Condition Monitoring of Helicopter Drivetrain Components Using BispectralAnalysisMohammed A. [email protected] ResearcherCBM research centerUniversity of South CarolinaColumbia, SC, USADavid [email protected] Research AssistantCBM research centerUniversity of South CarolinaColumbia, SC, USAAbdel E. [email protected], DirectorCBM research centerUniversity of South CarolinaColumbia, SC, USAABSTRACTIn this paper, bispectral analysis of vibration signals is used to assess health conditions of different rotatingcomponents in an AH-64D helicopter tail rotor drive train. First, cross-bispectral analysis is used to investigatedrive-shaft faulted conditions -- namely misalignment, imbalance, and a combination of misalignment andimbalance -- with respect to a baseline case. The magnitude of the cross-bispectrum shows high sensitivity toabnormalities in the drive shaft, and phase information can be used to distinguish between different shaft conditions.Auto-bispectral analysis is used to study vibration signals collected from a faulted hanger bearing with simultaneousdrive shaft misalignment and imbalance. In the presence of drive-shaft faults, shaft harmonics dominate the powerspectrum of the vibration signals, making it hard to detect the bearing’s fault using only the power spectrum.Application of bispectral analysis provides information about the fault’s characteristic frequency and relates spectralcontents in the vibration to their physical root is observed around the characterizing frequency ofthat component.INTRODUCTION Over the past decade, great advancements have beenmade in the field of Condition-Based Maintenance (CBM)for aircraft systems [1]-[3]. The successes to date inimplementing CBM practices on military helicopters haveresulted in the large-scale deployment of Health and UsageMonitoring Systems (HUMS), which have generated anumber of benefits ranging from an increased sense of safetyto reduced maintenance costs [4]-[6]. To avoid unexpectedfailure of critical rotorcraft components, on-board HUMSdevices continuously collect and process a variety of timevarying waveforms to assess the health conditions of acomponent. Nevertheless, vibration signals are the mostcommon waveform data used in the condition monitoring ofrotating and reciprocating machineries [7].Collectedvibration data are analyzed using different signal processingtechniques to extract features that are used to diagnose thecurrent condition of a component, or to estimate itsremaining useful life using prognostic models.However, power spectral analysis has limitedperformance in describing frequency correlations higherthan the second order [9]. The power spectrum is the Fouriertransform of the well-known correlation function (secondorder moment of the signal) as described by WienerKhinchin theorem [10]. Studying higher-order correlationfunctions and their corresponding spectra could providemore information about the mechanical system, which inturn could help in building more accurate diagnostic models.This information comes with no additional cost in terms ofadding more hardware (sensors, wiring, etc.), since furtherprocessing of the same collected vibration data is all that isneeded. For example, when two faults produce similarcharacterizing power spectra, such as the case of shaftmisalignment and imbalance, further processing of the samevibration data will result in a proper diagnosis of the faults.Another example is when two faults with differentcharacterizing frequencies occur simultaneously such thatone fault frequency dominates the power spectrum andmasks that of the other fault.Power spectral analysis is the most common techniqueused in the field of vibration monitoring [8]. The powerspectrum describes how the mean square power in a signal isdistributed over the frequency. A faulted mechanicalcomponent can be detected and isolated when high vibrationThe bispectrum is the Fourier transform of thebicorrelation function (third-order moment), as will bediscussed in the following section. It is a very useful tool forinvestigating quadratic coupling between spectralcomponents [11]. When the system under study has someform of quadratic nonlinearity, various frequencycomponents tend to interact with one another. Thisfrequency mix produces new spectral components which arephase-coupled to the permanent interacting ones. ThePresented at the AHS 70th Annual Forum, Montréal,Québec, Canada, May 20–22, 2014. Copyright 2014 bythe American Helicopter Society International, Inc. Allrights reserved.1

