there are signaturefrequencies related to the gear mesh frequencies and sidebands; the use of the fast Fourier transform and analysis of thegear mesh frequency peaks and sidebands can provide an initial evaluation of the gear wheel health condition. Gears ina nominal healthy or degraded condition typically have a similar gear mesh frequency peak; however, the magnitude ofthe sidebands is more useful for assessing the gear wheel health condition. In addition, the spacing of the sidebands canindicate which particular shaft and associated gear wheel is degraded.12 An example vibration spectrum from thisstudy is provided in Figure 1, in which one can clearly identify the gear mesh frequency peak (for the high-speed shaftgear and pinion) at 662Hz for the gearbox in the nominal baseline condition. The gear mesh frequency peak is alsopresent in the vibration spectrum of the degraded gearbox; however, there are very large sidebands at 631 and691Hz for the degraded gearbox. The sidebands are spaced at 30Hz, which is the high-speed shaft rotational speed;this initial example provides some evidence that the high-speed pinion is degraded because of the sidebands observedin the vibration spectrum.

To further quantify these observations from the vibration spectrum, a set of gear vibration features was extracted usingthe baseline spectrum and the spectrum from the degraded gearbox. To quantify the magnitude of the sidebands, the side-band level was calculated using (1). In this calculation, SBLa stands for the sideband level, Sba1 is the magnitude of thelower sideband and SBa2 is the magnitude of the upper sideband. In addition, a sideband ratio was also calculated using(2); this normalizes the sideband ratio by the gear mesh frequency peak. Prior work has shown this sideband ratio featureto be an effective metric for quantifying gear health since it is less dependent on the torque load.18 For each respective gear,

Figure 1. Vibration spectrum—caseC: top plot, AN7 baseline; bottom plot, AN7 degraded gearbox.



four features were calculated, since the sideband ratio and sideband level were calculated for the gear mesh frequency andthe first harmonic of the gear mesh frequency. Also, the frequency domain gear features were only calculated for the fourgears on the parallel gearbox stage. The analysis of the sideband patterns for the planetary gearbox is quite complicated;thus, more advanced techniques were evaluated for the planetary gearbox.

SBLa ! SBa1 " SBa2 (1)

SBRa !SBa1 " SBa2

GMFpeak(2)

Example results using the frequency domain gear features are provided in Figure 2. In this example, the sideband ratiofor the intermediate-speed pinion and the high-speed pinion are larger in magnitude for each sample from the degradedgearbox compared with the gearbox from the baseline condition. However, there is more separation in this conditionmonitoring feature for the high-speed pinion than what is observed for the intermediate-speed pinion. The sideband ratiofor the high-speed gear is very similar to the baseline level and would imply that this particular gear wheel is normal usingthis frequency domain feature. It should be noted in the failure report that high-speed gear set was observed to have severescuffing for both gears. In addition, the failure study reported that the intermediate-speed gear set had severe frettingcorrosion and scuffing for both gears as well. From the frequency domain method, it appears that there is a strong indicationthat there is damage on the high-speed pinion. There also is an indication but with lower confidence of damage on theintermediate-speed pinion. However, there is little evidence from the frequency domain gear features of damage on thehigh-speed gear or intermediate-speed gear despite the reported damage in the failure report. The other processingalgorithms were used to further investigate the health condition of the parallel stage gear wheels as well as the other bearingand gear components. If several processing methods provide evidence of a degraded component, this can provide anincreased level of confidence that the component is damaged.

3.2. Cepstrum processing method

The real cepstrum provides a processing method that is ideally suited for analyzing a family of harmonics in a muchmore consolidated way than the frequency domain representation. For calculating the real cepstrum, the inverse Fouriertransform is applied to the logarithm of the power spectrum as shown in (3), where Cxx(t) is the real cepstrum and A(f)is the frequency spectrum.13 For mechanical systems and gears in particular, the cepstrum provides a convenient way ofanalyzing a series of sidebands that are spaced at a given shaft speed; comparing the cepstrum from a baseline and currentstate can be used to infer the health condition of each gear wheel. The example cepstrum result in Figure 3 further illustratesthis aspect in which the cepstrum from the baseline gearbox is compared with the degraded gearbox. In both instances, onecan observe a peak in the cepstrum at 0.133 s, which corresponds to 7.5Hz and the intermediate-speed shaft (ISS).This implies that a family of harmonics spaced at 7.5Hz was always present in this gearbox. However, an additionalpeak at 0.0325 s, which corresponds to 30Hz and the high-speed shaft, can be seen in the cepstrum of the degraded

Figure 2. Sideband ratio gear features—caseC: (a) ISS pinion, (b) HSS gear, (c) HSS pinion.



gearbox. This additional set of harmonics spaced at 30Hz for the degraded gearbox provides evidence that the gear wheelon the high-speed shaft (high-speed pinion) is degraded and is responsible for this noticeable change in the cepstrum.

