I2MTC 2008 – IEEE International Instrumentation and
Measurement Technology Conference
British Columbia, Canada, May 12-15, 2008
Diagnostics and Prognostics of Electric Cables in Ship Power Systems
via Joint Time-Frequency Domain Reflectometry
Jingjiang Wang, Philip Crapse, Yong-June Shin, and Roger Dougal
Department of Electrical Engineering,
The University of South Carolina,
301 South Main St., Columbia, SC 29208, USA
Abstract – The integrity of the wiring in the electric power system of
a ship is vital to its safe operation. To ensure the wiring integrity,
it must be tested to determine if any incipient defects exist. Due to
this problem, a non-destructive, non-intrusive condition assessment
technique is highly desirable. Joint time-frequency domain reflec-
tometry (JTFDR) is proposed and the theory behind JTFDR is also
discussed. The experimental results demonstrate and verify the abil-
ity of JTFDR to be effective for polytetrafluoroethylene (PTFE) coax-
ial cable, which has been widely adopted for military applications in
ship power systems. It is shown that JTFDR has the ability to detect
and locate incipient defects with high accuracy and monitor the aging
process of the cables to predict both future defects and the remaining
service life of the cables.
Keywords – Joint Time-Frequency Domain Reflectometry (JTFDR),
Diagnostics, Prognostics, PTFE
The safe operation of the ship power system depends
largely on the integrity of the wiring system.
electric ship power system contains miles of wiring. Some of
which is difficult to reach and most of which is exposed to
constant vibration, routine maintenance operations, heat and
other age-related disturbances .
technique is needed which can detect and locate these defects
accurately before they lead to any kind of damage. However,
the ideal scenario is for these incipient defects to be detected
before they evolve into hard defects. In order to both prevent
hard defects and save cost on periodically changing cables,
a non-destructive,non-intrusive prognostic technique is
required, which can monitor the status of the cable and predict
the remaining life of the cable ,.
The current state-of-the-art technology for wiring diagnos-
tics can be largely categorized as time-domain analysis or
frequency-domain analysis. Time-domain analysis typically
employs time-domain reflectometry (TDR); frequency-domain
analysis commonly involves either frequency-domain reflec-
tometry (FDR) or standing-wave reflectometry (SWR) .
These reflectometry techniques are based on the analysis of a
reference signal and any signal(s) reflected by imperfections
on the wire being tested. However, these classical techniques
are limited by the fact that they analyze the reference and
Therefore, a diagnostic
reflected signals in either the time domain or the frequency
Thus far, all available techniques are destructive, need
to be performed in a laboratory setting, or cannot provide
information about the remaining useful life of the cables
.Ideally, a technique would exist that could eliminate
the disadvantages and undesired effects of these techniques
for diagnostics, while also providing prognostic information.
However, presently there is no single, feasible technical
solution that can achieve both diagnostics and prognostics
for all the types of cables and environments in ship power
systems. JTFDR is proposed as a comprehensive solution.
In this paper, JTFDR is first applied to a M17/95-RG180
military grade cable protected by PTFE insulation with
incipient defects to verify the efficacy and configurability of
this technique. The theory of JTFDR is discussed in Section
II. The experimental setup of JTFDR is described in Section
III. In Section IV, we will discuss the experimental results of
JTFDR, how JTFDR can achieve scientific prognosis of an
aging cable, and how JTFDR can monitor a cable for signs of
insulation degradation. Conclusions are provided in Section V.
II. JOINT TIME-FREQUENCY DOMAIN
In this paper, a new signal processing-based reflectom-
etry technique, joint time-frequency domain reflectometry
(JTFDR) is proposed. This innovative technique captures the
advantages of both TDR and FDR while avoiding some of
their limitations by using advanced digital signal processing.
JTFDR utilizes a reference signal that is localized in both the
time and frequency domains simultaneously. This reference
signal is composed of a Gaussian envelope applied to a linear
chirp signal as below:
s(t) = (α/π)1/4e−α(t−t0)2/2+jβ(t−t0)2/2+jω0(t−t0)
where coefficient α determines the time duration of the refer-
ence signal; coefficients α and β determine the bandwidth of
the reference signal; and ω0is the center frequency.
erence signal is created in MATLAB and displayed in Fig. 1.
The real-world reference signal used in the experiment can be
Fig. 1. Reference signal in MATLAB.
observed from the oscilloscope and is shown in Fig. 3(a). A
distinct advantage of this reference signal is its configurability.
The user can properly select the parameters of the reference
signal, including frequency bandwidth, center frequency, and
time duration, by considering the frequency characteristics of
the wire being tested .