Rxx ( ) E{x(t ) x* (t )}bispectrum describes the correlation between the source andthe result of quadratic-frequency interaction in bi-frequencyspace.(1)PXX ( f ) E{ X ( f ) X * ( f )} E{ X ( f ) }2In this paper, different signal processing techniquesbased on vibration bispectral analysis are used to assesshealth conditions of rotating-components in the tail rotordrive train of an AH-64D helicopter. First, different driveshaft faulted conditions, namely misalignment andimbalance, are investigated using cross-bispectral analysis.Two vibration signals are simultaneously collected from thebearings that support the shafts, then used to estimate thecross-bispectrum and compare it to the classical cross-powerspectrum in each case. Condition indicators (CIs) based onmagnitude of the cross-bispectrum show higher sensitivity tofaults in the studied shaft cases than currently used CIsbased on the power spectrum. Also, phase values of the CIsshow wider margins between different studied shaft cases,which makes it easy to distinguish each case. Another usefulapplication of the bispectrum is presented to study faultedinner-race of a hanger bearing in the presence of shaftmisalignment and imbalance. Analysis of vibration signalsfrom the faulted bearing shows that shaft harmonicsdominate the power spectra, making it hard to detect thebearing’s fault. Also, unexpected frequencies appear in thevibration spectrum which cannot be explained usingconventional power spectral analysis. However, using theauto-bispectral analysis demonstrates better capability inboth detecting the fault frequency and relating frequencies inthe power spectrum to their physical root causes.(2)where E{.} denotes a statistical expected value operator,X(f) is the Fourier transform of x(t), and superscript asterisk denotes a complex conjugate.Auto-power spectrum, PXX(f), is one of the mostcommonly used tools in vibration spectral analysis [8]. Itdescribes how the mean square power of the vibration signalis distributed over single-frequency space. When twovibration signals are collected simultaneously, crosscorrelation, Rxy(τ), is a useful function which investigatesthe linear relationship between the two signals x(t) and y(t),as given in equation (3). The Fourier transform of the crosscorrelation function is the cross-power spectrum, CXY(f), asgiven in equation (4).Rxy ( ) E{x(t ) y* (t )}(3)CXY ( f ) E{ X ( f )Y * ( f )} Cxy ( f ) e j XY(4)Auto- and Cross-BispectraAuto-bispectrum, SXXX(f1,f2), is the Fourier transform ofthe second-order correlation function Rxxx(τ1, τ2), as given in(5) and (6), and it describes second-order statisticaldependence between spectral components of signal x(t) [11].The paper is organized as follows: First, the backgroundof bispectral analysis is sketched. Then, the experimentaltest stand used to conduct this study is described. Two casestudies are presented to demonstrate the applications ofbispectrum. These are followed by some concludingremarks.Rxxx ( 1 , 2 ) E{x(t 1 ) x(t 2 ) x* (t )}(5)S XXX ( f1 , f 2 ) E{X ( f1 ) X ( f 2 ) X * ( f1 f 2 )}(6)The advantage of bispectral over power spectralanalysis is its ability to characterize quadratic nonlinearitiesin monitored systems. Due to quadratic nonlinearities,various spectral components of the vibration signal interactwith one another producing cross-term (second-order term),as indicated in the left side of equation (7). This interactionresults in new combinations of frequencies at both the sumand the difference values of the interacting frequencies, asindicated in the right side of equation (7). An importantsignature for detecting nonlinearity is based on theknowledge that phase coherence (phase coupling) existsbetween the primary interacting frequencies and the resultantnew sum and difference frequencies. The bispectrumdescribes this correlation between the three waves (theinteracting frequencies i) f1 and ii) f2, and the result iii)(f1 f2) of