Cxx t# $ ! I%1 2 ln A f# $# &' & (3)

Additional vibration features were extracted from the cepstrum at the corresponding shafts by using data from both thebaseline gearbox and the degraded gearbox. Example results from the cepstrum features are provided in Figure 4, in whichseveral peaks in the cepstrum are larger in magnitude when comparing the degraded gearbox to the baseline gearbox. Thecepstrum peak related to the high-speed pinion is clearly larger in magnitude for the degraded gearbox. This provides anadditional set of evidence that the high-speed pinion is damaged.

3.3. Spectral kurtosis filtering

For condition monitoring of mechanical systems, the vibration signals for damaged gear and bearing components typicallydisplay an impulsive signature; detecting that impulsive signature is not a trivial task since the signature could be maskedby other sources of vibration. Techniques and filtering methods based on spectral kurtosis are aimed at finding the optimalfrequency band for recovering that impulsive fault signature that could be hidden in the raw vibration waveform. A briefreview of the calculation procedure and the results for this study are provided. The interested reader is referred to the work

Figure 3. Real cepstrum—caseC: top plot, AN7 baseline; bottom plot, AN7 degraded gearbox.

Figure 4. Cepstrum peak features from caseC: blue, baseline; red, degraded gearbox.



by Antoni and Randall17 and Combet and Gelman19 for a more detailed discussion on the use of spectral kurtosis forfiltering vibration signals. The initial step in this algorithm is to calculate the short-time Fourier transform of the vibrationsignal, denoted by H(t,f). Equation (4) indicates that the average value of the fourth power of H(t,f) is divided by the meansquare value of H(t,f), which provides a kurtosis value as a function of frequency. The Wiener filter is constructed using thekurtosis values for each frequency bin as shown in (5); the frequency bin is only included if the kurtosis value is above astatistical threshold at a given confidence level.17 The Wiener filter is then multiplied by the frequency domain representa-tion of the original signal, X(f), and the result is transformed back to the time domain as indicated in (6). The advantage ofthis method is that the signal is filtered without any a priori knowledge of which frequency band to filter in, and instead it isbased on which frequency band is the most impulsive.

Kr f# $ !H4 t; f# $! "

H2 t; f# $h i2% 2 (4)

W f# $ !###########Kr f# $

pfor Kr f# $ > sa

0 Otherwise

$(5)

y t# $ ! I%1 W f# $X f# $% &

(6)

In this study, the filtering algorithm was used to process data for all 12 accelerometers using a block size of 256data samples and an overlap of 80% when performing the short-time Fourier transform calculation. When applying thisprocessing method, only high kurtosis values were observed for accelerometers AN3 and AN4, and thus the exampleresults do not include the other accelerometers. An example result from the filtering method is provided in Figure 5 fromaccelerometer AN4, in which one can observe that the Wiener filter is focused on the high-frequency content of the signalfrom approximately 8 to 18 kHz. This implies that although the rotational frequencies of the carrier are quite low, structuralresonances at a high frequency appear to be excited by defects and damage from the internal components within theplanetary gearbox. Figure 5 illustrates how the impulsive signature is masked in the raw time signal but is quite clear inthe filtered signal, the raw signal having a kurtosis value of only 3.39 compared with a kurtosis value of 169 for the filteredsignal. Further examination of the filtered signal shows a pattern that repeats every 2 revolutions of the carrier; this periodicpattern in the filtered signal from accelerometer AN4 is shown in Figure 6. The high kurtosis value of the filtered signal,the periodic pattern that is related to the carrier rotation and the location of the accelerometer would point to a problem withthe internal components in the planetary gearbox. However, it was quite difficult to determine which gear or bearingcomponent was the cause of this problem from the filtered signal and the envelope spectrum; a potential reason is thatmultiple faults occurred in the planetary gearbox. The failure report indicated that the ring gear and sun pinion had scuffingand corrosion damage, and the planet carrier upwind bearing had damage on the outer race.

The filtering results in Figures 5 and 6 are from an example data file from caseA. The same filtering method was alsoapplied to the remaining data files, and the kurtosis feature from the filtered signal was stored. The results of the filteredkurtosis value are shown in Figure 7 and provide an interesting point for discussion. The kurtosis values were very largefor files from caseA, with values above 50. It is also worth noting that the kurtosis values show a decreasing trend forthe data files in caseA, in which each file was collected in sequential order. For cases B andC, the kurtosis values are quitelow and in a normal range between 2 and 4. This implies that the fault signature was not present for the operating conditions

Figure 5. (a) Wiener filter based on spectral kurtosis; (b) raw and filtered AN4 accelerometer signal—caseA.



in cases B andC. This could imply that the operating conditions for caseA are more conducive for detecting this type ofproblem in the planetary gearbox. However, it is also worth noting that the data were collected in sequential order fromcaseA to case C; this could imply that the vibration signature became less impulsive with the running time of the gearbox.Despite these discussion points on potential reasons on 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 caseA onthe basis of the very high kurtosis values. This provided enough confidence and evidence to believe that the internalcomponents in the planetary gearbox stage were degraded.

