probabilistic latent component analysis for gearbox...

Annual Conference of the Prognostics and Health Management Society, 2010

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Probabilistic Latent Component Analysis forGearbox Vibration Source Separation

Joshua Isom, Madhusudana Shashanka,Ashutosh Tewari, and Aleksandar Lazarevic

United Technologies Research Center, East Hartford, CT, 06108, USA{isomjd, shasham, tewaria, lazarea} @utrc.utc.com

ABSTRACT

Probabilistic latent component analysis (PLCA) isapplied to the problem of gearbox vibration sourceseparation. A model for the probability distribution ofgearbox vibration employs a latent variable intended tocorrespond to a particular vibration source, with themeasured vibration at a particular sensor for eachsource the product of a marginal distribution ofvibration by frequency, a marginal distribution ofvibration by shaft rotation, and a sensor weightdistribution. An expectation-maximization algorithm isused to approximate a maximum-likelihoodparameterization for the model. In contrast to otherunsupervised source-separation methods, PLCA allowsfor separation of vibration sources when there are fewervibration sensors than vibration sources. Once thevibration components of a healthy gearbox have beenidentified, the vibration characteristics of damagedgearbox elements can be determined. The efficacy ofthe technique is demonstrated with an application on agearbox vibration data set.*

1. INTRODUCTION

In a wide variety of mechanical systems, gearboxestransfer power from a rotating power source to otherdevices and provide speed and torque conversions.Complex gearbox designs are used in order tomaximize efficiency, minimize volume, andaccommodate automatic transmission designs. Anexample of a particularly complex gearbox design isthe main gearbox in a turboshaft-engine helicopter.This gearbox may have several dozen gears, as manybearings, and five or more shafts rotating at differentspeeds.

* This is an open-access article distributed under the terms ofthe Creative Commons Attribution 3.0 United States License,which permits unrestricted use, distribution, and reproductionin any medium, provided the original author and source arecredited.

A single-point failure in a gearbox often disables themechanical system, creating a need for gearbox healthmonitoring using vibration measurements. Vibrationscannot usually be measured directly at the source, sothe exterior of a gearbox may be equipped with one ormore accelerometers to measure the compositevibration spectrum of the gearbox. Generally, thenumber of accelerometers is less than the number ofvibration sources on non-experimental machinery.

The capability to separate a measured vibration signalinto components corresponding to sources allows forthe characterization of the vibration of a healthygearbox and for the development of conditionindicators that are sensitive to component degradationbut robust to the normal vibration characteristics of thehealthy gearbox.

The development of a new technique for vibrationsource separation is motivated by the fact that existingtechniques for gearbox vibration source separation haveimportant limitations. Consider five characteristicsthat are desirable features for a gearbox vibrationsource separation technique: 1) a source separationmethod should be applicable to cases where there arefewer accelerometers than vibration sources, 2) itshould identify the vibration resonance spectrumcharacteristic of various structural elements in thegearbox, 3) it should allow for the separation of thevibration features of damaged gearbox componentsfrom features characteristic of undamaged gearboxcomponents, 4) it should characterize the physicalproximity of the vibration source to each of the gearboxaccelerometers, and 5) it should identify the periodicityof a vibration features. By identifying the resonancespectrum, the physical proximity, and periodicity of avibration source, the determination of the physicalsource is facilitated.

In this work, we apply a technique called ProbabilisticLatent Component Analysis (PLCA) to the problem of


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gearbox vibration source separation. The proposedtechnique satisfies the five criteria established above.The technique applies to instances where there arefewer sensors than vibration sources. The PLCAtechnique explicitly estimates the frequency spectra androtational location characteristics associated withestimated vibration sources. This is not true of the timesynchronous average or principal component analysistechniques for vibration source separation.

The paper is organized as follows. Section 2 is asurvey of prior work on gearbox vibration sourceseparation. Section 3 describes a model and analgorithm for gearbox vibration source separation usingPLCA. Section 4 describes the application of themethod to a gearbox data set. Section 5 describeslimitations and extensions of PLCA for gearboxvibration source separation.