nonlinear process) in two-dimensional frequencyspace (f1-f2). The definition of the bispectrum in (6) impliesthat SXXX(f1,f2) will be zero unless phase coherence is presentbetween the three frequency components f1, f2, and f1 f2.BISPECTRUM BACKGROUNDVibration signals collected from rotating mechanicalcomponents can be considered as realizations of randomprocesses. Just as random variables are characterized bycertain expected values (or, moments), such as mean andvariance, random processes are also characterized by theirmean value, correlation function, and various higher-ordercorrelation functions. Alternatively, random processes maybe characterized by the Fourier transforms of the variousorder correlation functions [11]. Of particular interest are thecorrelation and bicorrelation functions and their Fouriertransform, as will be discussed in the following subsections.Auto- and Cross-Power Spectracos(2 f1t 1 ) cos(2 f 2t 2 )For a zero-mean stationary vibration signal x(t), theautocorrelation function Rxx(τ) and the auto-power spectrumPXX(f) are Fourier transform pairs according to the WienerKhinchin theorem [10], and can be estimated by equations(1) and (2) as follows:1 [cos(2 ( f1 f 2 )t ( 1 2 )) (7)2 cos(2 ( f1 f 2 )t ( 1 2 ))]2

Similarly, the cross-bispectrum CXXY(f1,f2) is the Fouriertransform of the cross-bicorrelation function Rxxy(τ1,τ2) asgiven in (8) and (9) [11]:Rxxy ( 1 , 2 ) E{x(t 1 ) x(t 2 ) y* (t )}(8)CXXY ( f1 , f 2 ) E{X ( f1 ) X ( f 2 )Y * ( f1 f 2 )}(9)drive train (TRDT) test stand for on-site data collection andanalysis, as shown in Figure 2-(b).The TRDT test stand emulates the complete tail rotordrive train from the main transmission tail rotor powertakeoff to the tail rotor swashplate assembly, as shown inFigure 2-(a). This multi-shaft drive train consists of fourshafts. Three of these shafts, denoted as shafts #3, #4 and #5, lead from the tail rotor power take off point to theintermediate gearbox (IGB). These shafts are supported bytwo hanger bearings denoted as forward (FHB) and aft(AHB), and flexible couplings at shaft joining points. Thefourth shaft is installed on the vertical stabilizer between theIGB and the tail rotor gearbox (TRGB).The cross-bispectrum given in (9) investigates thenonlinear coupling between any two frequency componentsf1 and f2 in signal X(f) that interact, due to quadraticnonlinearity, to produce a third frequency f1 f2 at anothersignal Y(f).Both auto- and cross-bispectrum will be evaluateddigitally. Sampling theory implies that f1, f2, and f3 f1 f2must be less than or equal to (fS /2), where fS is the samplingfrequency. Due to sampling theory limitations in addition toFourier transform symmetry properties, cross-bispectrum,CXXY(f1,f2), is usually plotted in the sum-frequency regiondenoted by “Σ” and the difference-frequency region “ ”, asshown in Figure 1, while auto- bispectrum, SXXX(f1,f2), isusually plotted only in the sum-frequency region “ ” [11].All drive train parts on the test stand are actual aircrafthardware. The prime mover for the drive train is an 800hpAC induction motor controlled by a variable-frequencydrive. An absorption motor of matching rating, controlled bya separate variable-frequency drive, is used to simulate thetorque loads that would be applied by the tail rotor. Theinput and the output motors work in dynamometricconfiguration to save energy.(a) TRDT on the AH-64D helicopterFigure 1: Region of computation of the bispectrumTRDT TEST STAND AT USC(b) TRDT test stand at USCSince 1998, the University of South Carolina (USC) hasbeen working closely with the South Carolina ArmyNational Guard on a number of projects directed at reducingthe Army’s aviation costs and at increasing its operationalreadiness through the implementation of CBM [5]-[6]. Theseefforts expanded into a fully-matured CBM research centerwhich hosts several aircraft component test stands in supportof current US Army CBM objectives [2]. Within the USCtest facility is an AH-64D (Apache helicopter) tail rotorFigure 2: Tail Rotor Drive Train (TRDT)The structure, instrumentation, data acquisition systems,and supporting hardware are in accordance with militarystandards. The signals being collected during the operationalrun of the stand include vibration data measured byaccelerometers, temperature measured via thermocouples,and speed and torque measurements. The measurement3

