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International Journal of Prognostics and Health Management, ISSN 2153-2648, 2013 021
Targeting Faulty Bearings for an Ocean Turbine Dynamometer
Nicholas Waters1
, Pierre-Philippe Beaujean2
, and David J. Vendittis3
1,2,3
Florida Atlantic University, 777 Glades Rd, Boca Raton, FL, 33431, USA
ncwaters1@gmail.com
pbeaujea@fau.edu (corresponding author)
dvendittis@aol.com
ABSTRACT
A real-time, vibrations-based condition monitoring method
used to detect, localize, and identify a faulty bearing in an
ocean turbine electric motor is presented in this paper. The
electric motor is installed in a dynamometer emulating the
functions of the actual ocean turbine. High frequency modal
analysis and power trending are combined to assess the
operational health of the dynamometer’s bearings across an
array of accelerometers. Once a defect has been detected,
envelope analysis is used to identify the exact bearing
containing the defect. After a brief background on bearing
fault detection, this paper introduces a simplified
mathematical model of the bearing fault, followed with the
signal processing approach used to detect, locate, and
identify the fault. In the results section, effectiveness of the
methods of bearing fault detection presented in this paper is
demonstrated through processing data collected, first, from a
controlled lathe setup and, second, from the dynamometer.
By mounting a bearing containing a defect punched into its
inner raceway to a lathe and placing an array of
accelerometers along the length of lathe, the bearing fault is
clearly detected, localized, and identified as an inner
raceway defect. Through retroactively trending the data
leading to the near-failure of one of the electric motors in
the dynamometer, the authors identified a positive trend in
energy levels for a specific frequency band present across
the array of accelerometers and identify two bearings as
possible sources of the fault.
1. INTRODUCTION
The Southeast National Marine Renewable Energy Center
(SNMREC) is developing an Ocean Turbine (OT) that is
capable of harnessing some of the energy contained in the
Florida Current (Driscoll, 2008). Autonomy and minimal
maintenance are of the utmost importance due to the high
cost of accessing the OT for maintenance. By creating a
self-diagnostic program capable of not only identifying the
occurrence of a fault, but evaluating its severity and
localizing it, said maintenance costs could be significantly
reduced.
In addition to proper prognoses, early detection is critical
due to the rapid deterioration of mechanisms under
unexpected loads. Through vibrational analysis, which has
been used to effectively detect and diagnose faults within
other rotating machinery, one can achieve a level of
awareness associated with the type of fault occurring, its
location, and a relative level of severity. This information
can then be used to determine whether maintenance is
pertinent to prevent further damage to the system (Jayaswal,
Wadhwani, & Malchandani, 2008).
SNMREC has also developed a dynamometer to emulate
some of the electrical and mechanical features of the OT. To
do so, the dynamometer mimics the loads of the ocean
current acting on the shaft connected to an electric
motor/generator. A program, the Smart Vibrations
Monitoring System (SVMS), was created by Mjit, Beaujean,
and Vendittis (Mjit, Beaujean, & Vendittis, 2011) for
autonomous online monitoring of the dynamometer. SVMS
is implemented using LabVIEW. The program uses such
methods of fault detection and identification as Power
Spectral Density (PSD) analysis, fractional octave analysis,
kurtosis, cepstrum, and time waveform analysis (Mjit,
2009). The SVMS program was designed following the
standards outlined by the International Standards
Organization (ISO) on vibration condition monitoring (ISO,
2002; ISO, 2005) and, as such, the procedure for the high
frequency analysis of the vibration signal outlined in this
paper is carried out following the same guidelines.
The methods presented in this paper are implemented on an
OT dynamometer, which operates on the same principal as
wind turbines. Not unlike OTs, accessing wind turbines for
maintenance can be difficult and costly. Thus, application of
_____________________
Nicholas Waters et al. This is an open-access article distributed under the
terms of the Creative Commons Attribution 3.0 United States License,
which permits unrestricted use, distribution, and reproduction in any
medium, provided the original author and source are credited.