After obtaining the signals reflected by defects in the cable
under test, JTFDR uses a predetermined kernel (the Wigner
kernel is used in this paper) to find the time-frequency distri-
butions of the reference signal and the reflection. The Wigner
distribution of the time signal, s(t), is obtained by the following
JTFDR then computes the time-frequency cross-correlation
between the reference signal and the reflected signal(s) with
the following equation:
2τ) · s(t +1
where Wr(t, ω) is the distribution of the reflected signal;
Ws(t,ω) is the distribution of reference signal; and Esand Er
are normalization factors.
The peaks of the time-frequency cross-correlation are used
to detect the defects and determine their locations. JTFDR has
been proven to be able to accurately and sensitively detect both
hard and incipient defects on coaxial cables . The unique
features of the time-frequency cross-correlation function
employed by JTFDR also allow it to sensitively monitor all
minor imperfections. Changes or growth in the time-frequency
cross-correlation indicate that the faulty condition of a wire or
cable is degrading.
III. EXPERIMENTAL SETUP
The experimental JTFDR wiring test bed is composed of
a signal generator (Tektronix Arbitrary Waveform Generator
610), a data acquisition device (Agilent Infiniium 54754A),
and a control PC. The computer controls the arbitrary wave-
form generator (AWG) to produce the Gaussian-envelope
chirp signal, which propagates into the target cable via the
circulator or T-connector. This reference signal is reflected at
the fault location and travels back to the circulator. The circu-
lator redirects the reflected signal to the digital oscilloscope.
The computer program acquires the reference and reflected
signals from the oscilloscope, calculates the time-frequency
distribution of the reference and reflected signals, and executes
the time-frequency cross-correlation algorithm to detect,
locate, and assess any defects on the cable.
An EC17 Environmental Chamber is used for accelerated
thermal aging for prognostics verification.
A. Diagnostics - Incipient Defect Detection and Location
In this paper, the cable samples studied are M17/95-RG180,
with PTFE insulation. This type of cable is traditional military
(MIL) specification coaxial cable that was developed 50-60
years ago. It was originally created to support WWII military
applications and continues to be used today. Its solid dielectric
provides superior crush resistance and its excellent mechanical
properties make it well suited for tactical applications. How-
ever, these tactical applications increase the chance of defects.
The incident signal of JTFDR can be configured to maxi-
mize the capability of the technique for the cable under test
based on the physical properties of the cable. For this reason,
the transfer function of a 10 m sample of the cable was found
and the Bode plot is shown in Fig. 2. There is a trade off
between frequency-based signal attenuation and location reso-
lution in choosing the center frequency of the incident signal:
the higher the center frequency, the greater the attenuation but
also the higher the resolution, and vice versa. Because the
cable sample is relatively short (only 10 m long), the resolution
is more important than attenuation for detection and location
purposes. Also, the phase of the frequency response at the
corresponding center frequency should be linear or else errors
could be introduced in the detection and location process. The
linearity of the phase of the frequency response can also affect
the impedance measurement of the defect. Such quantitative
information will be helpful to identify the type of defect in
future research. For these reasons, the incident signal for this
experiment is chosen to have a 425 MHz center frequency and
a 100 MHz bandwidth as shown in Fig. 2.
A defect corresponding to the removal of 0.25 in. of outer
insulation around half the circumference of the cable is created
at 5.5 m. For a comparison of the reflectometry techniques,
TDR is first applied to the cable, and then JTFDR is applied
to the same cable. The results of these tests are given in Figs.
Figure 3(a) shows the waveforms of the incident and
reflected waveforms in the time domain, in which it is difficult
to observe the reflections from the defect. Fig. 3(c) reveals
that TDR is of little use on the cable. Although the beginning
Fig. 2. Bode plot of M17/95-RG180.
and end of the cable are readily observable, it is difficult to
distinguish the reflection of the incipient defect from other
false reflections. However, the plot of the corresponding joint
time-frequency cross-correlation function of the waveforms
[Fig. 3(b)] shows an obvious peak, which corresponds to the
defect. The correlation function is normalized between 0 and
1 so that the detection of the defects can be quantified within
bounded values; i.e., the function indicates the probability of
reflection from potential defects. According to calculations
from Fig. 3(b), the defect is located at 5.43 m. The experi-
mental results above show that JTFDR can accurately detect
and locate incipient defects on PTFE cables, which is shown
to be a difficult job for TDR.