use “1R, 2R, 3R, etc.” to denote “first, second, third, etc.”harmonics of the shaft rotating frequency (1R 81.05Hz).devices are placed at the FHB and AHB hanger bearings andthe two gearboxes as shown in Figure 2-(b).Figure 3 shows the magnitude plot of the cross-powerspectrum for all the studied shaft settings. Although weexpect to see very low vibration power in the case of thebaseline, Figure 3(a) shows a high spectral peak at f 3R thatdominates the vibration spectrum in this case. Highvibration power at this frequency can be caused byoscillations due to unsymmetrical loading on one end of thedrive shafts as torque transferred to the shafts through theIGB from the tail rotor. A high spectral peak at frequency3R continues to dominate all the studied faulted cases, asshown in Figure 3(b-d).DRIVE-SHAFT CASE STUDYIn this section, we utilize the cross-bispectrum as a toolto investigate and model quadratic nonlinear relationshipsbetween two vibration signals simultaneously collected atthe FHB and AHB positions in an AH-64D helicopter tailrotor drive train.Experiment Setup and Vibration Data DescriptionThe data used in this study were collected from fourexperiment runs testing different shaft alignment andbalance conditions. In order to keep data organized, anaming convention, summarized in Table 1, was adopted.The original configuration of the test stand used balanceddrive-shafts, straightly aligned, as a baseline for normaloperations (case “00373” in Table 1). The case of alignedbut unbalanced shafts (“10373” in Table 1) is simulated withdrive shaft #4 unbalanced by 0.135 oz-in, and drive shaft #5unbalanced by 0.190 oz-in. Angular misalignment betweenshafts (case “20373” in Table 1) was tested with a 1.3misalignment between the #3 and the #4 drive shafts and asimilar misalignment between the #4 and the #5 drive shafts.A combination of the last two cases, imbalance andmisalignment, was also tested (case “30373” in Table 1).(a) Baseline case (00373)Table 1. Vibration Data Set and Test NumbersShaft SettingTest NumberBaseline (Aligned-Balanced) (BL)00373Aligned-Unbalanced (UB)10373Misaligned-Balanced (MA)20373Misaligned-Unbalanced (MA-UB)30373(b) Unbalanced case (10373)During each thirty-minute run, accelerometer data werecollected simultaneously from the FHB and AHB once everytwo minutes, making total of 15 data samples. Each datasample consists of 65536 data points collected at a samplingrate of 48 kHz (fS), which results in a data collection time ofapproximately 1.31 seconds per acquisition. Vibrationsignals are collected during operation of the test stand at aconstant rotational speed of 4863 rpm (81.05 Hz), with asimulation of the output torque at 111 ft-lb. Rotational speedis the speed of the input shafts and hanger bearings. Outputtorque is given by the torque at the output of the tail rotorgearbox simulating rotor operation while the torque appliedto the input shafts is equal to 32.35 ft-lb.(c) Misaligned case (20373)Results and DiscussionVibration signals at the FHB and AHB in Figure 2 areused as x(t) and y(t) in equations (4) and (9). In the followingdiscussion, for easier notation of frequency values, we will(d) Misaligned-Unbalanced case (30373)Figure 3. Cross-power spectrum between FHB and AHBvibration signals under different shaft settings4

Current practice in monitoring rotating shaft conditionsinvolves using the vibration magnitude at the spectral peakscorresponding to the first three rotating shaft harmonics (1R,2R, and 3R) as shaft’s condition indicators [12], [13]. Inorder to calculate those condition indicators, either an autopower spectrum is averaged between the two vibrationsignals at one particular frequency (for example, 2R) or across-power spectrum between the two vibration signals iscalculated at that frequency. Comparison with the baseline isusually done on a logarithmic amplitude scale, whereincreases of 6-8 dB (double the baseline values) areconsidered to be significant and changes greater than 20 dB(ten times the baseline values) are considered serious [14].Therefore, we will focus our attention on