Analysis of Nonlinear Vibration-Interaction Using
Higher Order Spectra to Diagnose Aerospace System
Faults
Mohammed A. Hassan, David Coats, Kareem Gouda*, Yong-June Shin, and Abdel Bayoumi*
Department of Electrical Engineering/ Department of Mechanical Engineering*
University of South Carolina
301 Main Street
Columbia, SC
803-454-9461
shinjune@cec.sc.edu, bayoumi@cec.sc.edu
ponents [1], [2]. In contrast, traditional time-based maintenance (TBM) involves replacing existing parts after a certain
time period or a certain number of operational hours. Implementation of the CBM helps to avoid failures in critical
parts due to unexpected wear which may cause operational
downtime and/or potential safety hazards [3], [4], [5]. We
have sought to improve the accuracy of condition indicators
(CIs) used in the Vibration Management Enhancement Program. VMEP implementation resulted in on-board Modern
Signal Processing Unit (a vibration data acquisition and
signal-processing equipment for the health monitoring of
critical mechanical components) for AH-64 (Apache), UH60 (Blackhawk) and CH-47 (Chinook) fleets [6] and aims to
provide rotorcraft maintainers with a collection of diagnostic and progressively prognostic vibration-based indicators
summarized by CIs or Health Indicators (HIs), which collect
several CI metrics. Pre-established and baseline measurements of these typically one-dimensional CI and HI values
from existing historical data and testbed verifications under
extreme conditions provide rankings for the status of individual aerospace and rotorcraft components with ratings such as
“Good,” “Caution,” and “Exceeded,” which in turn provide
maintainers of these fleets proactive time-independent condition based maintenance decision making [7].
Abstract— For efficient maintenance of a diverse fleet of aging air- and rotorcraft, effective condition based maintenance
(CBM) must be established based on rotating components monitored vibration signals. Traditional linear spectral analysis
techniques of the vibration signals, based on auto-power spectrum, are used as common tools of rotating components diagnoses. Unfortunately, linear spectral analysis techniques are of
limited value when various spectral components interact with
one another due to nonlinear or parametric process. In such a
case, higher order spectral (HOS) techniques are recommended
to accurately and completely characterize the vibration signals.
Since the nonlinearities result in new spectral components being
formed with coherency in phase, the detection of such phase coherence may be carried out with the aid of higher order spectra.
In this paper, we use the bispectrum as a higher order spectral
analysis tool to investigate nonlinear wave-wave interaction in
vibration signals. Accelerometer data has been collected from
baseline tests of accelerated conditioning in tail rotor drive-train
components of an AH-64 helicopter drive-train research test bed
simulating drive-train conditions. Through bispectrum analysis,
we compare the harmonics interaction patterns contained in
vibration signals from different physical setting of helicopter
drive train and compare that with classical power spectral
density plots. The analysis advances the development of higher
order statistics and two dimensional frequency health indicators
in order to qualify health conditions in mechanical systems.
TABLE
OF
Our aim is to improve the effectiveness of the MSPU by developing new general methods for fault analysis that could be
used in existing or new CIs. Unfortunately, some of the existing CIs based on conventional time or spectral analysis have
limited diagnostic capabilities and are used to detect more
than one fault associated with the same rotating component.
For example, SP2 (Spectral Peak 2) is currently employed in
the MSPU to detect unbalanced and/or misaligned shafts in a
tail rotor drive-train of a rotorcraft [8]. However, this CI does
not specify whether the fault is unbalance, misalignment or
a combination of those faults. The maintainers are told to
check for more than one source that might cause that CI to
exceed its limit. We use the concept of higher order spectra
in vibration analysis toward the development of more robust
diagnostic CI metrics, as well as the furthered understanding
of underlying physical and electromechanical interactions.
C ONTENTS
1 I NTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 S TATISTICAL RELATIONSHIPS BETWEEN VI BRATION SIGNALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 E XPERIMENT SETUP AND DATA DESCRIPTION . .
4 A PPLICATION OF BISPECTRUM TO ANALYZE
VIBRATION INTERACTIONS . . . . . . . . . . . . . . . . . . . . . .