2. PRIOR WORK ON GEARBOX VIBRATIONSOURCE SEPARATION

Vibration-based methods are the most commondiagnostic techniques used in gearbox healthmonitoring for distinguishing the nature of damage inhelicopter transmissions. The potential benefits ofeffective gearbox monitoring have motivated thedevelopment of source separation techniques andapplication to the gearbox domain.

A key feature of gearbox vibration source separationexploited by most techniques is the fact that gearboxvibration typically has one or more cyclostationarycomponents. A basic source separation techniquelong employed for gearbox health monitoring is thetime synchronous average. The time synchronousaveraging extracts periodic waveforms from additivenoise by averaging vibration signals over severalrevolutions of the shaft (Stewart, 1977). This can bedone in either the time or frequency domains. The timesynchronous average technique amplifies vibrationfeatures that are synchronous with a particular shaft,and attenuates features that are not synchronous withthe shaft. The technique has proved to be useful formonitoring of gear and shaft health. However, a timesynchronous average cannot isolate a vibrationcomponent among the various components on aparticular shaft. Also, the time synchronous averageobscures vibration characteristic of bearing degradationthat are not cyclostationary.

Specialized techniques for the separation of bearingvibration from other gearbox vibration sources areavailable. The methods include the high-frequencyresonance technique and adaptive filtering. The

techniques are not applicable to the more generalproblem of unsupervised vibration source separation.

Independent component analysis has been applied toseparate signals from two independent vibrationsources recorded at two separate locations on a gearbox(Zhong-sheng et al., 2004). The utility of thistechnique is limited to cases where the number ofsensors is equal to or greater than the number ofvibration sources, a condition that does not generallyhold.

Principal component analysis has also been used toidentify the number of gearbox vibration sources (Gelleet al., 2003, Serviere et al., 2004). The utility of thisdimensionality-reduction technique is limited by thefact that the reduced-dimension vibration features maynot have physical significance and thus may not beused to create a mapping between features and physicalvibration sources.

3. LATENT COMPONENT MODEL

Latent component models enable one to attribute theobservations as being due to hidden or latent factors.The main characteristic of these models is conditionalindependence multivariate data are modeled asbelonging to latent classes such that the randomvariables within a latent class are independent of oneanother. Several models have been proposed that fit thisgeneral framework and in this paper, we useProbabilistic Latent Component Analysis (PLCA) asproposed by (Smaragdis et al., 2007).

The model has been used in analyzing image and audiodata among other applications (eg: Smaragdis et al.,2007b). Specifically, it has been successfully used inseparating audio signals (Smaragdis et al., 2006) whichis analogous to the problem addressed in this paper.

3.1 PLCA for gearbox data

The model employed here is probabilistic; the objectiveis to develop a structured representation for anempirically developed probability mass function() characterizing the probability distribution forvibration amplitude quanta as a function of vibrationfrequency , gearbox rotational coordinate, andsensor identity .

In a gearbox with a single shaft, the rotationalcoordinate corresponds to the rotationalangle of the single shaft. In a gearbox with multipleshafts, the coordinate ] can correspond to therotational position of the slowest shaft, and themaximum value should be chosen such as the


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smallest value such that every shaft in thegearbox is at the same position at and .

The first key aspect of the latent component model isthe introduction of the dependence of the vibrationdistribution on a latent component taking a finitenumber of values, small relative to the number of binsfor and

() () = () . (1)

It is further assumed that, given a certain latentvibration , the distribution of vibration as a function offrequency is independent of the shaft rotationalcoordinate and the sensor:

() = (|)() (2)= )() (|)(|)(| ,

with ( (| the marginal distribution for vibrationover the frequency domain and (|) the marginaldistribution for vibration over the rotational coordinate.(|) is a marginal distribution for vibrationcomponent by sensor, in effect a mixing weight todescribe how each vibration component is representedin each sensor measurement.

The intent of the latent component model is that eachvalue of corresponds to a different vibration source,and that the frequency spectrum (|) for that sourceis independent of the rotational coordinate and thesensor at which the vibration is measured.