INTERNATIONAL JOURNAL OF PROGNOSTICS AND HEALTH MANAGEMENT
2
the methods outlined in this paper could greatly serve to
minimize maintenance costs in the wind turbine sector of
engineering. The methodology of detecting, localizing, and
identifying is described in a manner to allow for
straightforward application to wind turbines.
The terms detection, localization and identification are
defined as follows: detection refers to detecting the presence
of a bearing with a raceway defect as the defect forms,
localization refers to localizing the faulty bearing location
with respect to the position of the array of accelerometers
placed along the length of the dynamometer, and
identification refers to identifying the exact defective
bearing and raceway.
The approach outlined in this paper relies on analysis of the
high-frequency component of vibrations over an array of
accelerometers placed along the length of the dynamometer.
The vibrations (measured as an acceleration) caused by a
defect in the inner or outer raceway of a given bearing is an
amplitude-modulated signal (McFadden & Smith, 1984).
As each ball within a given bearing rolls over the defect, it
causes a spike in the acceleration signal, which can be
unidentifiable in the time waveform due to background
noise and vibrations caused from other rotating components
(gears, other bearings, etc.). This spike is modulated by the
modes of vibration of the structure and the uneven load on
the shaft (McFadden & Smith, 1984).
Ideally, the resulting vibrations from the bearing defect
alone would appear as an exponentially decreasing
sinusoidal curve (Sheen, 2007). The difficulty in application
of this faulty bearing detection method to the dynamometer
mainly resides in identification of the faulty bearing, in the
overall structural vibrations due to the multiple rotating
components contributing to the vibration signature and slow
rotational speeds leading to low signal to noise ratios. To do
so, narrow-band envelope analysis is used to isolate several
high-frequency modes of vibration (Sheen, 2004). This
envelope analysis is performed on the vibration data
collected across the array of accelerometers.
Bearing fault detection is carried out by trending the average
power levels for specific frequency bands and for each
accelerometer. In addition to trending average power levels,
envelope power levels are computed across the array of
accelerometers. An envelope power threshold is determined
for each accelerometer’s envelope power signal to further
detect the presence of a faulty bearing.
Localization of the faulty bearing with respect to placement
of each accelerometer is performed by comparing the
average power levels computed over specific frequency
bands for the entire array of accelerometers. The
accelerometer with the highest average power level for a
given frequency band is selected as the closest to the faulty
bearing location, if the power level for this frequency band
across the remaining accelerometers is significantly lower.
Identification of a bearing raceway defect is accomplished
through demodulation of each accelerometer’s signal about
predetermined frequency bands, which allows for periodic
impacts in the vibration signal to be clearly observed in the
presence of a bearing with a raceway defect.
In the following section, this paper introduces a simplified
mathematical model to provide a rudimentary understanding
of the physics involved in the vibrations caused by ball
bearings periodically coming in contact with a raceway
defect. This model is also used to justify the assumption that
the acquired vibrations due to bearing defects are the result
of modulation. This model is also used to explain how the
process of demodulation will be utilized to indicate which
bearing is defective. Next, the signal processing approach
used to detect, localize, and identify the fault is presented.
Lastly, the approach is illustrated through a series of
experimental data collected from a controlled lathe setup
with a faulty bearing and from data collected from the
dynamometer over the course of several weeks, leading up
to a bearing failure.
2. SCIENTIFIC APPROACH
In this section, the authors introduce a simplified mathematical
model describing the vibrations caused by a bearing with an
inner raceway defect. This model relies on many assumptions
that are summed up in the concluding section. This model is
introduced solely to provide a very rudimentary understanding
of the vibrations caused by the periodic impact of a ball coming
in contact with a defect along the inner raceway of a bearing. It
is also introduced to justify the use of the Hilbert transform
demodulation technique used to identify the faulty bearing
(Section 3.3).
As a first approach to modeling the vibrations induced by
bearing raceway defects, we first consider the vibrations caused
by a single ball bearing rolling over a single defect in the inner
raceway. The forces acting on a single roller bearing are
depicted in Figure 1.
Figure 1. A shaft with a single ball bearing and a single
defect on the inner raceway.

3
The vertical force vector q0
represents the loading due to
the mass of the shaft and bearing. q is the angle measured
from the vertical to the center of the defect. The vector mb
g
represents the force due to gravity acting on the ball. The
vector q(q) represents the x-component of the shaft and
bearing loading acting on the ball as it passes over the inner
raceway defect. The vectors êr
and êt
represent the radial
and tangential unit vectors along the x and y axes,
respectively. Through analysis of the equivalent lumped
parameter model, the displacement for a single impact and
mode of vibration n is described by,
xn
(t) = Xn
e
-w0,n znt
cos(wd,n
t -f0,n
)u(t), (1)
where Cn is the amplitude of the displacement for mode n
at time t 0 . w0,n
is the natural angular frequency. xn is
the damping ratio (we assume the system is underdamped,
so that xn 1). wd,n is the damped natural angular
frequency. f0,n
is the initial phase for this mode and
u(t) is a unit step function introduced into the equation, as
this system is causal.
Assuming that every ball is identical and accounting for all
the modes of vibration, multiple balls passing over the
defect, and all the modes of vibration,
x(t) =
n=1
Ns
å
k=-¥
¥
å
Xn
(kTd
)e
-w0,nzn t-kTd( )
u(t - kTd
)
ćos wd,n
t - kTd( )-f kTd( )é
ë
ù
û
æ
è
ç
ç
ö
ø
÷
÷
. (2)
Here, Td is the period of rotation for a single ball, KTd is the
time delay associated with the kth
impact, and Ns is the total
number of modes of vibration. Differentiating Eq. (2) twice
yields the equation that describes these vibrations in terms
of acceleration.
 