5 N UMBER OF N ONLINEAR H ARMONIC I NTER ACTION AS A CI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . .
R EFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B IOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
2
3
4
6
7
7
7
8
In order to obtain better understanding of the fault sources,
statistical relationship (or, dependence) between vibration
signals can be investigated using various orders of the correlation function. The Fourier transform of the auto-correlation
is the classical auto-power spectrum which is one of the most
commonly used tools in spectrum analysis [9], [10]. Similarly, higher-order correlations, and their Fourier transforms
describe higher order statistical relationships. Higher order
spectral densities (HOS), such as bispectrum and trispectrum,
1. I NTRODUCTION
Condition Based Maintenance (CBM) is a practice that recommends maintenance actions for machines, or systems,
based on the continuous condition-monitoring of their comc
978-1-4577-0557-1/12/$26.00 ⃝2012
IEEE.
1 IEEEAC Paper #1345, Version 4, 04/01/2012.
1
Sxx (f ) is shortened to S(f ) and is referred to as the power
spectrum.
are the Fourier transforms of third order and the fourth order
correlation functions respectively. The advantage of HOS
over linear power spectral analysis is its ability to characterize nonlinearities in monitored systems [11], [12]. When
various spectral components interact with one another due to
nonlinear or parametric processes, new spectral components
are formed which are phase coupled with the permanent
interacted frequencies [13]. The bispectrum describes this
correlation between the source and the result of interaction
process in two-dimensional frequency space. Since faulted
components are often related to nonlinear phenomena, bispectrum can provide more diagnostics information than the
classical power spectrum which carry no phase information.
Higher order correlation and higher order spectra
Higher order spectral (HOS) analysis is a powerful signal
processing technique in detecting nonlinearities. When various frequency components inside the vibration signal interact
with one another due to nonlinear physical phenomena, new
combinations of frequencies are generated at the sum and
difference of the interacting frequencies. Those frequency
components are phase coupled to the primary interacted
frequencies. HOS uses this phase coupling signature between
frequency components to detect nonlinearities [14]. The third
order auto-correlation function is called auto-bicorrelation
Rxxx (τ1 , τ2 ) , and its two-dimensional Fourier transform is
called auto-bispectrum Sxxx (f1 , f2 ). In common practice,
when bispectrum is mentioned, it is meant to be the autobispectrum. Rxxx (τ1 , τ2 ) and Sxxx (f1 , f2 ) for zero-mean
strongly stationary random signal x(t) are defined in (4) and
(5) respectively [11].
In this paper, we use the bispectrum as a signal processing
tool to analyze vibration data to distinguish between different
seeded faults in AH-64 drive-train namely (1) misaligned
shafts, (2) unbalanced shafts and (3) combination of both
misaligned and unbalanced as will be described in section
3. In the following section, we will start with reviewing
general concepts of the linear correlation and linear spectra
and then extend those concepts to higher order spectra. In
section 4, analysis of vibration signals using bispectrum will
be discussed. Based on this analysis, a CI is proposed in
section 5 based on nonlinear harmonic interaction
Rxxx (τ1 , τ2 ) = E{x∗ (t)x(t + τ1 )x(t + τ2 )}
Sxxx (f1 , f2 ) = E{X(f1 )X(f2 )X ∗ (f3 = f1 + f2 )}
2. S TATISTICAL RELATIONSHIPS BETWEEN
VIBRATION SIGNALS
Rxx (τ ) = x(t) ⋆ x(t) =
∞
x∗ (t)x(t + τ )dt
(1)
−∞
If waves present at f1 , f2 , and f1 + f2 are spontaneously
excited independent waves, each wave will be characterized
by statistical independent random phase. Thus, the sum phase
of the three spectral components will be randomly distributed
over (−π, π). When a statistical averaging denoted by the
expectation operator is carried out, the bispectrum will vanish
due to the random phase mixing effect. On the other hand, if
the three spectral components are nonlinearly coupled to each
other, the total phase of three waves will not be random at
all, although phases of each wave are randomly changing for
each realization. Consequently, the statistical averaging will
not lead to a zero value of the bispectrum.
where the superscript asterisk (∗) denotes complex conjugate
and the operation of correlation is indicated by a five-pointed
star (⋆). Auto-correlation Rxx (τ ) is a measure of similarity (statistical dependence) between a signal x(t) and timeshifted version x(t + τ ).