To illustrate the intent of this model, consider how itwould apply to the characterization of the vibration of amusic box. A typical music box has a set of pinsarranged on a rotating cylinder that pluck the tunedteeth of a steel comb. The tune repeats with a periodcorresponding to one rotation of the cylinder. Whenapplying the PLCA methodology to a music box, thenumber of latent components should be set equal to thenumber of teeth on the steel comb; the frequencymarginal for a given component would correspond tothe tone of a particular plucked tooth; and the rotationalmarginal for the component would correspond to thelocation on the cylinder of the pins aligned to pluck theparticular tooth.

3.2 Data Pre-processing

To develop parameterizations for the latent variablemodels, the starting point is to develop the empiricaldistribution for .() One method for developingthe distribution () is to apply the Hilbert-Huangtransform to time-domain accelerometer data. The firststep is to adaptively decompose the signal into a finite

set of empirical mode functions, and then apply theHilbert transform to compute the instantaneousamplitude and frequency for each intrinsic modefunction. The amplitude, frequency, and time data isbinned to create a probability mass function() in the time domain. The Hilbert-Huangtransform may permit better localization of time andfrequency features than alternative techniques such asthe short-time Fourier transform (Huang, et. al. 1998).

Once () has been parameterized, it is convertedto a distribution by() using a tachometer signalto compute a one-to many mapping from time to therotational coordinate . Note that thisprocedure for calculating the empirical distribution() is not the same as calculating the timesynchronous average. Whereas the time synchronousaverage is the mean vibration signal over multiplerotations, () is a probability mass function fullycharacterizing the distribution of vibration amplitude asobserved over multiple rotations.

3.3 Algorithm

Given the empirical distribution(), anexpectation-maximization algorithm can be used toestimate the maximum-likelihood parameterization forthe probabilistic latent component model () = (|)(|)(|)() .

Expectation-maximization is an iterative procedurewidely used in a variety of contexts (Dempster et al.,1977, Neal et al., 1998). For example, an expectation-maximization algorithm for parameterization of HiddenMarkov models is known as the Baum-Welchalgorithm.

Each iteration of the expectation-maximizationalgorithm has two phases. The expectation phasecalculates the probability of a latent componentconditioned on frequency, rotation, and sensor, and thecurrent parameterization for the marginal distributions:

(|) =(|)(|)(|)()

)() (|)(|. (3)

For the first iteration, the marginal distributions can beinitialized with randomly generated probability massfunctions.

The maximization phase updates the marginaldistributions and the total probability of each latentcomponent based on the result of the expectation phase:

( (| = () (|)

() (|), (4)


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(|) = () (|)

() (|),

(|) = () (|)

() (|),

() = () ) )

() ) ).

Expectation-maximization produces monotoneconvergence to a locally optimal solution, and theconvergence towards a fixed point can be monitored bycalculating the log-likelihood associated with theparameterization for each iteration.

3.4 Characterizing healthy and damaged gearboxes

A gearbox with one or more damaged componentsoperated at the same condition as a healthy gearbox,identical with the exception of the damagedcomponents, should have the vibration components ofthe healthy gearbox plus some additional vibrationcomponents corresponding to the damaged. Principallatent component analysis can be used to identify thevibration components associated with damaged gearboxelements. To do so, the set of latent variables isdefined as the union of a set of latent variables corresponding to vibration components of healthygearbox elements with another set of latent variableswith corresponding to vibration components ofdamaged gearbox elements, .

The frequency marginal distribution (|) isinitialized to that learned for the healthy case for all . The expectation phase of the algorithm isunchanged. The maximization phase is modified so thatthe frequency marginals are iteratively updated only for , while the marginals for rotation and sensors areupdated for all latent components:

( (| = () (|)

() (|) ;

(5)

(|) = () (|)

() (|)

(|) = () (|)

() (|)

() = () ) )

() ) )

3.5 Implementation Notes

Let denote the number of latent variables selected.Let the number of bins along be respectively. Let ( (| (|) (|) and () berepresented by multi-dimensional tensors , , and respectively.