comparing theexperimental data using 1R, 2R, and 3R condition indicatorscalculated from the cross-power spectrum between the FHBand AHB vibrations.More information can be extracted from the samevibration data by extending the analysis to investigate thequadratic-nonlinear behavior of the drive shafts using thecross-bispectrum. Magnitude of the cross-bispectrum isplotted for the same data set studied before, as shown inFigures 4. The baseline case (aligned-balanced), shown inFigure 4(a), has the least quadratic nonlinear frequencyinteraction of all cases. The highest bispectral peak in thebaseline case is found at the coordinate point (3R,3R) whosemagnitude is equal to 0.17 g3. For faulted shaft cases,increased frequency-interaction takes place along f1 1R, 2R,and 3R frequency axes, as can be observed in Figure 4(b-d).One interesting observation is the high bispectral peaks atthe frequency coordinate points of (1R,1R), (2R,1R), and(3R,1R) in all the faulted cases compared to the baseline.Interpretation of these frequency coupling points suggeststhat quadratic nonlinearity of the faulted drive shaftsstimulates interaction between time-varying forces at theshaft rotation frequency, 1R, and its harmonics.Table 2 summarizes the results of the spectral peakcomparison of the three faulted cases (UB, MA, and MAUB) against the baseline case (BL). Values of spectral peaksat the first three harmonics of the shaft speed (1R, 2R, and3R) are extracted from the cross-power spectral plots inFigure 3(b-d), and compared with their counterparts from thebaseline case (Figure 3(a)) in logarithmic scale. Results ofthe spectral peak comparison in Table 2 show that vibrationpower at shaft rotation frequency (f 1R) exceeds the 6 dBthreshold in all the faulted cases, and hence is considered agood indicator of the faults. However, using only themagnitude of 1R condition indicator does not give muchinformation to distinguish between different studied faults.Bispectral peaks at the three frequency coordinatepoints mentioned above are used to compare the threefaulted cases with the baseline case, as summarized in Table4. Bispectral peaks at (1R,1R), (2R,1R), and (3R,1R) areextracted from each faulted case and compared to theircounterparts from the baseline in logarithmic scale. Resultsof the bispectral peak comparison in Table 4 show thesensitivity of all the selected bispectral condition indicatorsto any abnormalities in the drive shafts. Values of thosebispectral peaks increase more than 6dB in all the faultedcases compared to the baseline.Table 2. Spectral Peak Comparison with Baseline(dB)fUB(10373)MA(20373)Table 4. Bispectral Peak Comparison with R3.514.589.12(2R, 511.93In order to gain more diagnostic capabilities, phaseinformation of the cross-power spectral peaks can beemployed. Phase differences between spectral peaks offaulted cases compared to the baseline are listed in Table 3for the first three harmonics of the rotating shaft frequency(1R, 2R, and 3R). For the 1R frequency, whose magnitude isused as a fault indicator, narrow phase margins can beobserved between different cases, as shown in Table 3.Again, phase information of the cross-bispectral peakscan be used to gain more diagnostic capabilities. Phasedifferences are calculated between the bispectral peaks infaulted cases and their counterparts in the baseline, as listedin Table 5. Wider phase margins can be observed betweendifferent faulted cases. These wider margins relax therequirement to set threshold values and make it easy todistinguish between different cases.Table 3. Cross-Power Phase Comparison withBaseline (Degrees)fUB(10373)MA(20373)Table 5. Cross-Bispectrum Phase Comparison withBaseline 602R-19.0422.691.93(2R, 302.0971.305