For vibration signals collected from physical systems, it is
not possible (from experimental point of view) to have access
to all possible realizations of x(t). Therefore, the autocorrelation in this case is statistically estimated based on a
finite number of realizations as
Rxx (τ ) = E{x∗ (t)x(t + τ )}
The auto-bispectrum Sxxx (f1 , f2 ) is a true spectral density
function indicates how the mean cube value of x(t) is distributed over a two-dimensional frequency plane. Using the
symmetry property of Fourier transform, X(−f ) = X ∗ (f ),
in (5), one can easily prove the four symmetry properties of
the bispectrum [11] which make it enough to compute the
bispectrum only for the octant labeled A in Figure 1.
(2)
where E{.} denotes the expected value operator.
The auto-power spectrum Sxx (f ) is the Fourier transform of
the auto-correlation Rxx (τ ) and is given by
Sxx (f ) = E{X ∗ (f )X(f )} = E{|X(f )|2 }
(5)
The definition of the bispectrum in (5) shows how the bispectrum measures the statistical dependence between three
waves. That is, Sxxx (f1 , f2 ) will be zero unless the following
two conditions are met:
1. Waves must be present at the frequencies f1 , f2 , and
f1 + f2 . That is, X(f1 ), X(f2 ), and X(f1 + f2 ) must be
non-zero.
2. A phase coherence must be present between the three
frequencies f1 , f2 , and f1 + f2 .
Linear correlation and linear spectra
In signal processing, the auto-correlation function Rxx (τ ) for
a stationary signal x(t) is defined as
∫
(4)
In fact, bispectrum will be evaluated digitally. Thus, the sampling theory implies that all f1 , f2 and f3 = f1 + f2 must be
less than or equal to f2s , where fs is the sampling frequency.
Thus, when auto-bispectrum is digitally computed, it will
be plotted within the triangular region defined by the lines
f2 = 0, f2 = f1 , and f2 = f2s − f1 . The auto-bispectrum
can be estimated directly from the discrete Fourier transform
of M realization of sampled version of x(t) as follows [11];
(3)
where X(f ) is the Fourier transform of x(t).
The auto-power spectrum, Sxx (f ), has the dimensions of
mean square values/Hz and it indicates how the mean square
value is distributed over frequency. In common practice,
2
Figure 2.
Experimental helicopter tail rotor drive-train
assembly with labeled shaft and supporting components.
precedes the forward hanger bearing shown in Figure 2 while
the #4 driveshaft connects the two vital bearings. Segment
#5 precedes the intermediate gearbox (IGB) while the #6
driveshaft serves as link between the intermediate and tail
rotor gearboxes (TRGB). The high speed shafts numbered 3-5
operate at a rotation speed of 4863 RPM (81.05Hz) while the
gearboxes step the rotational speed down to 3660 and 1414
RPM respectively at increased torque, each corresponding to
full-speed of shaft rotation on the fielded rotorcraft. Vibration
and temperature data along with speed and torque measurements are all taken with the focus of this study centered
on accelerometer vibration data at each hanger bearing and
each of the two gear boxes (the intermediate and tail rotor
gearboxes).
Figure 1. Symmetry regions and region of computation for
the auto-bispectrum
Ŝxxx (l, k) =
M
1 ∑
Xi (l)Xi (k)Xi∗ (l + k)}
M i=1
(6)
The magnitude of the bispectrum at coordinate point (l, k)
measures the degree of phase coherence between the three
frequency components l, k,and l + k. However, this magnitude is also dependent on the magnitude of the relevant
Fourier coefficients. Therefore, a normalized version of
the bispectrum estimator in (6) is adopted throughout this
research as indicated in (7).