Let the tensor denote the preprocesseddata where the entries correspond to the empiricaldistribution .() Let the tensor denote the approximation of this distribution given by (|)(|)(|)() . Let the operators .*and ./ represent elementwise multiplication andelementwise division respectively.

The algorithm can be summarized as follows using thematrix multiprod notation (de Leva, P., 2005) andMATLAB conventions. Below, mprod refers to themultiprod function of de Leva that allows matrixmultiplications between arrays of matrices.

Initialize , and .Iterate until convergence

repmat(,[m 1 1 1]); repmat(1], n 1 1]);1],)repmat 1 l 1]); mprod( mprod( , ,( ,*. 4, 4);

nW=( ).*mprod(,mprod(3,3,(2,2,,/.);nT=().*mprod( ,mprod(1,1,(3,3,,/.);nS=().*mprod(,mprod(,/. ,1,1),2,2);nZ=sum(nW);

W=nW; T=nT; S=nS; Z=nZ;Normalize , and appropriately.

Effective application of the PLCA model requires theselection of a proper number of latent variables. Agood starting point is to set the number of latentvariables equal to the number of locations wheremoving surfaces come in contact. Once algorithmresults have been produced, the results can be examinedto validate the initial choice.

Evidence that there are too few latent componentsinclude the absence of any rotational marginals that arestrongly periodic, and frequency marginals that includemultiple peaks not in a harmonic sequence. Evidenceof the use of too many latent variables is two or morelatent components with strongly similar rotationalmarginal distributions.


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4. EXPERIMENTS AND RESULTS

4.1 Data

The use of probabilistic latent component analysis forgearbox vibration source separation is illustrated ongearbox data from the 2009 PHM challenge(http://www.phmsociety.org/competition/PHM/09).The gearbox has three shafts, an input shaft, an idlershaft, and an output shaft, each with an input side andoutput side bearing, and a total of six gears, one on theinput shaft, two on the idler shaft, and one on the outputshaft. The frequency ratio of the input, idler, andoutput shafts is 15:5:3. The helical gear configuration,illustrated in Figure 1, was tested under six differenthealth configurations, as indicated in Table 1.

Table 1: Component health by case24-toothgear

Inputshaftoutputsidebearing

Idlershaftoutputsidebearing

Inputshaft

Case 1 Good Good Good Good

Case 2 Chipped Good Good Good

Case 3 Broken Defect Inner Bent

Case 4 Good Defect Ball Imbalance

Case 5 Broken Good Inner Good

Case 6 Good Good Good Bent

4.2 Experimental set-up

The PLCA algorithm was applied to the helical gearhigh torque cases run at an input shaft frequency of 30Hz. To apply the PLCA algorithm, empirical modedecomposition was performed on each accelerometersignal. The Hilbert transform was applied to eachintrinsic mode function to generate a probability massfunction .() Tachometer data was used togenerate a many-to-one mapping from to togenerate a mapping .() The rotationalcoordinate was defined as the rotational angle at theoutput shaft, with the domain covering threerotations. Three rotations of the output shaftcorresponds to an integer number of rotations for theidler shaft (5 rotations) and for the input shaft (15rotations), and thus vibration features for all three shaftshould be cyclostationary over the interval [].

For the healthy gearbox, case 1, PLCA was used toidentify 7 vibration components. Once the frequencymarginal distributions for the healthy gearbox had beenidentified, the PLCA model was applied to each of the

five damaged gearbox cases in order to identify thevibration components associated with the damage. Foreach of the five damaged cases, the seven frequencymarginals for the healthy gearbox were retained andthree additional vibration components were identified.The frequency marginals for these seven vibrationcomponents were fixed and used as inputs to identifynew rotational marginals and three additional vibrationcomponents for cases 2-6.

4.3 Results and Interpretation

As described and illustrated below, the sourceseparation results produced by PLCA are plausible andprovide insight on the vibration characteristicsassociated with the gearbox and its degradation modes.The results of the PLCA algorithm for each of the sixgearbox conditions are displayed in Figures 2-7.