   
0,
,
1 ,
( )
( )
cos
n n d
s
t kTN
n k d
n k d n d n d
A e u t kT
a t
t kT kT
 
 
 

 
 
 
      
  . (3)
Equation (3) assumes that the accelerometer is placed
directly over the source of vibrations. Since there is some
signal loss in the vibrations as they propagate through the
structure, new constants are introduced into Eq. (3) to
account for this signal attenuation: HC1
, HT
, HC2
, and HG
(Figure 2) represent the complex loss coefficients (or
transfer functions) associated with the faulty bearing, first
coupler, torque meter, second coupler, and gearbox,
respectively. Note that these coefficients change with the
natural angular frequency w0,n .
Also, the symbol a(1)
is used to denote the acceleration
measured over the faulty bearing. a(mi )
represents the
acceleration measured at a distance d from the faulty
bearing location.
Figure 2. Simplified diagram of dynamometer components
and associated loss coefficients.
For the acceleration measured at location im on the
dynamometer, ( )im
 represents the modal attenuation of the
vibrations,
b(m i )
= e
-wd,nxntd,n
(m i )
H(mi )
. (4)
The parameter H(mi )
is defined according to Eq. (5),
H
(mi )
=
HC1
× HT
, for i =1
HC1
× HT
× HC2
× HG
, for i = 2
ì
í
ï
î
ï
. (5)
Thus, accounting for signal attenuation due to the vibrations
propagating through the structure, the acceleration at
location mi is defined according to Eq. (6),
( )
( )im
a t 
n=1
Ns
å
k=-¥
¥
å
b(mi )
An,k
(1)
e
-w0,nxn t-kTd( )
u t - kTd( )
ćos wd,n
t - kTd( )- ¢fn
(1)
kTd( )é
ë
ù
û
æ
è
ç
ç
ö
ø
÷
÷ .
(6)
According to Eq. (6), the maximum observed acceleration
for an accelerometer placed along the length of the
dynamometer will be ( ) (1)
,
im
n kA . In order to determine
which bearing is the source of the fault, demodulation of the
acquired vibration signal is needed, which yields the
envelope. The envelope of Eq. (6), is defined by the leading
terms b(m i )
An,k
(1)
e
-w0,nxn t-kTd( )
u t - kTd( ). From the envelope, the
period between impacts can be determined, indicating which
bearing is the source of the defect and whether or not it is
within the inner or outer raceway of this bearing.
3. SIGNAL PROCESSING
The methodology used to detect, localize and identify
bearing raceway faults are presented in section 4. This
methodology refers to several signal processing tools
presented in this section.

4
3.1. PSD and Coherency
We define r mi( )
t( ) as output of accelerometer mi collected
on a specific day. r(mi )
(t) represents the measurement
equivalent of a(mi )
(t). We estimate the one-sided PSD of
r(mi )
(t) as ˆGr(mi ) (w) of the accelerometer output r(mi )
(t)
through block averaging (Ifeachor & Jervis, 2002), using
Blackman windows and 50% overlap. The window length
depends on the mode of vibration studied. ˆGr
( m i ) (w) is used
to identify the bands that contain the natural angular
frequencies described in the previous section.
The coherency estimate ˆg
r
( m i )
r
(m j ) (w) between the
accelerometer outputs ( )
( )im
r t and ( )
( )jm
r t indicates, as a
function of the angular frequency, the fraction of power
originating from the same physical process,
( )( )
( )( )
( ) ( )
2
ˆ ( )
ˆ ( )
ˆ ˆ( ) ( )
mm ji
mm ji
m mi j
r r
r r
r r
G
G G

 
 
 . (7)
( )( )
ˆ ( )mm jir r
G  is the one-sided Cross Spectral Density (CSD)
between the accelerometer outputs ( )
( )im
r t and ( )
( )jm
r t . The
coherency is a dimensionless, frequency-dependent function
that varies between 0 and 1. For a specific angular
frequency, a coherency value of 1 indicates that the
vibration measured by the two accelerometers originates
from the same physical process. ( )( )
ˆ ( )mm jir r
G  is estimated
with the same block averaging routine used for the PSD
estimate.
3.2. Power and Confidence Interval
Power-trending is performed across the period of data
acquisition (an illustration of the trending process is shown
in section 4.2). For each day of data acquisition, the
estimated power is calculated within every predetermined
frequency band
2 2
n n
n n
 
  
 
    and for every
accelerometer mi ,
( )
2
,
2
ˆ ˆ ( ) .
n
n
m ii
n
n
m n r
G d




 




   (8)
The confidence interval for a given confidence level for this
power level estimate is calculated as shown in Eq. (9),
, ,
,
2 2
1
, ,
2 2
ˆ ˆ
1 Pr i i
i
m n m n
m n
v v
v v
 

 
 
  
     
 
 
. (9)
,im n is the true average power across the same frequency
band, wv K Q is the degree of freedom ( wK is the window
scaling factor; Q is the number of block averages used to
calculate ˆGr(mi ) (w) ) and c2
is the chi-square distribution).
3.3. Envelope Analysis
Theoretically, the complex envelope of the acceleration
measured at accelerometer mi for mode n is of the form
shown in Eq. (10).
an
mi( )
(t) = b(mi )
An,k
(1)
e
-w0,nxn t-kTd( )
u t - kTd( ). (10)
This complex envelope contains valuable information
regarding the time signature of every mode as a function of
the sensor location.
As mentioned earlier, the actual measured acceleration is
( )
( )im
r t . In this paper, the authors use the Hilbert transform
of the measured acceleration to isolate the envelope of
individual modes of vibration (demodulation of the signal).
To do so, discrete Finite Impulse Response (FIR) filters are
designed for every frequency band
2 2
n n
n n
 