Ŝxxx (l, k)
S̄xxx (l, k) = √∑ ∑
2
∀i
∀j |Ŝxxx (i, j)|
Signals denoted as FHB and AHB in Figure 2, measured at
forward and aft hanger bearings vibrations respectively, are
gathered at two minutes intervals at a sampling rate of 48 kHz
over the course of thirty minute baseline test runs. Measurements are taken for each set of new bearings under test which
include baseline shaft and bearing configuration, unbalance
in different shafts configuration, and shaft misalignment, all
common issues on AH-64 drivetrains. Misalignment between
drive-shafts #3, #4 and #5 is introduced by moving shaft #4
distance 2.5 inches parallel to the center centerline to simulate
the maximum severe condition in the actual aircraft. This
causes different angles of misalignment between shafts #3
and #4, and shafts #4 and #5 where their lengths are 30, 130,
and 130 inches for drive-shafts #3, #4, and #5 respectively as
illustrated in Figure 3.
(7)
The magnitude of the normalized bispectrum S̄xxx (l, k) is
bounded between “0” and “1” and it evaluates the share of
that magnitude to the norm of the overall bispectrum matrix.
3. E XPERIMENT SETUP AND DATA
DESCRIPTION
The CBM center at The University of South Carolina has an
AH-64 helicopter tail rotor driveshaft apparatus for on-site
data collection and analysis from which data has previously
been gathered in [15]. The apparatus is a dynamometric
configuration which includes a pair of 400 horsepower motors
for drive and regenerative tail end loading of a multi-shaft
drive train. These shafts support tests of a pair of gearboxes
connected to the absorption motor to simulate the torque
loads that would be applied by the tail rotor blade as well
as a pair of hanger bearings tested typically under faulted
conditions.
Figure 3. Misalignment conditions comparing (a) an aligned
drive-train diagram focused on #4 shaft and associated bearings (b) configuration for misalignment of shafts #3-#5.
Four drive train shaft segments (actual helicopter components
designed to military specifications) are of interest in this
study and are numbered as segments #3-#6. Segment #3
3
third harmonic of the shafts (243 Hz) dominates all other
harmonics due to the loading effect in both the AHB and the
FHB spectra. Moreover, other different spectral components
are affected by either attenuation or amplification.
Unbalance of the shafts was also applied in the test conditions
as a comparison point for baseline operation. The unbalance
in the shafts of the drivetrain is introduced by adding thin,
weighted foil lining segments to the interior wall of the
driveshafts #4 and #5. Different combination misalignment
and unbalance are tested with Table 1 summarizing these test
conditions and their designations.
Table 1. Tail Rotor Driveshaft Experimental Settings
Shaft Status
Aligned
Misaligned
Balanced
00321
20321
Unbalanced
10321
30321
4. A PPLICATION OF BISPECTRUM TO
ANALYZE VIBRATION INTERACTIONS
As described in the previous section, for each test setting
described in Table 1, 17 acquisitions (realizations) have been
gathered at sampling rate 48 kHz with 65536 points each.
However, the bigger the number of realizations we use, the
more accurate bispectrum estimation we get. In order to
increase the number of realizations, we split each acquisition
file into two realizations to have 34 total realizations for
each test (32768 sample points in each realization). Then,
the stationarity assumption of the vibration realizations is
validated using the nonparametric runs test with 0.05 level
of significance [16].
Figure 5. Cascaded plot of FHB power spectrum showing
change of load conditions for unbalanced case (10321)
The average power spectra of AHB during loaded condition
of all tested faults are summarized in Figures 6 and 7 with
the 3rd harmonic dominating all other harmonics in all tested
cases. It is not an easy task to distinguish between different
cases using only the traditional linear power spectrum. For
example, the power spectra of the baseline (00321) and
the misaligned (20321) cases in Figure 6 have the same
dominating spectral peaks with very slight changes in the
minor peaks. A similar situation occurs when we compare the
unbalanced (10321) and the misaligned-unbalanced (20321)
cases in Figure 7.