(a) 00373 Baseline case(b) 10373 Unbalanced case(c) 20373 Misaligned case(d) 30373 Unbalanced-Misaligned caseFigure 4: Cross-bispectrum between FHB and AHB vibration signals under different shaft settingsIn this section, the auto-bispectrum is used to analyzevibration data collected from a faulted hanger bearing withtypically misaligned and unbalanced shafts.BEARING CASE STUDYMost of the conventional fault analysis techniquesassume that a defect occurs in a rotating element separately,that we can identify a fault by the characterizing frequencyof that component. For example, ball pass frequency innerrace (BPFI) is used to detect faults in the inner-race ofbearings [15]. However, in the presence of drive shaft faults,shaft harmonics dominate the power spectra of the vibrationsignals collected form the faulted hanger bearing, making ithard to detect bearing faults. Also, spectral interactionbetween different fault frequencies leads to the appearanceof unexpected frequencies in the vibration spectrum whichcannot be explained using conventional power spectralanalysis.Experiment Setup and Vibration Data DescriptionA seeded hanger bearing fault experiment was designedto test multi-faulted drive train components. The FHB wasmachined to replicate a bearing with a spalled inner-race, asshown in Figure 5. The faulted hanger bearing was testedwith 1.3 misalignment between drive shafts #3 and #4, 1.3 misalignment between drive shafts #4 and #5, and driveshafts #3, #4, and #5 unbalanced by 0.14 oz-in, 0.135 oz-in,and 0.19 oz-in, respectively.6

(BPFI) that characterizes the faulted hanger bearing undertest (441Hz as reported by the Aviation EngineeringDirectorate (AED)). However, vibration power at PBFI hasvery low magnitude, making it very hard to detect, as shownin Figure 6. The highest non-shaft frequency in thisspectrum is at 684.1Hz, which does not match any frequencyreported by AED for the tail rotor drive train components.(a)(b)Figure 6: Power spectrum of the spalled inner-race FHBwith misaligned-unbalanced shafts(c)Auto-bispectrum is utilized to investigate the samevibration data from the faulted inner-race bearing, as shownin Figure 7. It can be seen that a number of quadraticfrequency interactions exist along the first three shaftrotating harmonics (f1 80.57Hz, 161.1Hz, and 243.2Hz).These shaft harmonic patterns have been used before todescribe shaft abnormalities. Among frequency interactionpairs, the high bispectral peak at the (442.4Hz, 243.2Hz)coordinate point has very interesting interpretation. First,physical interpretation of this bispectral peak suggests thatthe 442.4Hz frequency nonlinearly interacts with thirdharmonic of the shaft, 243.2Hz, to produce the sum value,684.6Hz. The existence of the 685.6Hz frequency value inthe power spectrum of the bearing’s vibration could not beexplained using information from the power spectrum alone.Also, 442.4Hz is equal to the BPFI, which implies that afault exists in the inner race of the hanger bearing.Figure 5: Faulted FHB: (a) assembled bearing in the drivetrain, (b) schematic of assembly components, and(c) zoom-in view of the spalled inner-race faultThree holes were milled into the inner-race with a ballmill and were machined to the specifications summarized inTable 6. Vibration data were collected every two minutesover a 50 minutes run. Each acquisition consisted of 65536data points collected at a sampling rate of 48 kHz (fS).Vibration signals were collected during operation of the teststand at a constant rotational speed of 4863 rpm (81.05 Hz)from the prime mover, and output torque at the tail rotorequals to 371 ft-lb.Table 6. Spalled Inner-Race Specifications (inch)SpallDiameter DepthDistancefrom leftshoulderDistancefrom .0160.19560.19850.0170.25670.1376#3Results and DiscussionMagnitude of the auto-power spectrum for vibrationdata collected form the spalled inner-race FHB is shown inFigure 6. Due to the presence of the drive shaftsmisalignment and imbalance, high magnitudes of thevibration exist at the 80.57Hz, 162.5Hz, and 243.2Hz. Thesefrequencies match 1R , 2R, and 3R, and indicate drive shaftfaults as discussed in the previous section. Due to the Figure 7: Aut-bispectrum of the spalled inner-race FHBpresence of the fault in the inner-race of the bearing, onewith misaligned-unbalanced shaftsshould also expect to see the ball pass inner-race frequency7