3.4. Time synchronous averaging

This section discusses the results using time synchronous averaging for the parallel stage gears and the ring gear. Therationale for excluding the results for the planet and sun gears in this section is that a specific algorithm is needed forextracting the synchronous average signals for the individual planet and sun gears. The synchronous averaging

Figure 6. Filtered AN4 signal showing the periodic repetition based on 2 revolutions of the carrier—caseA.

Figure 7. Kurtosis of filtered signal—shown for all three cases.



algorithm and results for the plant and sun gears are provided in Section 3.5. The results from the residual signal,amplitude modulation signal and the phase modulation signal are extracted and analyzed to determine the healthcondition of each gear.

The additional processing methods for the residual signal (Section 3.4.1) and the amplitude and phase modulationsignals (Section 3.4.2) first require the extraction of the time synchronous average signal for each shaft. The time synchronousaveraging algorithm requires a reference pulse train for aligning the data with respect to a given shaft and ensemble averagingthe signal over several rotations. In this study, a tachometer signal was not provided, but an alternative method was used forextracting a reference signal. The provided speed signal had a clear tone at the generator shaft speed (20 or 30Hz); band-passfiltering in a range between 15 and 35Hz provided a way of extracting a pulse train from the speed signal. The filteredspeed signal was used as a surrogate for the tachometer signal; alternative methods that use the gear mesh frequency peakfor estimating a synthetic tachometer signal could also have been used.20 With the necessary reference signal, the vibrationsignals could be re-sampled in the angular domain and ensemble averaged with respect to each respective shaft by using theestablished synchronous averaging methods. More specific details on the synchronous averaging method including thedifferent interpolation methods and the frequency domain implementation can be found in the work of Bechhoefer andKingsley21; in this study, a time-domain interpolation method was used. For the provided vibration signals, accelerometerAN3 was used for calculating the time synchronous average signal for the carrier shaft, AN5 was used for the low-speedshaft, AN6 was used for the ISS and AN7 was used for the high-speed shaft.

3.4.1. Gear residual signal.The extraction of the periodic vibration waveform by using time synchronous averaging allows one to further analyze

the vibration signature and meshing pattern for each gear wheel. Departures of the regular meshing pattern could beindicative of a fault in the gear wheel. The residual signal aims to remove the regular meshing pattern from the synchronoussignal to further examine this aspect. The residual signal for a gear of interest can be calculated by removing the shaftharmonics and the gear mesh frequency and harmonics from the time synchronous average signal.14 Considering thatthe time synchronous average signal is aligned with the shaft of interest, the signal is periodic, and the filtering can beconveniently performed in the frequency domain and transformed back to the time domain. It is common to remove thefirst five shaft harmonics, and the gear mesh frequency and all of the gear mesh frequency harmonics when calculatingthe residual signal. Prior work from seeded fault studies has also shown the residual signal to be effective for detecting geartooth pitting faults.22

The time synchronous average signal and the residual signal are shown in Figure 8 for the high-speed pinion. Thekurtosis value of the residual signal for this gear is quite low (2.34), and there appears to be no abnormalities that canbe seen in the time-averaged signal or the residual signal. However, previous results from the cepstrum and frequencydomain methods indicated large sidebands and a significant problem with the high-speed pinion, which were confirmed bythe failure report. The inability for the residual signal to detect this fault on the high-speed pinion highlights the importanceof extracting multiple gear vibration features to have better coverage for the different failure modes.

Figure 8. Time synchronous average signal and residual signal from accelerometer AN7—caseC: top plot, TSA signal for HSS pinion;bottom plot, residual signal for HSS pinion.



Another example residual signal is shown for the ring gear in Figure 9. The kurtosis value of the ring gear is also in anormal range (3.36), and there appears to be no abnormal patterns or an indication of a fault in the time synchronousaverage signal or the residual signal for the ring gear. This is in sharp contrast to the results from the phase modulationfunction provided in the subsequent section, in which there is a clear indication of a damaged gear tooth for the ring gear.The residual signal for the other parallel shaft gears also provided no indication of damage. This highlights that the residualsignal was not the most appropriate algorithm for detecting the failure modes that were occurring on the parallel shaft gearsand the ring gear.