A number of characteristics of the separated vibrationcomponents may be used in interpreting the componentand making an assignment of a vibration component toa particular physical source in the gearbox.

The first characteristic that is useful for resultinterpretation is the sensor mixing weights. If themixing weight of a component is much stronger forsensor 1 than for sensor 2, then the physical source ofthe vibration is likely to be on the input side of thegearbox. Conversely, if the mixing weight of avibration component is stronger for sensor 2 than forsensor 1, then the physical source of the vibration islikely to be on the output side of the gearbox.

The second characteristic that is useful for resultinterpretation is the appearance of known forcing orresonant frequencies in a frequency marginal. For thegearbox analyzed in this study, known forcingfrequencies include the frequency of the input shaftrotation (30 Hz), the gear mesh frequency of theinput/idler gear pair (480 Hz), and the gear meshfrequency of the idler/output gear pair (240 Hz).Resonant frequencies in this case were not known apriori.

The third characteristic that is useful for resultinterpretation is the nature of the rotational marginal.The appearance of the marginal may be impulsive,sinusoidal, or nearly constant. Impulsive rotationalmarginals are likely to be due to the impacts associatedwith bearing or gear defects. Nearly constant rotationalmarginals are likely to be associated with constantforcing, such as the rotation of a shaft.

The fourth characteristic that is useful for resultinterpretation is the periodicity of the rotational

Annual Conference of the

marginal. If the periodicity of a rotational marginalcoincides with the periodicity of a particular shaft, thenthe vibration source is likely to be associated with thatshaft.

Figure 1: Configuration of the gearbox used to generate vibration data

Table 2: Characteristics of vibration components and source assignments for the no# Peak

Frequency,Hz

StrongestSensorMixingWeight

Content atforcing

frequencies

1 230Hz

480Hz

1 212 X

2 2089 X

3 985 X X

4 347 X

5 271 X

6 171 X X

7 8710 X

*The electronic version of this document has embeddedseparated vibration components.

ce of the Prognostics and Health Management Society, 2010

of a rotational marginalcoincides with the periodicity of a particular shaft, thenthe vibration source is likely to be associated with that

The four characteristics discussed above were used tointerpret the source separation results and make soassignments, as shown in Table 1 and Table 2.

Configuration of the gearbox used to generate vibration data

Characteristics of vibration components and source assignments for the nominal gearbox conditionContent at

frequencies

Highfrequencyresonance

Frequency marginal characteristic Periodicity ofrotationalmarginal,

periods perrotational

period

240Hz

Impulsive Sinusoidal Sustained 15

X

X X

X

X

X X

X X X

*The electronic version of this document has embedded sound files which are audio reconstructions of the source

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The four characteristics discussed above were used tointerpret the source separation results and make source

in Table 1 and Table 2.

minal gearbox condition*Periodicity of

rotationalmarginal,


period

SourceAssignment

5 3

Idler/outputgear mesh

X Idler shaftinput sidebearing

X Input/idlergear mesh

Idler/outputgear mesh

Idler/outputgear meshInput shaft

inducedresonanceInput shaftoutput side

bearing

sound files which are audio reconstructions of the source-


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Table 3: Characteristics of vibration components and source assignments for seeded fault conditions*# Peak

Frequency,Hz

StrongestSensorMixingWeight

Content atforcing

frequencies

Highfrequencyresonance

Frequency marginal characteristic Periodicity ofrotationalmarginal,


period

SourceAssignment

1 230Hz

480Hz

240Hz

Impulsive Sinusoidal Sustained 15 5 3

Case 2: Chipped 24-tooth gear

8 845 X X X Input/idlergear mesh

9 255 X X Chipped 24-tooth gear

10 369 X Chipped 24-tooth gear

Case 3: Broken 24-tooth gear, input shaft output side bearing defect, idler shaft output side bearing inner race damage, bent input shaft

8 985 X X X Input shaftoutputbearing

9 233 X X Broken 24-tooth gear

10 341 X X X Idler shaftoutputbearing

Case 4: defect in input shaft output side bearing, ball fault in idler shaft output side bearing, imbalanced input shaft