[3] M. A. Hassan, D. Coats, Yong-June Shin, and A. Bayoumi,“Quadratic-Nonlinearity Power-Index Spectrum and ItsApplication in Condition Based Maintenance (CBM) ofHelicopter Drive Trains,” Proceeding of the IEEEInternational Instrumentation and Measurement TechnologyConference (I2MTC), pp. 1456-1460, May 2012.CONCLUSIONIn this paper, bispectral analysis has been used toinvestigate and understand quadratic nonlinear wave-waveinteraction in vibration signals in order to assess healthconditions of rotating components in the AH-64D helicoptertail rotor drive train. First, cross-bispectrum has beenemployed to study quadratic coupling in faulted drive shafts.Compared with conventional power spectral analysis,condition indicators based on magnitude of the crossbispectrum have shown higher sensitivity to abnormalities inthe drive shafts. Moreover, phase information from thebispectrum has shown wider phase margins among differentstudied shaft cases which makes it easy to distinguishbetween different shaft conditions.[4] P. Grabill, T. Brotherton, J. Berry, and L. Grant, “The USArmy and National Guard Vibration ManagementEnhancement Program (VMEP): Data Analysis and StatisticalResults,” American Helicopter Society 58th Annual Forum,Montreal, Cananda, June, 2002.[5] A. Bayoumi, W. Ranson, L. Eisner, and L.E. Grant, “Cost andeffectiveness analysis of the AH-64 and UH-60 on-boardvibrations monitoring system,” IEEE Aerospace Conference,pp. 3921-3940, Mar. 2005.Auto-bispectrum has also been used to study vibrationsignals from a faulted hanger bearing under simultaneousdrive shaft misalignment and imbalance. In the presence ofthe drive-shaft faults, shaft harmonics have dominated thepower spectra of the vibration signals collected from thefaulted hanger-bearing, making it hard to detect thebearing’s fault. Also, unexpected frequencies have appearedin the vibration spectra which could not be explained usingconventional power spectral analysis. However, bispectralanalysis has not only detected the bearing’s fault, but alsohas shown better ability to relate all frequencies in the powerspectrum to their root causes and successfully link the signalprocessing to the physics of the underlying faults.[6] A. Bayoumi, and L. Eisner, “Transforming the US enance,” Journal of Army Aviation, May 2007.Future research in this area includes studying the effectof loading by the trail-rotor blades on the proposed metrics,and extending the application of bispectral analysis to studymore faults and failure modes in aircraft. The uniquequadratic nonlinearity signature of each fault can be used todesign more accurate and reliable diagnostic algorithms forcondition-based maintenance (CBM) practice.[9] M. A. Hassan, A. E. Bayoumi, and Y.-J. Shin “QuadraticNonlinearity Index Based on Bicoherence and Its Applicationin Condition Monitoring of Drive-Train Components,” IEEETransactions on Instrumentation and Measurement, vol. 63,no. 3, pp. 719-728, March 2014.[7] P. D. Samuel, and D. J. Pines, “A Review of Vibration-BasedTechniques for Helicopter Transmission Diagnostics,” Journalof Sound and Vibration, vol. 282, no. 1-2, pp. 475-508, Apr.2005.[8] A. S. Sait, and Y. I. Sharaf-Eldeen, “A Review of GearboxCondition Monitoring Based on Vibration AnalysisTechniques Diagnostics and Prognostics,” in RotatingMachinery, Structural Health Monitoring, Shock andVibration, Vol. 8, T. Proulx, Ed. New York: Springer, pp.307- 324, 2011.[10] John G. Proakis, and Dimitris G. Manolakis, “Power SpectrumEstimation," in Digital Signal Proccessing: Principles,Algorithms, and Applications, 4th ed. New Jersey: PrenticeHall, 2007, pp. 960-1040.ACKNOWLEDGMENTThis research was funded by the South Carolina ArmyNational Guard and United States Army Aviation andMissile Command via the Conditioned-Based Maintenance(CBM) Research Center at the University of South CarolinaColumbia.[11] B. Boashash, E. J. Powers, A. M. Zoubir, “Higher-OrderStatistical Signal Processing,” Wiley, 1996.[12] Damian Carr. ”AH-64A/D Conditioned Based Maintenance(CBM) Component Inspection and Maintenance ManualUsing the Modernized Signal Processor Unit (MSPU) orVMU (Vibration Management Unit),” Aviation EngineeringDirectorate Apache Systems, Alabama, Tech. Rep., Oct. 2010.REFERENCES[1] A. K.S. Jardine, D. Lin, and D. Banjevic, “A Review onMachin

spectrum of the vibration signals, making it hard to detect the bearing’s fault using only the power spectrum. Application of bispectral analysis provides information about the fault’s characteristic frequency and relates spectral . Monitoring Systems (HUMS), which have generated a