3.4.2. Amplitude and phase modulation signal.For detecting local defects such as a fatigue crack in a gear wheel, the prior work carried out by McFadden23 suggested

the analysis of the amplitude and phase modulation signals of the gear vibration. For performing this analysis, thesynchronous average signal for each shaft is extracted. A band-pass filter around a dominant gear mesh frequency is usedand typically includes a number of sidebands around the gear mesh frequency peak. The Hilbert transform is thenperformed on the filtered signal; the modulus and phase of the analytical signal provide the envelope and phase modulationsignals, respectively. The amplitude and phase modulation signals were calculated for each gear wheel in this study. Inaddition, the kurtosis of the amplitude modulation signal and the kurtosis of the derivative of the phase modulation signalwere also calculated in order to quantify the health condition of each gear. For the parallel shaft gears, the band-pass filterincluded four sidebands, whereas the band-pass filter for the ring gear included six sidebands. The accelerometer AN3 wasalso effectively downsampled to 200Hz prior to extracting the synchronous average for the ring gear. Sample results forthis method are provided in Figure 10, in which the amplitude and phase modulation signals are plotted for the high-speedpinion. As one can observe, there is significant jumps in the phase modulation signal for this gear and a high kurtosis valueat 12.8. This would be a strong indication of damage on the high-speed pinion. In addition, the amplitude modulation signalis close to zero when these significant changes in phase occur. The phase modulation signal for the high-speed gear had amoderate indication of a gear problem, with a kurtosis value of 5.2. However, there was no indication of a problem for theintermediate-speed gear or pinion. Another example is provided in Figure 11, in which the amplitude and phase modulationsignals for the ring gear are provided. There appears to be a clear indication of a problem with the ring gear by visualobservation of the amplitude and phase modulation signals. The phase modulation signal in particular has a high kurtosisvalue and two noticeable shifts in phase. In summary, the amplitude and phase modulation signals provided a strongindication of a problem for the ring gear and high-speed shaft pinion, and a moderate indication for the high-speed gear;however, there was no indication of a problem for the other gear wheels.

3.5. Planet separation algorithm

Considering the multiple mesh points that occur between the planet gears meshing with the ring gear and sun gear simul-taneously, it is necessary to use a specific algorithm for extracting the time synchronous average signal for the individualplanet and sun gears. The algorithm considered in this study follows the algorithm proposed by McFadden et al.15 There are

Figure 9. Time synchronous average signal and residual signal from accelerometer AN3—caseC: top plot, TSA signal for ring gear;bottom plot, residual signal for ring gear.



variations of this algorithm, including the method proposed by researchers at the Defence Science and TechnologyOrganisation24 as well as a version that uses multiple accelerometers on the planetary gearbox housing.25 A flow chartof the algorithm is provided in Figure 12 in order to highlight the algorithm processing steps. The initial step is to calculatethe time synchronous average signal with respect to the carrier rotation. The central idea in this method is to capture ameshing period of each tooth when the planet gear is very close to the fixed accelerometer on the gearbox housing. Toaccomplish this, it is necessary to know when the planet gear is passing by the fixed accelerometer. Considering theamplitude modulation effect from the increased vibration level as each planet passes the fixed accelerometer, thenarrowband envelope signal can be used for determining the planet passing instances. A window function is applied tothe synchronous average signal when each planet gear passes for a short period; the short period is typically one to three

Figure 11. Ring gear amplitude and phase modulation signal from accelerometer AN3—caseC: top plot, time synchronous average;middle plot, amplitude modulation signal; bottom plot, phase modulation signal.

Figure 10. High-speed pinion amplitude and phase modulation signal from accelerometer AN7—caseC: top plot, time synchronousaverage; middle plot, amplitude modulation signal; bottom plot, phase modulation signal.



gear mesh periods. On the basis of the number of teeth for each gear, a lookup table can be used to know which tooth wasmeshing during that captured time signal and stored in the proper location in the array. This capturing of the windowed datais repeated for each tooth and requires several rotations of the carrier. The number of rotations is equal to the reset time forthe planet or sun gear. This provides an assembled vibration signal for each gear tooth. This process is repeated until severalassembled signals can be constructed. Lastly, the constructed waveforms are ensemble averaged, and this completes theprocess for extracting the time synchronous average signal.

For implementing this method, accelerometer AN3 was initially downsampled to a 200Hz sampling rate. Considering thenumber of carrier rotations and time needed by this algorithm, five files from caseC were concatenated and combined prior toapplying the algorithm. A narrowband filter that included four sidebands around the gear mesh frequency was applied to thetime synchronous average signal for the carrier. The envelope signal of the filtered signal is provided in Figure 13, and onecan clearly observe noticeable peaks that are related to the planet passing the fixed accelerometer. The angular spacing ofthe peaks is approximately 120(, 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. A Tukey window was used to capturethe vibration for three mesh periods when the planet gear is close to the fixed accelerometer on the gearbox housing. Using theseparameters for the planet separation algorithm, we extracted the synchronous average signal for each planet gear and the sungear; the number of averages was 8 for the planet gears and 15 for the sun gear. The residual signals, and amplitude and phasemodulation signals were also calculated in order to further analyze the health condition of the gear wheels. For the amplitudeand phase modulation signals, a band-pass filter that included three sidebands was used.