8 331 X X Imbalancedinput shaft

9 437 X X Input / idlergear mesh

10 240 X X Idler shaftoutput side

bearingCase 5: broken 24-tooth gear, inner race defect on idler shaft output bearing

8 31 X X Input shaft

9 244 X X Broken 24-tooth gear

10 8844 X X Idler shaftoutputbearing

Case 6: bent input shaft

8 8844 X X X Input shaftoutput side

bearing9 222 X X Idler/output

gear mesh10 3067 X Unknown

*The electronic version of this document has embedded sound files which are audio reconstructions of the source-separated vibration components.


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Figure 2: Source separation results for the baseline gearbox condition


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Figure 3: Source separation results for case 2, which has a chipped gear tooth on the 24-tooth gear on the idler shaft


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Figure 4: Source separation results for case 3, which has a broken gear tooth on the 24-tooth gear on the idler shaft,a bent input shaft, and bearing faults on the output side of the input and idler shafts


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Figure 5: Source separation results for case 4, which has an imbalanced input shaft and bearing faults on the outputside of the input and idler shafts


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Figure 6: Source separation results for case 5, which has a broken 24-tooth gear and an inner-race defect on the idlershaft output side bearing


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Figure 7: Source separation results for the cyclostationary spectra for case 6, which includes a bent input shaft


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5. LIMITATIONS AND EXTENSIONS

The PLCA method has been illustrated as a techniquefor source separation of the cyclostationary componentof gearbox vibration, but could be extended for analysisof the non-stationary vibration components. This maybe useful for additional characterization of bearingdefects which are not cyclostationary. There are leasttwo possible methods for integrating cyclostationaryspectrum analysis with time-spectrum analysis. Thefirst method is to identify vibration componentsassociated with cyclostationary spectrum, fix thefrequency marginals of these components and use theseas inputs for analysis of the time spectrum, and identifyadditional vibration components unique to the timespectrum. A second potential method is to 1) use thefrequency marginals of cyclostationary vibrationcomponents to attempt to reconstruct the timespectrum, 2) subtract the reconstructed time spectrumfrom the original time spectrum, and 3) apply PLCA tothe residual time spectrum to identify new vibrationcomponents.

The model employed here for the mixing of vibrationcomponents in a sensor signal is simple, and morecomplicated models could be employed for betterfidelity at the cost of increased complexity. Forexample, one could formulate a convolutive mixingmodel that allows for delays in the propagation ofvibration from source to sensor.

Finally, although the experimental results presentedhere make plausible the efficacy of PLCA as atechnique for vibration source separation, furthervalidation of the technique could be obtainedexperimentally using laser Doppler vibrometery tomeasure gearbox component vibrations at the source.

6. CONCLUSIONS

Probabilistic latent component analysis has beendeveloped as a technique for gearbox vibration sourceseparation. Unlike independent component analysis,the method is applicable when there are fewer sensorsthan vibration sources. The method identifies thefrequency spectrum and rotational marginal distributionassociated with vibration components. Experimentalresults make plausible the effectiveness of the sourceseparation performance, and it was shown that thetechnique could be used to identify the characteristicsof a healthy gearbox, and then used to isolate vibrationcomponents associated with gearbox damage.

NOMENCLATURE

Probability

Sensor Probability distribution for vibration

amplitude Latent variable Period for cyclostationary vibration component Rotational coordinate Frequency

REFERENCES

Dempster, A.P., Laird, N.M., Rubin, D.B. (1977).Maximum Likelihood from incomplete data via theEM algorithm, Journal of the Royal StatisticalSociety B, vol. 39, pp 1-38.

G. Gelle, M. Colas, C. Serviere (2003). Blind sourceseparation: a new pre-processing tool for rotatingmachines monitoring. IEEE Transactions onInstrumentation and Measurement, vol. 52, pp. 790-795.