Figure 4. Cascaded plot of AHB power spectrum showing
change of load conditions for unbalanced case (10321)
The vibration signals from the forward (FHB) and aft (AHB)
hanger bearings have been investigated under different loading conditions by controlling the torque applied by the absorbtion motor. It was found that the power spectral content
of the vibration signals vary dramatically considering the
normal loading and the free loading operations. Figures 4
and 5 show this effect during the test of unbalanced shafts
for the AHB and the FHB signals respectively. During this
test, the speed of shafts #3-#5 is maintained constant at 4863
RPM (81.05Hz). A total 18 runs of the power density spectra
(PDS) are plotted during the no load setting, then 16 runs
are plotted with output torque loading. It is clear that the
Figure 6. Average power spectrum of the AHB in loading
conditions: baseline (00321) in (a), and misaligned (20321)
in (b)
4
Figure 9 shows the bispectrum of the misaligned case. More
interactions among harmonics appear along 1R frequency
axis. Along this axis, interaction with the 3R and 2R are
the most obvious. Other interactions exist with very low
magnitudes. The increased magnitude of frequency interactions along the 1R axis can be used as an indicator of the
misalignment between shafts.
Figure 7. Average power spectrum of the AHB in loading conditions: unbalanced (10321) in (a), and misalignedunbalanced (30321) in (b)
The vibration signals under loading conditions are then analyzed using the bispectrum as shown in Figures 8-11 for the
AHB. The vibration interaction in the baseline case shown
in Figure 8 shows the least nonlinearity with only the 3rd
harmonic interacting almost exclusively with itself. In fact,
this coordinate point representing this 3rd harmonic interaction shows up in all the other faulted cases. However,
unlike the case of linear power spectrum, the bispectrum
shows different harmonic interaction patterns between the
different cases which might be used to design a more accurate
diagnoses model and condition metrics. Since our discussion
in the following part will be based on different harmonic
interactions, we will use “1R, 2R, 3R, ...” for easier notation
of “first, second, third, ...” harmonics of the rotating shafts
frequency.
Figure 9. Bispectrum for the misaligned case (20321)
Pure unbalanced shafts act on the 3R axis of interaction as
shown in Figure 10. Along this axis, 3R interacts with 6R and
9R (notice that 6R and 9R are the second and third harmonics
of 3R itself). Although high magnitudes exist along the
1R axis, we can easily distinguish between the misaligned
(20321) and the unbalanced (10321) cases by those 6R and
9R interaction with 3R.
Figure 8. Bispectrum for the baseline case (00321)
Figure 10. Bispectrum for the unbalanced case (10321)
5
Table 2. Comparison with baseline case in terms of SP1,
SP2, and SP3 (dB)
Combining the misalignment and unbalance faults, one may
expect a combined signature of interactions discussed in
each separate case. This conjecture can be justified by the
bispectrum shown in Figure 11. In this case (misalignedunbalanced 30321), increased harmonic interactions along
both 1R and 3R are obvious. Moreover, minor magnitudes
along 2R and 4R axes exist in this case.
Although careful inspection of the two dimensional bispectra in Figures 8-11 gives better insight to all wave-wave
interaction inside the signal spectrum, it would be useful to
follow an automated procedure similar to the spectral peak
comparison discussed above to diagnose and isolate a certain
fault signature in the frequency domain. As discussed in the
previous section, increased number of harmonic interactions
along 1R axis alone indicates pure misalignment. Unbalance
adds more interaction along 3R axis, and a combination
of the two faults results in increased number of harmonic
interactions in both 1R and 3R axes. Therefore, Number of
Nonlinear Harmonic Interaction (NNLHI) in the bispcetrum
of the vibration signal can be used as a condition indicator to
diagnose shaft faults. NNLHI(1R)/NNLHI(3R) is a number
that indicates how many harmonic interactions exceed the
threshold limit along 1R/3R axis.
Table 3 shows how NNLHI(1R) and NNLHI(3R) indices are
calculated for each faulted case. Values of the bispectral
peaks at shaft harmonic interaction points (with 1R or 3R)
are compared to their counterparts from the baseline case in
logarithmic scale. When a value exceeds the threshold limit
(we used 6 dB in our case), it counts toward the total NNLHI
at the corresponding axis (1R or 3R) as summarized in the
last row of Table 3. In both the unbalanced (10321) and the
misaligned (20321) cases, 1R interacts with 1R, 2R, 3R, 4R,
and 9R and the value of each bispectral peak at those points
exceed 6 dB compared to the baseline case, NNLHI(1R)=5.