Sample results from the synchronous averaging signal and the residual signal are provided in Figure 14 in which theresult is shown for one of the planet gears. In this example, the time synchronous average signal and the residual signalshow no abnormal behavior for the planet gear; the failure report found no defects on any of the planet gears. Theother two planet gears were also considered to be in a normal condition since similar results were observed in their timesynchronous average signal and residual signal.

The time synchronous average signal and residual signal analyses were also performed for the sun gear, with the resultsprovided in Figure 15. In this example, the residual signal provides a moderate indication of damage on the sun gear with akurtosis value of 5.36. The failure report confirms this result; there was scuffing and fretting corrosion on the sun pinion.

Figure 12. Flow chart for planet separation algorithm.



Additional narrowband amplitude modulation and phase modulation analyses were also performed on the time synchronousaverage signals for the planet gears and the sun gear. Although the residual signal provided an indication of damage on thesun gear, the amplitude and phase modulation signals did not provide any indication of a defect on the sun gear. In addition,the results for the three planet gears did not have any indication of damage from the amplitude and phase modulation analyses;this agrees with the failure report in which all three planet gears were reported to be in a defect-free condition.

3.6. Bearing envelope analysis

Although the area of bearing condition monitoring has been an area of research for quite some time with new algorithmsand methods proposed each year, the bearing envelope analysis method is still one of the more effective techniques forbearing condition monitoring.16 A more detailed description of bearing envelope analysis can be found in other priorwork,16,26 and a brief review is provided prior to discussing the results from this study. A flow chart that shows the keysteps in this algorithm are provided in Figure 16, in which the initial step is to apply a band-pass filter around an excitednatural frequency. After filtering the signal, the Hilbert transform is used to extract the envelope signal, which is furtheranalyzed in the frequency domain. For a bearing with damage on the rolling element or bearing races, the bearing faultfrequency peaks are usually much easier to distinguish in the envelope spectrum when compared with the frequency spectrum.

The selection of the band-pass filter center frequency and bandwidth is an important step and also a current area ofresearch.16 In this study, the filter parameters were selected by inspection of the frequency domain spectrum for the

Figure 14. Top, time synchronous average signal for planet 2; bottom, residual signal for planet 2—caseC.

Figure 13. Narrow band amplitude modulation signal for determining planet passing—caseC.



respective accelerometers and also by using the kurtogram method. By inspection of the frequency domain spectrum, aband-pass filter centered at 10,000Hz and a bandwidth of 1000Hz were used, with the exception of accelerometerAN10 in which a different frequency band was evaluated. The kurtogram method used the code available in the workof Antoni,27 in which the short-time Fourier transform and the classic kurtosis calculation were selected. An examplekurtogram is provided in Figure 17 for accelerometer AN7, although similar results from the kurtogram calculation werealso obtained for AN6. From these results, the kurtogram is suggesting a center frequency at 12,500Hz; a band-pass filterwith this center frequency and a bandwidth of 1000Hz were also evaluated in this study.

Figure 16. Bearing envelope analysis flow chart.

Figure 15. Top, time synchronous average signal for sun gear; bottom, residual signal for sun gear—caseC.



Sample results from the envelope analysis are provided in Figure 18, in which the envelope spectrum is shown foraccelerometers AN6 and AN7 by using a band-pass filter of 9500%10,500Hz. The envelope spectrum for AN6 showsnoticeable peaks at 73 and 345Hz. The peak at 73Hz corresponds to the ball pass frequency inner race (BPFI) for theintermediate shaft upwind bearing. The failure report confirms the inner race failure for this particular intermediate shaftbearing. The peak at 345Hz is very close to the calculated BPFI frequency (336Hz) for the high-speed shaft downwindbearing; the failure report confirms that this bearing had an inner race failure with overheating as the failure mode. Theenvelope spectrum for AN7 also clearly shows a peak at the BPFI frequency (345Hz) for the high-speed shaft downwindbearing. However, the envelope spectrum using the filter band suggested by the kurtogram (12,000–13,000Hz) provided aless clear detection of the bearing faults. The envelope spectrum results using the kurtogram suggested frequency band areprovided in Figure 19 for accelerometers AN6 and AN7. The BPFI peak (345Hz) for the high-speed shaft downwindbearing can be observed in the envelope spectrum for AN6 and AN7 in Figure 19. However, the BPFI for the intermediateshaft upwind bearing at 73Hz cannot be distinguished in the envelope spectrum by using the filter band suggested by thekurtogram.

The envelope spectrum for accelerometer AN10 in Figure 20 is provided using two different band-pass filter ranges; thefirst one is at a frequency range from 9500Hz to 10,500Hz, and the latter is from a frequency range of 4000–6000Hz. Theresults shown in Figure 20(a) clearly show a peak at 105Hz, which is the ball pass frequency outer race (BPFO), and itsfirst harmonic (210Hz) for the ISS downwind bearing. The failure report confirms that there was an outer race failureon this bearing. The envelope spectrum in Figure 20(b) shows a peak at the BPFO for the planet carrier upwind bearingat 8.8Hz; this bearing also had an outer race failure according to the failure report. Using a filter from 9500 to10,500Hz would have resulted in a missed detection for the planet carrier upwind bearing. Using the frequency band from

Figure 17. Kurtogram plot for accelerometer AN7 and damaged gearbox.