  
 
    . The discrete filter response for
each band is labeled  
 R
nh t (for the real part) and  
 I
nh t
(for the imaginary part). The estimated complex envelope
at accelerometer mi for mode n, denoted by ˆan
(mi )
(t), is the
circular convolution between  
   
  R I
n nh t jh t and ( )
( )im
r t
ˆan
mi( )
(t) = r mi( )
t( )Ä hn
R( )
(t)+ jhn
I( )
(t)( ). (11)
4. METHODOLOGY
In this section, the staged approach to detecting, localizing,
and identifying a growing raceway defect in a bearing is
presented. It is important to note that these methods are
performed under steady state conditions and at constant
shaft rotational speeds for the dynamometer.
4.1. Dynamometer’s impulse response and frequency
band selection
The dynamometer’s impulse response is measured to isolate
the best frequency bands for the fault detection process.
Here, the dynamometer does not rotate. Vibrations are
produced across the array of accelerometers by striking the
dynamometer with a calibrated hammer directly next to one
of the accelerometers. The hammer strikes are administered
such that vibrations are observed across the entire array of
accelerometers without signal clipping. Also, the period
between the hammer strikes is large enough to prevent

5
signal overlap between vibrations due to subsequent
impacts.
As the dynamometer is struck, structural resonances are
excited, leading to peaks in the PSD of the vibration signals
acquired by the accelerometers (estimated as described in
section 3.2). In order to maximize the signal-to-noise ratio
(SNR) in this PSD estimate, the dead time between strikes is
minimized by cropping and concatenating the collected data
about sections of the signal containing each impact and the
resulting vibrations produced. As a result, the strikes appear
at even intervals (approximately 0.2 seconds in length). The
PSD is estimated for each accelerometer, using the same
window length of 0.2 seconds.
Frequency bands in the PSD that preferably show a single
peak for two accelerometers are initially considered for
analysis. Each frequency band identified for modal analysis
is selected for trending of average power levels based on the
following criteria:
 The frequency band is preferably located in the upper
frequency range to (a) avoid low frequency
interferences transmitted through the floor and
conduits; (b) accentuate the high frequency attenuation
of a signal due to the accelerometers spacing.
 The frequency band shows high coherency (Eq. (7))
between accelerometers (i.e. the coherency is close to
1).
 If possible, the frequency band isolates a single peak in
the PSD (no modal overlap).
 We can clearly observe the decrease in in-band power
(Eq. (8)) across the array of accelerometers as the
distance from the strike to the accelerometer increases.
 The frequency band contains sufficient damping to
prevent overlap between decaying impulse responses.
4.2. Detection: Envelope Power
Detection refers to determining whether the vibrations
propagating through the structure are characteristic of the
presence of a faulty bearing. The process of detecting a
faulty bearing is carried out at constant shaft rotational
speed, once the system has reached steady state conditions.
Thresholds are established for each accelerometer’s
envelope power signal, as a cap for healthy vibration
signals. As a result, vibration levels exceeding the threshold
would be indicative of a fault occurring within the system.
In order to establish thresholds, each accelerometer’s signal
is demodulated by applying Hilbert filters about frequency
bands satisfying the frequency band criteria and the
envelopes are extracted for each set of data. For each
accelerometer’s demodulated signal, the envelope power is
computed as an instantaneous power according to Eq. (12),
Pn
( m i
)
(t) =
rn
( m i
)
(t)
2
Ts
, (12)
where Ts
is the sampling period. When thresholding the
subscript healthy is introduced to the envelope power and
envelope signals, i.e. P
(mi )
n,healthy
(t) and r
( mi
)
n,healthy
(t) , to denote
that the data used for thresholding is acquired while the
system is operating under healthy operating conditions. The
mean of each accelerometer’s envelope power is computed
and thresholds are set for each accelerometer’s healthy
envelope power such that inequality (13) holds.
P
( mi
)
n,healthy
(t) < Thrn
( mi
)
´ P
( mi
)
n,healthy
, "t (13)
Pn,healthy
(mi )
is the mean value of the healthy envelope power
for the isolated mode(s) of vibration n and accelerometer
mi
,
P
( mi
)
n,healthy
= E
r
( mi
)
n,healthy
(t)
2
Ts
é
ë
ê
ê
ù
û
ú
ú
. (14)
Thn
( m i
)
is a constant chosen based on the accelerometer and
mode(s) of vibration for the given envelope signal such that
the healthy envelope power, when normalized with respect
to the mean of the healthy envelope power, does not exceed
this constant value for all time.
The constant Thn
( m i
)
is also chosen such that inequality (13)
is valid for the smallest value of Thn
( m i
)
that allows for slight
transients in the healthy vibrations envelope power, but
vibrations due to any sort of defect, exceed the threshold
Thrn
( m
i
)
´ Õn ,healthy
( m
i
)
in envelope power.
Once thresholds have been determined for each
accelerometer and isolated mode(s) of vibration, each
accelerometer’s envelope power is plotted against its
respective envelope power threshold for the isolated
mode(s) of vibration, Thn
( mi
)
´ Pn,healthy
( mi
)
.
Envelope power levels that exceed the thresholds are
averaged to obtain the average excess power level per time
that exceeds the threshold for the accelerometer and
mode(s) of vibration. This average envelope power level is
denoted by Pn,exceed
( m i
)
.