However, no interaction with 3R exceeds the 6 dB threshold,
NNLHI(3R)=0, in the misaligned (20321) case compared
to NNLHI(3R)=2 in the unbalanced (10321) case. The
misaligned-unbalanced case (30321) shows increased number of both 1R and 3R interactions, NNLHI(1R)=8 and
NNLHI(3R)=3.
Figure 11. Bispectrum for the misaligned-unbalanced case
(30321)
5. N UMBER OF N ONLINEAR H ARMONIC
I NTERACTION AS A CI
In order to develop a CI based on the bispectrum analysis
discussed in the previous section, we will start with reviewing
the current CI being used to detect the fault cases under study.
As mentioned in section 1, SP2 is currently used in the MSPU
to indicate shafts misalignment and/or unbalance. This CI
calculates the magnitude of the spectral peak at the second
harmonic of the shaft rotating frequency and compares it
with reference baseline case (taken under well defined normal operating conditions with the rotorcraft in known good
condition). When the SP2 exceeds certain predefined limits
compared to the baseline, the “Caution” or “Exceeded” status
of this CI are designated. However, this CI can not specify
whether the fault is misalignment or unbalance.
Table 3. Comparison with baseline case in terms of NNLHI
(dB)
For the sake of discussion, we recall that the comparison
with the baseline is usually done on a logarithmic amplitude
scale with increases of 6-8 dB considered to be significant
and changes greater than 20 dB from the baseline considered
serious [17]. Table 2 summarizes the results of the spectral
peak comparison of the three faulted cases (10321, 20321,
and 30321) with the baseline case (00321) in terms of SP1,
SP2, and SP3. Values of spectral peaks at the first three
harmonics of the shaft rotating speed (1R, 2R and 3R) are
extracted from the averaged PSD plots in Figures 6 and 7,
and compared with the baseline case in logarithmic scale. It
is clear that values of the SP2 for all faulted cases exceed
the 6 dB threshold compared to the baseline and therefore it
provides a good Indicator for all of the three faulted cases.
However, SP2 has limited diagnostic capability to distinguish
between those health conditions of the shafts.
It is worthwhile to mention here that although bispectral
analysis provides a more accurate tool to diagnose different
faults compared to the conventional power spectral analysis,
this comes on the cost of computational resources and time.
6
6.
nance (CBM) Component Inspection and Maintenance
Manual Using the Modernized Signal Processor Unit
(MSPU) or VMU (Vibration Management Unit),” Aviation Engineering Directorate Apache Systems, Alabama,
Tech. Rep., Oct. 2010.
CONCLUSION
Bispectral analysis has been used to study vibration signals
from an AH-64 helicopter tail rotor drive-train. A normalized
version of the bispectrum has been proposed and then used
to compare between different seeded fault cases in the shafts
of the drive-train using hanger bearing vibrations. It has been
shown that using the bispectral analysis provides more details
about the spectral content of the vibration signal and how
different harmonics nonlinearly interact with one another.
Different faults have shown different harmonic interaction
patterns which have been used to design a diagnostic algorithm based on the number of nonlinear harmonic interaction
(NNLHI) in the vibration signal. The proposed indicator
has shown more diagnostic capability to differentiate between shafts misalignment/unbalace than the currently used
CI based on conventional spectral peak comparison. The
tradeoff of the proposed technique is its higher complexity
and computational cost. Current work is focusing on the
application of bispectral analysis to study vibrations from the
intermediate and tail rotor gearboxes in the AH-64 helicopter
tail rotor drive-train.
[7] N. Goodman, and A. Bayoumi, “Fault Class Identification Through Applied Data Mining Of Ah-64 Condition
Indicators,” Proceedings of AHS 66th Annual Forum and
Technology Display, May 2010.