Figure 18. Envelope spectrum caseC using filter band of 9500–10,500Hz. (a) AN6—peaks at BPFI for ISS upwind bearing and HSSdownwind bearing. (b) AN7—BPFI peak for HSS downwind bearing.



4000 to 6000Hz resulted in a detection of an outer race fault on the planet carrier bearing. However, it provided a less cleardetection for the ISS downwind bearing, in which only the first harmonic of the BPFO could be identified. Althoughenvelope analysis is an effective method for condition monitoring of rolling element bearings, this study highlights thechallenge in selecting the appropriate band-pass filter for a complicated system comprising many gear, shaft and bearingcomponents. The suggested frequency band using the kurtogram did not provide the most suitable band for envelopeanalysis, but this could be due to the damage level of the bearings being quite severe.

4. SUMMARY OF RESULTS

For each data processing method, a qualitative metric was assigned to its ability to detect each failed components in thegearbox used in this study; the results of which are provided in Table VI. For each failed component and its detectionalgorithm, a ranking of three levels is assigned of low, medium and high confidence; the rankings are based on examining

Figure 19. Envelope spectrum caseC using filter band of 12,000–13,000Hz. (a) AN6—peaks at BPFI for HSS downwind bearing.(b) AN7—BPFI peak for HSS downwind bearing.

Figure 20. Envelope spectrum accelerometer AN10 caseC: (a) band-pass filter from 9500 to 10,500Hz, peaks at BPFO and 2X BPFOfor ISS downwind bearing; (b) band-pass filter from 4000 to 6000Hz, peak at BPFO for planet carrier upwind bearing and also peak at

2X BPFO for ISS downwind bearing.



the output plots and the calculated features. An example of a high confidence rating would be the amplitude and phasemodulation results for the high-speed pinion in which the output plots and large kurtosis values are clear indications ofdamage. In certain instances, an algorithm was not evaluated for detecting a failed component, or the algorithm is notdesigned or suited for that task. In this case, the label of NA (not applicable) was assigned. An example of a not applicableranking would be bearing envelope analysis for detecting damage on any of the gear wheels. The spectral kurtosis methodwas only applied to the planetary gearbox (signals AN3 and AN4) and could only provide an indication of degradation tothe 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 presented in italics if the method was applied prior to therelease of the failure report and in bold italics if the method was applied after the failure report was provided. Bearingenvelope analysis, time synchronous averaging and the planet separation algorithm were all performed after the failurereport was released.

From the results in Table VI, one can observe that the high-speed pinion had several indications of damage from multipletechniques, including the vibration spectrum, cepstrum processing and narrowband analysis from the phase modulationsignal. Only the residual signal did not provide an indication of a fault for the high-speed pinion. The residual signal ingeneral 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 pinion had a moderate indication of damage from both frequency domain analysis and the cepstrumfeatures; however, there was no indication provided by the narrowband phase and amplitude modulation analyses. Bearingenvelope analysis provided high confident indications for three of the bearing failures that were on the intermediate-speedand high-speed shafts. The bearing damage on the planet carrier upwind bearing was only a moderate detection since thepeak 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 phasemodulation signal. It should be noted that none of the planet gears had damage according to the failure report; this agreeswith the results in which none of the algorithms detected any abnormality or damage for the planet gears.

Although the summarized results in Table VI are encouraging, it is worth highlighting the challenges for implementingthese vibration-based algorithms for a wind turbine condition monitoring system. Wind turbine condition monitoring hasthree main challenges: the number of components and scale of the drive train, general challenges in monitoring planetarygearboxes and the variation in torque load and rotational speed. The aspect of a larger scale system presents challenges withregard to separating vibration sources, from the different shaft, gear and bearing components. This is an active researchtopic, and various processing methods exist for separating gear and shaft (discrete) and bearing vibration (random).28

The authors feel that although the scale of the system does present some challenges, there are available methods that havebeen evaluated for other larger drive trains such as the ones found in rotorcraft. Planetary gearboxes present unique chal-lenges because of the changing transmission path, multiple mesh points and moving location of the fault. There are specificsynchronous averaging methods for planetary gearboxes that are used in this study.

The aspect of the variation in torque and rotational speed probably represents the most difficult task, since the research is atan earlier stage. A recent study by Bechhoefer et al.29 applied a modified synchronous average method to account for the torqueripple and rotational speed fluctuations observed for an in-field wind turbine condition monitoring system. The improvedsynchronous averaging method appears to reduce the leakage and provide an appropriate method for monitoring gear and shaftcomponents for a wind turbine drive train. However, further work is needed to validate these results with more data sets. Inaddition, the interpretation of the calculated vibration indicators is more difficult if there is more load or speed fluctuation.Changes in load or speed would also affect the magnitude of the vibration indicators, and these effects would have to benormalized or separated from changes in the vibration indicators due to component degradation or damage.