6
Figure 3. Zoomed in portion of an accelerometer’s envelope
power for mode of vibration n.
For the envelope power signals depicted in Figure 3, Pn,exceed
( m i
)
is defined according to Eq. (15)
Pn,exceed
( m i
)
=
rn
( mi
)
(t)
2
j= j1
l1
å + ...+ rn
( m i
)
(t)
2
j= j4
l4
å
(l1
- j1
+1) + ...+ (l4
- j4
+1)[ ]Ts
. (15)
For each accelerometer’s envelope power, if there is no fault
occurring on the dynamometer, then Pn,exceed
( m i
)
= 0 indicating
that the system is healthy.
It is important to note that effective thresholds are
established over some period of observation with the system
operating under healthy operating conditions and once it has
reached steady state conditions for a given shaft rotational
speed. In order to avoid false alarms due to transients in the
vibration signal resulting from impacts unrelated to
mechanical failure (e.g., fish impacts) it is important to
monitor the average envelope power level over multiple
data sets. An alarm will be triggered assuming that the
average envelope power is greater than zero for consecutive
data sets.
4.3. Detection: Trending
In addition to thresholding the envelope power levels for
detecting the presence of a fault, average power levels
across predetermined frequency bands are trended to
indicate a worsening condition:
1. The dynamometer is operated at various shaft rotational
speeds. For each rotational speed, the power level
within every predetermined frequency band is
computed across the array of accelerometers, along
with the confidence interval for each power level.
2. Each average power level is compared to its respective
baseline average power level for the given shaft
rotational speed.
3. Measurements are repeated over the course of weeks to
determine whether the power levels across any of the
frequency bands increases for any of the accelerometers
over time.
4. If an upward trend in the power levels for any of the
frequency bands appears across at least the majority of
accelerometers and if the power levels approach or
exceed an upper threshold, then there is a fault
occurring (Figure 4).
Figure 4. Trending of the average power levels over the
course of weeks to detect presence of a faulty bearing.
4.4. Localization
Localization refers to determining the proximity of the
faulty bearing location to the accelerometer placement
(Figure 5). It is carried out at constant shaft rotational
speed, under steady state conditions, and once the presence
of a faulty bearing has been detected.
1. The power levels for specified frequency bands are
computed for each accelerometer.
2. If an accelerometer acquires data with the highest
power level within the frequency band and if for the
same frequency band, the remaining accelerometers
show a decrease in the power level as their distance
increases, then this accelerometer is closest to the
defect.
Figure 5. Localization of a faulty bearing based on
comparing power levels for one frequency band and RPM
across the array of accelerometers.