Huang, N.E., Shen, Z., Long, Sr., Wu, M.C., Shih, H.H,Zheng, Q., Yen, N.C., Tung, C.C., & Liu, H.H.(1998). The empirical mode decomposition and theHilbert spectrum for nonlinear and non-stationarytime series analysis. Proceedings of the RoyalSociety of London, vol. 454, pp. 903-995.

de Leva, P (2005). Multiple matrix multiplications,with array expansion enabled, MATLAB CentralFile Exchange. Retrieved Aug 2010.

Neal, R. & Hinton, G.E. (1998). A View of EMalgorithm that justifies incremental, sparse, andother variants, Learning in Graphical Models, pp355-368.

Serviere, C. & Fabry, P. (2004). Blind sourceseparation of noisy harmonic signals for rotatingmachine diagnosis. Journal of Sound andVibration, vol. 272, pp. 317-339.

Smaragdis, P. & Raj, B. (2007). Shift-InvariantProbabilistic Latent Component Analysis.Mitsubishi Ele. Res. Labs. Technical ReportTR2007-009, 2007.

Smaragdis, P., Raj, B., & M. Shashanka (2007).Supervised and semi-supervised separation ofsounds from single-channel mixtures, inProceedings of the 7th International Conference onIndependent Component Analysis and Blind SignalSeparation (ICA 07), pp. 414421, London, UK.

Smaragdis, P., Raj, B., & Shashanka, M. (2006). Aprobabilistic latent variable model for acousticmodeling, in Proceedings of the Advances inModels for Acoustic Processing Workshop (NIPS06),Whistler, BC, Canada.

Stewart, R.M. (1977). Some Useful Data AnalysisTechniques for Gearbox Diagnostics. MachineHealth Monitoring Group, Institute of Sound and


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Vibration Research, University of Southhampton,Report MHM/R/10/77.

Zhong-shen, C. Yong-min, Y. & Guo-ji, S. (2004).Application of independent component analysis toearly diagnosis of helicopter gearboxes. MechanicalScience and Technology, vol. 4.

Joshua D. Isom received the B.S. from YaleUniversity in 2000, the M.S. from Rensselaer atHartford in 2002, and the PhD from the University ofIllinois at Urbana-Champaign in 2009. He is aPrincipal Engineer in the area of prognostics and healthmanagement at United Technologies Research Center.Before joining United Technologies Research Center in2010, he was the technical lead for prognostics andhealth management at Sikorsky Aircraft Corporationfrom 2007 to 2010. He was a lead systems engineer atUTC Power in South Windsor, CT from 2000 through2007. He is a member of IEEE.

Madhusudana Shashanka is a Staff Scientist atUnited Technologies Research Center. His interestsinclude machine learning, data mining, diagnostics andprognostics and related fields. Prior to joining UnitedTechnologies Research Center, he worked as a Scientistin Analytics for Mars, Inc from 2007 to 2010. Heworked as a Research Intern at Mitsubishi ElectricResearch Labs prior to that working on applyingmachine learning methods for audio source separation.He has a BE (Hons) in Computer Science from Birla

Institute of Technology and Science, Pilani, India and aPhD in Cognitive & Neural Systems from BostonUniversity.

Ashutosh Tewari received a BS in Material Sciencefrom Indian Institute of Technology, Bombay in 2003,and PhD in Engineering Sciences and Mechanics fromPenn State in 2008. Currently he is a Senior ResearchScientist at United Technology Research Center. Hisresearch interests include application of machinelearning and statistical methods in detection, diagnosisand prognosis in complex engineering systems.

Aleksandar Lazarevic is a Staff Research Scientist atUnited Technologies Research Center. His researchinterests include data mining, prognostics anddiagnostics, and security applications. He receivedB.Sc and MSc degrees in Computer Science andEngineering from University of Belgrade, Yugoslaviain 1994 and 1997 respectively. He received the PhDdegree in Computer Science from Temple University in2001. He has co-edited the book "Managing CyberThreats" published by Springer in May 2005, andauthored more than 40 research articles. He wasserving as a Technical Chair at the NASA's Conferenceon Intelligent Data Understanding in 2008 and as aProgram Committee member on more than 20prestigious data mining conferences in the last fewyears.

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