[8] P. Grabill, J. Seale, D. Wroblewski, and T. Brotherton,
“iTEDS: the intelligent Turbine Engine Diagnostic System,” Proceedings of 48 International Instrumentaion
Symposium, May 2002.
[9] A. S. Sait, and Y. I. Sharaf-Eldeen, “A Review of Gearbox Condition Monitoring Based on vibration Analysis
Techniques Diagnostics and Prognostics,” in Rotating
Machinery, Structural Health Monitoring, Shock and
Vibration, Vol. 8, T. Proulx, Ed. New York: Springer,
2011, pp. 307-324.
ACKNOWLEDGMENTS
[10] P. D. Samuel, and D. J. Pines, “A review of vibrationbased techniques for helicopter transmission diagnostics,” Journal of Sound and Vibration, vol. 282, no. 1-2,
pp. 475-508, Apr. 2005.
This research is funded by the South Carolina Army National
Guard and United States Army Aviation and Missile Command via the Conditioned-Based Maintenance (CBM) Research Center at the University of South Carolina-Columbia.
Also, this research is partially supported by the Egyptian
government via the Government Mission Program for Mohammed Hassan, and National Science Foundation Faculty
Early Career Development (CAREER) Program as well as a
National Science Foundation Graduate Research Fellowship
for David Coats.
[11] Y. C. Kim, and E. J. Powers, “Digital bispectral analysis
and its application to nonlinear wave interactions,” IEEE
Transactions on Plasma Science, vol. 7, no. 2, pp. 120131, July 1979.
[12] S. Elgar, and R.T. Guza, “Statistics of bicoherence,”
IEEE transaction on Acoustics Speech and Signal Processing, vol. 36, no. 10, pp. 1667-1668, Oct. 1988.
R EFERENCES
[1] A. Bayoumi, N. Goodman, R. Shah, L. Eisner, L. Grant,
and J. Keller, “Conditioned-Based Maintenance at USC
- Part I: Integration of Maintenance Management Systems and Health Monitoring Systems through Historical
Data Investigation,” Proceedings of AHS International
Specialists’ Meeting on Condition Based Maintenance,
Huntsville, AL, Feb. 2008.
[2] A. K.S. Jardine, D. Lin, and D. Banjevic, “A review
on machinery diagnostics and prognostics implementing
condition-based maintenance,” Mechanical Systems and
Signal Processing, vol. 20, no. 7, pp. 1483-1510, Oct.
2006.
[3] A. Bayoumi, W. Ranson, L. Eisner, and L.E. Grant, “Cost
and effectiveness analysis of the AH-64 and UH-60 onboard vibrations monitoring system,” IEEE Aerospace
Conference, pp. 3921-3940, Mar. 2005.
[4] A. Bayoumi, and L. Eisner, “Transforming the US Army
through the Implementation of Condition-Based Maintenance,” Journal of Army Aviation, May 2007.
[5] V. Blechertas, A. Bayoumi, N. Goodman, R. Shah, and
Yong-June Shin, “CBM Fundamental Research at the
University of South Carolina: A Systematic Approach to
U.S. Army Rotorcraft CBM and the Resulting Tangible
Benefits,” Proceedings of AHS International Specialists’
Meeting on Condition Based Maintenance, Huntsville,
AL, Feb. 2009.
[6] Damian Carr, “AH-64A/D Conditioned Based Mainte-
[13] T. Kim, W. Cho, E. J. Powers, W. M. Grady, and A.
Arapostathis, “ASD system condition monitoring using
cross bicoherence,” 2007 IEEE electricship technologies
symposium, pp. 378-383, May 2007.
[14] B. Jang, C. Shin, E. J. Powers, and W. M. Gardy,
“Machine fault detection using bicoherence spectra,”
Proceeding of the 21st IEEE Instrumentation and Measurement Technology Conference, vol. 3, no. 1, pp. 16611666, May 2004.
[15] D. Coats, Cho Kwangik, Yong-June Shin, N. Goodman, V. Blechertas, and A. Bayoumi, “Advanced TimeFrequency Mutual Information Measures for ConditionBased Maintenance of Helicopter Drivetrains,” IEEE
Transactions on Instrumentation and Measurement, vol.