7
4.5. Identification
Identification refers to determining the exact bearing
containing the raceway defect. Again, the following
procedure (also depicted in Figure 6) is performed under
constant shaft rotational speeds, under steady state
conditions, and once a faulty bearing has been detected:
1. Envelope analysis on the acquired vibration signals is
performed within the specified frequency bands and
across the array of accelerometers. From the envelope
the period between impacts due to balls coming in
contact with the defect is determined.
2. The period between impacts, denoted Timpact
, should
correspond to the Ball Pass Frequency for the inner
raceway (BPFI) or outer raceway (BPFO) of one of
the dynamometer’s bearings (Randall & Antoni, 2011).
These frequencies are defined as,
fo,bi
=
NB,bi
2
fr
1-
DB,bi
cos(qbi
)
DP,bi
æ
è
ç
ö
ø
÷ (16)
fi,bi
=
NB,bi
2
fr
1+
DB,bi
cos(qbi
)
DP,bi
æ
è
ç
ö
ø
÷
(17)
fo,bi
is the impact frequency for an outer raceway defect
(BPFO) in bearing bi
. fi,bi
is the impact frequency for an
inner raceway defect (BPFI) in bearing bi
. NB,bi
is the
number of balls within the bearing. fr
is the rotational
speed (in Hz) of the inner raceway, relative to the outer
raceway. DB,bi
is the ball diameter. DP,bi
is the ball pitch
diameter. qbi
is the ball contact angle (which is zero). The
ball pitch diameter is calculated as,
DP,bi
=
Ii,bi
+ Io,bi
2
æ
è
ç
ö
ø
÷ (18)
Ii,bi
and Io,bi
are the maximum diameter of the inner race
and maximum diameter of the outer race, respectively.
Although this paper focuses on detecting bearing raceway
faults, application of this methodology to identify a bearing
cage faults or ball defects, simply involves calculating the
Fundamental Train Frequency (FTF) or Ball Spin
Frequency (BSF) and comparing the impact frequency
extracted from the analytic signal to these two values.
Without providing any experimental evidence to validate the
claim, the authors anticipate the application of this bearing
fault detection technique to work for bearing cage faults and
ball defects. However, experimental justification is left for
future work.
Figure 6. The period between subsequent impacts found
from the modulus of the analytic signal formed by Hilbert
filtering around a specified frequency band.
Equations 19 and 20 describe calculation of the FTF and
BSF.
fC,bi
=
fr
2
1-
DB,bi
cos(qbi
)
DP,bi
æ
è
ç
ö
ø
÷ . (19)
fBS,bi
=
DP,bi
2DB,bi
1-
DB,bi
cos(qbi
)
DP,bi
æ
è
ç
ö
ø
÷
2
ì
í
ï
îï
ü
ý
ï
þï
. (20)
fC,bi
is the impact frequency for a cage defect in bearing bi
and fBS,bi
is the impact frequency for a ball defect within
bearing bi (Randall & Antoni, 2011).
The assumptions that are made for the methodology
described in this section are as follows:
 The system is operating at a constant shaft rotational
speed and there is minimal speed fluctuation.
 The system has reached steady state conditions.
 Thresholds for alarms are established while the system
is operating void of any defects.
A flowchart describing the overall process of detection,
localization, and identification of a bearing fault is provided
in Figure 7.
5. RESULTS
In the first set of experimental results, effectiveness of the
methods outlined in this thesis are demonstrated by
detecting, localizing, and identifying a bearing with a
raceway defect punched into its inner raceway. Each of the
steps involved in the process outlined in this thesis are
clearly demonstrated for straightforward application to the
dynamometer. In Experiment II, data leading up to a yet to
be determined fault occurring on the dynamometer was
retroactively trended. Prior to currently ongoing

8
maintenance on the dynamometer, it was possible to trend
data previously acquired and observe an increase in average
power levels for one of the frequency bands identified from
studying the impulse response of the system.
Figure 7. Bearing fault detection, localization, and
identification flowchart.
5.1. Experiment I: Controlled Lathe Setup
A tachometer, as well as a plastic collar with an
accelerometer fixed to its top surface that allowed for
interchanging of bearings, were fixed to the shaft of the
lathe (Figure 8). Four accelerometers were used to acquire
vibrations along the length of the lathe. Accelerometers 1 to
3 were high frequency accelerometers with frequency
responses ranging from 0.5 to 10,000 Hz (at ±3 dB), while
accelerometer 4 was a low frequency accelerometer with a
frequency response ranging from 0.2 to 3,000 Hz (at
±3 dB).
By collecting the vibrations across an array of
accelerometers with a healthy bearing (void of known
defects) in place, a baseline was established. A second
identical bearing was carefully disassembled and had a
defect punched into its inner raceway (referred to as the bad
bearing). Due to the large manufacturer tolerances for the
two bearings, even the healthy bearing produced a large
amount of vibrations. In order to get a better idea of the
background noise in the acquired signals for the healthy and
bad bearings, a steel bearing (referred to as the ideal
bearing) with much tighter manufacturer tolerances was
mounted to the lathe and the vibrations were acquired along
the array of accelerometers. The bearings used for the
healthy and bad bearings in this experiment were stainless
steel ball bearings with polymer ball cages, which allowed
for simple disassembly with nothing more than hand
pressure.
Figure 8. Lathe experimental setup.
The system was excited using calibrated hammer strikes
administered next to accelerometer 1 and the impulse
response for the system was studied (Figure 9).
Figure 9. Time waveform of hammer impacts for
accelerometers 1 (top) and 2 (bottom).

9
Time windows of length 0.182 seconds (4096 points), were
taken about each hammer impact to form the impacts signal
for the PSD and coherency estimates (Figure 10). The
frequency band 439-1126 Hz, proved to have the steepest
modal attenuation for the envelope with the most separation
between impact vibrations and background noise.
Figure 10. PSD for accelerometers 1 (top) and 2 (middle)
and coherency between accelerometers 1 and 2 (bottom).
Following analysis of the PSD and coherency between
accelerometers 1 and 2, the time waveform of the vibration
signals was demodulated for the two accelerometers to
check the modal decay for this frequency band (Figure 11).
Figure 11. Demodulated signals for accelerometers 1 (top)
and 2 (bottom) for the frequency band of 439-1126 Hz.
Following acquiring the vibrations across the array of
accelerometers for the impulse response of the system,
vibrations were collected for the healthy bearing, bad
bearing, and the ideal bearing for a shaft rotational speed of
120 RPM (Figure 12). Data are sampled at a sampling rate
of 22.5 kHz and each set of processed data was of 39.5
seconds in length. An 8-pole low-pass filter was applied to
the data with an edge frequency of 10 kHz.
With the healthy bearing in place, each accelerometer’s
envelope power was plotted for the Hilbert filtered
frequency band of 439-1126 Hz and thresholds were set at
Thi
´ Pn,healthy
( mi
)
(for i = 1, 2, 3, or 4) above the maximum
observed envelope power level. The constant Thi varied
depending on the accelerometer and was selected such that
the threshold was above the highest observed envelope
power level for each accelerometer and this frequency band,
as shown in Figure 13.