Table VI. Summary of results for each algorithm.

Failed componentFrequencydomain Cepstrum Spectral kurtosis

Bearing envelopeanalysis

TSA—residualsignal

TSA—amplitude/phase modulation

HSS pinion H H NA NA L HHSS gear L L NA NA L MISS pinion M M NA NA L LISS gear L M NA NA L LRing gear NA NA H-stage NA L HSun pinion NA NA H-stage NA M LISS upwind bearing NA NA NA H NA NAISS downwind bearings NA NA NA H NA NAHSS downwind bearings NA NA NA H NA NAPlanet carrier upwind bearing NA NA NA M NA NA

L= low confidence, M=medium confidence, H=high confidence, NA=not applicable or evaluated. Data in italics indicate a methodthat was evaluated before the failure report; data in bold italics indicate a method that was evaluated after the failure report.



5. CONCLUSIONS AND FUTURE WORK

The results show that most of the failed components could be detected by one or more of the processing methods; this is anencouraging result and highlights that vibration-based condition monitoring can be used to assess and diagnose whichcomponents 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. The residual signal in particular did not seem suited for the failuremodes exhibited by the damage gear wheels on the parallel stage shaft, whereas the cepstrum and narrowband analysisprovided more confident detections. Bearing envelope analysis was an effective method for diagnosing the bearing failures,with the most challenging aspect being the appropriate selection of the band-pass filter center frequency and bandwidth.

Although the results from this study were encouraging, there are some aspects that could have aided the study or shouldbe considered for future work. This study could have aided from time-domain waveforms instead of frequency spectrumsbeing provided for the baseline data. Many of the more advanced algorithms require the raw time waveform, and they couldnot be evaluated on the baseline data set. Considering that the gearbox was already in a degraded state, the algorithms wereevaluated on the basis of their ability to detect the health condition of various bearing and gear components. Unfortunately,this does not allow one to evaluate the algorithm’s ability to provide an early detection of a problem or whetherthe extracted vibration features are monotonic with the damage level. Both early detection and severity estimation areadditional aspects worth evaluating for vibration-based condition monitoring techniques for wind turbine drive trainsand are being considered for future work.

ACKNOWLEDGEMENTS

The authors would like to acknowledge Dr. Shawn Sheng and his colleagues at the National Renewable EnergyLaboratory for their organization of the Gearbox Reliability Collaborative Round Robin and consistent support throughoutthe analysis process. The authors would like to also acknowledge the National Science Foundation for its support of researchat Industry/University Cooperative Research Center on Intelligent Maintenance Systems (IMS) at the University of Cincinnatias well as its company members for collaborative industry projects that have been an important foundation for this study.

REFERENCES

1. NREL. In: U.S. D.o.E. (DOE), editor. Wind power today 2010. United States Department of Energy (DOE); 2010.2. Hameed Z, Hong YS, Cho YM, Ahn SH, Song CK. Condition monitoring of wind turbines and related algorithms: a

review. Renewable and Sustainable Energy Reviews 2009; 13: 1–39. DOI: 10.1016/j.rser.2007.05.0083. Hatch C. Improved wind turbine condition monitoring using acceleration enveloping. Orbit 2004; 58–61.4. Lu B, Li Y, Wu X, Yang Z. A review of recent advances in wind turbine condition monitoring and fault diagnosis.

Proceedings of IEEE Conference on Power Electronics and Machines in Wind Application, 2009. DOI: 10.1109/PEMWA.2009.5208325

5. Villa LF, Renones A, Peran JR, de Miguel LJ. Statistical fault diagnosis based on vibration analysis for gear test-benchunder non-stationary conditions of speed and load. Mechanical Systems and Signal Processing 2011; DOI: 10.1016/j.ymssp.2011.12.013

6. Lu Y, Tang J, Luo H. Wind turbine gearbox fault detection using multiple sensors with features level data fusion.Journal of Engineering for Gas Turbines and Power 2012; 134: 1–8. DOI: 10.1115/1.4004438

7. Lei Y, Lin J, He Z, Kong D. A method based on multi-sensor data fusion for fault detection of planetary gearboxes.Sensors 2012; 12: 2005–2017. DOI: 10.3390/s120202005

8. Barszcz T, Randall RB. Application of spectral kurtosis for detection of a tooth crack in the planetary gear of a windturbine. Mechanical Systems and Signal Processing 2009; 23: 1352–1365. DOI: 10.1016/j.ymssp.2008.07.019

9. Sheng S, Veers P. Wind turbine drivetrain condition monitoring—an overview. Proceedings of the MechanicalFailures Prevention Group: Applied Systems Health Management Conference 2011; 1–19.