60, no. 8, pp. 2984-2994, Aug. 2011.
[16] J. D. Gibbons, “Nonparametric Methods for Quantitative Analysis,” Columbus, Ohio: American Sciences
Press, 1985.
[17] R. B. Randall, “Fault Detection,” in Vibration-based
Condition Monitoring: Industrial, Aerospace and Automotive Applications, Wiley, 2011.
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B IOGRAPHY [
Abdel E. Bayoumi is Director of the
USC Biomedical Engineering Program
and Professor of Mechanical Engineering at the University of South CarolinaColumbia. He chaired the Department
of Mechanical Engineering from 1998
through 2006. Before joining USC,
he was a Professor and Director of the
Manufacturing Program at North Carolina State University-Raleigh, North
Carolina (1996-1998); Assistant, Associate, Professor, and
Distinguished Boeing Manufacturing Professor at Washington State University (1983-1996); a Project Manager at
Hewlett-Packard Company-Corvallis, Oregon (1993-1995 on professional leave from WSU); and a visiting scholar for
a year at the American University in Cairo (AUC) - Egypt
(1991-1992 - a sabbatical leave from WSU). During his
tenure at the University of South Carolina, North Carolina
State University, Washington State University, the American
University in Cairo, and Hewlett-Packard Company, Dr. Bayoumi has been actively involved in developing strong research
and educational programs. His current areas of interest can be
grouped into three categories, (1) Study of Condition-Based
Maintenance (CBM) of military aircraft in which diagnosis,
prognosis and health monitoring systems are effectively utilized using informatics and sensing technologies, (2) MicroElectro Mechanical Systems (MEMS) and Mechatronics in
which a MEMS device is designed, fabricated and used to
sense and control mechanical or biological systems, and (3)
Design and applications of efficient energy resources and
system.
Mohammed A. Hassan received the
B.S. degree with honors in Electrical
Engineering from Cairo University Fayoum Campus, Fayoum, Egypt, and the
M.S. degree in Electronics and Communication Engineering from Cairo University, Cairo, Egypt, in 2001 and 2004,
respectively. He is currently pursuing his
PhD degree in the Electrical Engineering
department at the University of South
Carolina. His current research interests include advanced
digital signal processing techniques: time-frequency analysis
and higher order statistical signal processing, and its application in condition based maintenance.
David Coats is pursuing his doctoral
degree in Electrical Engineering at the
University of South Carolina-Columbia.
He received his B.S. degree with summa
cum laude honors from the University of
South Carolina, and he was the recipient of the NASA EPSCoR Undergraduate Scholarship, Magellan Scholar, and
Valedictorian Scholars awards. His undergraduate research efforts culminated
in receipt of the National Science Foundation Graduate Research Fellowship in 2010. His research interests include
power electronics, condition based maintenance in aging aircraft and aerospace components, and digital signal processing
in cable diagnostics.
Kareem Gouda is a graduate research
assistant at the Condition Based Maintenance (CBM) research Centre, University of South Carolina (USC). He is
currently pursuing a doctoral degree in
Mechanical Engineering. Kareem had
his BS in Chemical Engineering. As an
disciplinarian, Kareem’s research focus
is on lubrication analysis and gearbox
health monitoring for the improvement
of the Condition Indicators (CIs) of the AH-64 drive train
gearboxes.
Yong-June Shin received his B.S. degree from Yonsei University, Seoul, Korea, in 1996 with early completion honors and the M.S. degree from The University of Michigan, Ann Arbor, in 1997.
He received the Ph.D. degree from the
Department of Electrical and Computer
Engineering, The University of Texas at
Austin, in 2004. Upon his graduation,
he joined the Department of Electrical
Engineering, The University of South Carolina in which he
is now an Associate Professor. His area of research is power
engineering/power electronics, with emphasis on power quality and harmonics. His research interests include advanced
signal processing theory: time-frequency analysis, wavelets,
and higher order statistical signal processing. He is a recipient
of National Science Foundation CAREER award in year 2008
and GE Korean- American Education Commission scholarship.
8