10
Figure 12. Time waveforms for the ideal bearing (green),
healthy bearing (yellow), and bad bearing (red) for
accelerometers 1 (top) and 2 (bottom).
Figure 13. Envelope power and envelope power thresholds
for accelerometers 1(top) and 2 (bottom) for the healthy
bearing.
Data was then acquired from the bad bearing and the
acquired vibration envelope power signals were plotted
against their respective envelope power levels. Envelope
power levels in excess can clearly be observed in Figure 14.
Figure 14. Envelope power levels acquired from the bad
bearing for accelerometers 1 (top) and 2 (bottom).
The results of summing the excess envelope power levels
across the array accelerometers for this demodulated
frequency band are summed up in the Table 1.
Accelerometer
number
Threshold
Thn
( mi
)
´ Pn
( mi
)
g
2
/ sec( )
Excess
Average
Envelope
Power
Pn,exceed
( m i
)
g
2
/ sec( )
1 3.110 x 104
1.089 x 105
2 3.159 x 102
6.663 x 102
Table 1. Average envelope power levels and thresholds for
bad bearing vibrations and accelerometers 1 and 2.

11
For the dynamometer, this would be the indication of the
presence of a fault occurring in the system. As a further
indicator of the presence of a fault occurring on the lathe, an
increase in the average power level for this frequency band
was observed across the array of accelerometers between
the healthy bearing data set and the bad bearing data set.
Figure 15. Average power levels across the frequency band
of 439-1126 Hz for accelerometers 1 (top) and 2 (bottom).
The increase in average power levels are summed up in
Table 2.
Accelerometer number
Percent increase in average
power level for frequency
band 439-1126 Hz
1 876 %
2 155%
Table 2. Increase in average power levels across the
frequency band of 439-1126 Hz for accelerometers 1 and 2.
Having detected the presence of a defect occurring on the
lathe, the next step was to localize this defect with respect to
the accelerometer placement. By plotting the increase in
average power levels across the array of accelerometers in a
single figure, localization of the fault to the position of
accelerometer 1 becomes apparent. The average power
levels across the frequency band 439-1126 Hz for the faulty
bearing data, along with their respective confidence
intervals are shown in Figure 16.
Figure 16. Average power levels with confidence intervals
for faulty bearing data and frequency band 439-1126 Hz for
accelerometers 1-4.
Accelerometer 1 showed the highest average power level for
this frequency band, with accelerometers 2-4 showing a
downward trend in power levels for this frequency band as
their distance from accelerometer 1 increased. Without prior
knowledge of the placement of the faulty bearing, Table 2
and Figure 16 make it apparent that the position of the faulty
bearing was closest to the placement of accelerometer 1.
Thus, by comparing the average power levels across the
array of accelerometers for a given frequency band, it was
possible to localize the position of the faulty bearing with
respect to the accelerometer placement to the position of
accelerometer 1.
Having detected the presence of a defect and localized its
position with respect to the accelerometer placement, the
next step was to identify the exact bearing and raceway the
defect corresponded to. From the envelope for
accelerometer 1 (Figure 17), the average period between
impacts was found to be 0.0914 seconds which corresponds
to an impact frequency of 10.94 Hz.
Figure 17. Envelope for bad bearing data acquired by
accelerometer 1 for with demodulation about the frequency
band of 439-1126 Hz.