10. Sheng S, Link L, LaCava W, van Dam J, Mcniff B, Veers P, Keller J, Butterfield S, Oyague F. Wind turbine drivetraincondition monitoring during GRC Phase 1 and Phase 2 testing. NREL/TP-5000-52748. Golden, CO: NationalRenewable Energy Laboratory, October, 2011. http://www.nrel.gov/docs/fy12osti/52748.pdf

11. Errichello R, Muller J. Gearbox reliability collaborative gearbox 1 failure analysis report. NREL/SR-5000-530262.Work performed by Geartech, Townsend, Montana. Golden, CO: National Renewable Energy Laboratory, February2012. http://www.nrel.gov/docs/fy12osti/53062.pdf



12. Mark WD, Lee H, Patrick R, Coker JD. A simple frequency-domain algorithm for early detection of damage gear teeth.Mechanical Systems and Signal Processing 2010; 24: 2807–2823. DOI: 10.1016/j.ymssp.2010.04.004

13. Randall RB. Vibration-based Condition Monitoring: Industrial, Aerospace and Automotive Applications. John Wileyand Sons Ltd: West Sussex, United Kingdom, 2011.

14. Lebold M, McClintic K, Campbell R, Byington C, Maynard K. Review of vibration analysis methods for gearboxdiagnostics and prognostics. Proceedings of the 54th Meeting of the Society for Machinery Failure PreventionTechnology, 2000.

15. McFadden PD. Window functions for the calculation of the time domain averages of the vibration of the individualplanet gears and sun gear in an epicyclic gearbox. ASME Transactions Journal of Vibration and Acoustics 1994;116: 179–187. DOI: 10.1115/1.2930410

16. Randall RB, Antoni J. Rolling element bearing diagnostics—a tutorial. Mechanical Systems and Signal Processing2011; 25: 485–520. DOI: 10.1016/j.ymssp.2010.07.017

17. Antoni J, Randall RB. The spectral kurtosis: application to the vibration surveillance and diagnostics of rotatingmachines. Mechanical Systems and Signal Processing 2006; 20: 308–331. DOI: 10.1016/j.ymssp.2004.09.002

18. Combet F, Gelman L. Novel adaptation of the demodulation technology for gear damage detection to the variableamplitude of mesh harmonics. Mechanical Systems and Signal Processing 2011; 25: 839–845. DOI: 10.1016/j.mssp.2010.07.008

19. Combet F, Gelman L. Optimal filtering of gear signals for early damage detection based on the spectral kurtosis.Mechanical Systems and Signal processing 2009; 23: 652–668. DOI: 10.1016/j.ymssp.2008.08.002

20. Bonnardot F, El Badaoui M, Randall RB, Daniere J, Guillet F. Use of the acceleration signal of a gearbox in order toperform angular resampling (with limited speed fluctuation). Mechanical Systems and Signal Processing 2005; 19:766–785. DOI: 10.1016/j.ymssp.2004.05.001

21. Bechhoefer E, Kingsley M. A review of time synchronous average algorithms. Annual Conference of the Prognosticsand Health Management Society, 2009.

22. Dempsey PJ. A comparison of vibration and oil debris gear damage detection methods applied to pitting damage.NASA TM-210371, 2000.

23. McFadden PD. Detecting fatigue cracks in gears by amplitude and phase modulation of the meshing vibration. ASMEJournal of Vibration, Acoustics, Stress, and Reliability in Design 1986; 108: 165–170.

24. Forrester D. A method for the separation of epicyclic planet gear vibration signatures. Proceedings of the Acousticaland Vibratory Surveillance Methods and Diagnostic Techniques, 1998.

25. Samuel PD, Conroy JK, Pines DJ. Planetary transmission diagnostics. NASA/CR 213068, 2004.26. McFadden PD, Smith JD. Vibration monitoring of rolling element bearings by the high-frequency resonance

technique—a review. Tribology International 1984; 17: 3–10. DOI: 10.1016/0301-679X(84) 90076–827. Antoni J. Kurtosis-based tools. Available: http://www.utc.fr/~antoni. (Accessed 27 September 2012).28. Randall RB, Sawalhi N, Coats M. A comparison of methods for separation of deterministic and random signals.

International Journal of Condition Monitoring 2011; 1: 11–19 DOI: 10.1784/20476421179808904829. Bechhoefer E, Wadham-Gagnon M, Jacobs L, Boucher B, Morton B. Improved TSA technique to correct main rotor

RPM variation due to wind shear. DOE/NREL Gearbox Reliability Collaborative All Members Meeting, Golden CO,USA, 2012 http://www.nrel.gov/wind/grc/pdfs/1-5-3_bechoefer_grc_thm_tsa.pdf



a comparative study on vibration-based condition monitoring algorithms for wind turbine drive trains

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