B. Prognostics - Accelerated Thermal Aging Testing
Conducting life tests on cables under normal operation con-
ditions is not practical because it is too time consuming; there-
fore accelerated aging tests are necessary. Accelerated aging
tests will apply higher stress levels than normal operating con-
ditions to more quickly induce age-related degradation of the
(a) Incident and reflected waveforms of JTFDR in the time domain.
(b) Corresponding time-frequency cross-correlation.
8 10 12 14
(c) Classical TDR results.
Fig. 3. Diagnotic results for a defect located at 5.5 m using various techniques.
The same M17/95-RG180 cable type that was used in the
previous diagnostic test will be used for the accelerated aging
test. The length of the new sample is again 10 m, and the seg-
ment to be tested is located from 5 m to 6 m; thus, the length of
the “hot spot” is 1 m. The same incident waveform as before
is applied to the cable sample.
To simulate exposure to a service temperature of 50◦C for
a duration of 60 years, the accelerated aging duration was de-
termined using the well known Arrhenius equation. This equa-
tion describes the relationship between the reaction rate and
the temperature of a chemical reaction. The equation has been
verified to be effective for many materials. The modified Ar-
rhenius equation for accelerated thermal aging is stated below:
• Tsis the service temperature;
• Tais the accelerated aging temperature;
• tsis the aging time at service temperature;
• tsis the aging time at acceleration temperature;
• Eais the activation energy; and
• B is the Boltzmann’s constant (given below).
B = (8.617 × 10−5eV/K)
Before the cable is put into the chamber, which is preheated
to 250◦C, the waveforms are acquired and processed to
obtain the time-frequency cross-correlation baseline for future
comparison. The intended hot spot of the sample is then put
into the chamber for 15 hours. To monitor the aging process,
the waveforms are acquired and processed after each hour to
obtain an updated time-frequency cross-correlation plot.
To demonstrate the capability of JTFDR to monitor the
severity of a defect over time, the results of the aging test at
250◦C (50◦C higher than the maximum operating temperature
of the cable under test) are shown in Fig.
the time-frequency cross-correlation function before the
aging, after 5 hours (20 simulated years), and after 15 hours
(60 simulated years) of thermal aging.
time-frequency cross-correlation function at the origin is the
result of the auto-correlation of the incident signal with itself
so it represents the beginning of the cable. The peak at 10
m is the result of the cross-correlation between the incident
signal and the reflections from the open-end, so it represents
the end of the cable. Both of them show a peak value close
to 1. These values at the beginning and end of the cable do
not change with thermal aging. However, the time-frequency
cross-correlation exhibits reflections from the hot spot located
at 5 m to 6 m away from the beginning of the cable. Notably,
the time-frequency cross-correlation peak value at this location
increases from around 0.1 before testing up to 0.5 after 15
The other peak, located at around 2.5 m, is caused by the
undesirable leakage due to the non-ideal circulator. We are
investigating methods for removing this minor abnormality.
Because the peak of the cross-correlation corresponding to
this non-defect is typically much smaller than the peak from
true defects, we ignore it by setting a threshold greater than the
cross-correlation peak of the non-defect, but still low enough
to detect any real defects.
This experiment demonstrates that JTFDR can successfully
monitor the aging process of a cable under duress. The peak
of the time-frequency cross-correlation function provides
information about the state of a wire under test, and this
The peak of the
Fig. 4. Time-frequency cross-correlation at various times during the aging
information can be monitored over time. With this capability,
JTFDR can predict a hard defect before it reaches its most
dangerous state. This technique also can be used to predict the
remaining life of the cable under test.
In this paper, the innovative JTFDR is proposed and verified
to be a robust, accurate, and sensitive diagnostic technique. It
captures the advantages of both TDR and FDR and features a
unique incident signal configurable to its application.
This research has also demonstrated that JTFDR is a
promising prognostic technique which can monitor the aging
process.The peak of the time-frequency cross-correlation
function provides information about the state of a cable under
test, and this information can be monitored over time. With
this capability, JTFDR can predict a hard defect before it
reaches its most dangerous state and predict the remaining life
of the cable.
The testing in this paper is limited to a certain type of
coaxial cable to allow a full range of testing to be performed
within the budget and schedule allocated for this study. Future
research is desirable to investigate the effectiveness of JTFDR
on other types of cables used in ship power systems; TXW-4
and MIL-C-27500 are our next targets.
The work reported in this paper was supported by the
ONR under grants # 00014-02-1-0623 and National Science
Foundation grants # 0747681, CAREER: Diagnostics and
Prognostics of Electric Cables in Aging Power Infrastructure.
The authors also appreciate support from Northrop Grumman.
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