12
The theoretical fault frequency for an inner raceway defect
within the bearing used for the experiment and for a shaft
rotational speed of 120 RPM was 10.86 Hz. Thus, the
defect was identified as an inner raceway defect with 0.74%
error.
5.2. Experiment II: Trending Data Leading to Fault on
the Dynamometer
The approach of detecting, localizing, identifying bearings
with raceway defects is illustrated through the analysis of a
series of experimental data collected over the course of a
month leading up to a fault in the dynamometer. By
retroactively trending the data leading to the near-failure of
one of the electric motors in the dynamometer, a positive
trend in energy levels for a specific frequency band was
observed, which was present across the array of
accelerometers and two bearings were identified as possible
sources of the fault. Shortly before the electric motor was
dismounted, excessive vibrations and sound radiation were
observed. The fault was then localized via a calibrated
stethoscope to the location of two of the dynamometer’s
bearings.
Data collected over the course of a month were processed
for accelerometers 3 and 5 (Figure 18) before the
dynamometer was disassembled and the electric motor was
sent for maintenance and repair.
Figure 18. Accelerometer placement on the dynamometer
and the location of the speculated faulty bearings.
The impulse response of the dynamometer was studied and
the frequency band of 278-463 Hz was identified as
satisfying the frequency band criteria (section 4.1). In
processing the data collected prior to detecting the fault, an
upward trend in the average power across the frequency
band of 278-463 Hz was observed (Figure 19).
Within the 278-463 Hz band, the data acquired by
accelerometer 3 showed an increase in averaged power level
of approximately 297% in four weeks, while accelerometer
5 showed an increase of approximately 321% over the same
time period. Given the confidence intervals shown in
Figure 19, these increases in power level are very significant
and clearly indicate a change in the structural response of
the dynamometer.
Figure 19. Average power levels across the frequency band
of 278-463 Hz for accelerometers 3 (top) and 5 (bottom).
The signal acquired by accelerometer 3 on the last day was
then demodulated about the same frequency band of 278-
463 Hz (Figure 20) and a periodic impact was noticed from
the envelope. The period between impacts was determined
to be 0.2761 seconds, which corresponds to an impact
frequency of approximately 3.62 Hz and closely matches the
impact frequency for the two motor bearings located at
position of accelerometer 3 (Figure 18).
Indeed, for a shaft rotational speed of 50 RPM, one bearing
would theoretically produce vibrations at an impact
frequency of 3.41 Hz (outer raceway defect), while the
second bearing would produce vibrations with an impact
frequency of 3.8 Hz (outer raceway defect). This is very
close to the impact frequency caused by a defect on the
outer raceway of two specific bearings. This periodicity in
the vibration signal was only observed in the data acquired
by accelerometer 3 which also indicated that one of the two
bearings in question contained a defect, since accelerometer
3 was placed directly over the speculated fault location
(Figure 18).

13
The maintenance on the dynamometer confirmed the
measurements. The two faulty bearings have since been
replaced.
Figure 20. Envelope for data acquired by accelerometer 3
from last day of data acquisition.
6. CONCLUSION
In this paper, a method of using an array of
accelerometer to detect the presence of bearing with a
raceway defect, localize its position with respect to the
placement of accelerometers, and identifying the exact
bearing and raceway to which the defect corresponds to has
been presented. The methodology outlined in this paper is
described for application to an ocean turbine dynamometer,
but is applicable to any rotating machinery containing
bearings.
The method outlined in this paper was carried out on a lathe
with a faulty bearing in order to demonstrate
implementation on a more ideal system, for straight forward
application to the more complex system, such as the
dynamometer. Following detecting the presence of the
defect, its position on the lathe was localized with respect to
the accelerometer placement. Lastly, the faulty bearing was
identified, in addition to the raceway the defect
corresponded to (inner raceway), with 0.74% error.
Next, the process of analyzing vibrations across an array of
accelerometers in order to specifically target bearing
raceway defects occurring on a dynamometer was
demonstrated. Through trending of the average power
within across a specific frequency band satisfying the
frequency band criteria, a growing defect occurring in the
dynamometer was detected. Following this, the defect was
localized relative to the accelerometer placement by
comparing the average power levels for the same frequency
band across the array of accelerometers. In addition, an
envelope analysis within this frequency band showed
periodic impacts, whose frequency of occurrence closely
matched the impact frequency (outer raceway) for two of
the motor bearings. The fault was also localized via a
calibrated stethoscope: this test supports the conclusions
obtained with the approach presented in this paper.
ACKNOWLEDGEMENT
This research was funded by the Southeast National Marine
Renewable Energy Center (SNMREC) at Florida Atlantic
University.
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BIOGRAPHIES
Nicholas C. Waters earned his
bachelor’s degree from the University of
California, Davis in Applied
Mathematics. In 2012, he received his
master’s degree from Florida Atlantic
University in Ocean Engineering under
the advisement of Dr. Pierre-Philippe Beaujean. His
graduate career field of study was focused on machine
condition monitoring and its application to an ocean turbine.
Nicholas is an active member of the Institute of Electrical
and Electronic Engineers (IEEE) and the Marine
Technology Society (MTS).

15
Pierre-Philippe J. Beaujean received the
Ph.D. degree in ocean engineering from
Florida Atlantic University in 2001. He is
an Associate Professor at the Department of
Ocean and Mechanical Engineering,
Florida Atlantic University. He specializes
in the field of underwater acoustics, signal
processing, sonar design, data analysis, machine health
monitoring, and vibrations control. Dr. Beaujean is an active
member of the Acoustical Society of America (ASA), the
Institute of Electrical and Electronic Engineers (IEEE) and
the Marine Technology Society (MTS).
Dr. David J. Vendittis [Ph.D. (Physics)
- American University, 1973] is a
Research Professor (part time) at the
Department of Ocean and Mechanical
Engineering, Florida Atlantic University.
Additionally, he is the Technical
Advisory Group (ASA/S2) chairman for an International
Standards Organization subcommittee, ISO/TC108/SC5 -
Machinery Monitoring for Diagnostics. This committee
writes international standards that support Machinery
Condition Monitoring for Diagnostics. He was appointed to
this position by the Acoustical Society of America (ASA)

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