Joint Time-Frequency Domain Reflectometry
for Diagnostics of Coaxial Cables
Yong June Shin, Assistant Professor and Roger Dougal, Professor
Department of Electrical Engineering, University of South Carolina
301 South Main Street, Rm 3A20, Columbia, SC 29208, USA
Jin Bae Park, Professor
Department of Electrical and Electronic Engineering, Yonsei University, Seoul, Korea
Edward Powers, Professor
Department of Electrical and Computer Engineering, The University of Texas at Austin
1 University Station C0803, Austin, Texas 78712-0240 USA
E. R. (Randy) Collins, Associate Professor
Holcombe Department of Electrical and Computer Engineering, Clemson University
P.O. Box 340915, Clemson, SC 29634-0915 USA
ABSTRACT
The importance of aging electrical wiring and associated faults in aircraft has been
highlighted due to the critical effects on the safety of overall systems. Traditional
reflectometry methods for the detection and localization of the faults on cable have been
achieved in either the time domain or frequency domain only.
In this paper, we introduce a new high-performance reflectometry technique that operates
simultaneously in both the time and frequency domains. The joint time-frequency domain
reflectometry (JTFDR) utilizes time and frequency information of a transient signal to
detect and locate the fault. The approach rests upon time-frequency signal analysis and
utilizes a chirp signal multiplied by a Gaussian time envelope. The Gaussian envelope
provides time localization, while the chirp allows one to excite the system under test with
a swept sinusoid covering a frequency band of interest. Sensitivity in detection and
accuracy in localization of the reflected signal are provided by a time-frequency cross
correlation function.
The proposed approach is verified by experimentally locating various types of faults,
located at various distances, in coaxial cables in comparison with classical time domain
reflectometry (TDR). Knowledge of time and frequency localized information for the
reference and reflected signal gained via time-frequency analysis, enables an automated
detection and accurate localization of the faults on cables.
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Introduction
The significance of aging wiring system brought to the forefront by high-profile
accidents of commercial aircraft, e.g., TWA Flight 800 and Swissair Flight 111 [1]. The
issues of the wiring integrity are not limited to commercial aviation only but also includes
systems where complicated wiring is involved and high degree of safety is required such
as the space shuttle, nuclear power plants and tall buildings. In November 2000, the
National Science and Technology Council Committee on Technology reported the
significance of wiring integrity, and several US Federal agencies are currently carrying
out research related with the safety of electric wire systems [2]. NASA recognized the
possible aging of aerospace vehicle wiring and the potential consequences of aging
aircraft. NASA recommended the development of an automated wiring integrity testing
technology, and the NASA Wiring Working Group was established [3].
The state-of-the-art for the diagnostics of wiring integrity can be categorized by time
domain analysis and frequency domain analysis. In time domain analysis, time domain
reflectometry (TDR) is used, whereas in frequency domain analysis, frequency domain
reflectometry (FDR) and standing wave reflectometry (SWR) can be utilized. Each
methodology is based on analysis of a reference signal and a reflected signal either in the
time or frequency domain “only”. Time domain reflectometry (TDR) is a well-known,
conventional method that has been applied to various types of applications. The
frequency domain reflectometry (FDR) and standing wave reflectometry (SWR) employ
analysis of the reference signal and reflected signal in the frequency domain, and the
SWR based systems are under development.
In this paper, we introduce a joint time-frequency domain reflectometry (JTFDR)
technique, which captures many of the advantages of TDR and FDR mentioned
previously. The reference signal is a type of chirp signal that allows one to apply the RF
power in the frequency band of interest. To provide time localization in JTFDR, the chirp
signal is localized by a Gaussian envelope in the time domain. The time-frequency
distributions of the reference signal and the reflected signals are calculated. Then these
two time-frequency distributions are cross-correlated in the time-frequency domain. The
peak in the time-frequency cross correlation function allows one to estimate an accurate
round-trip propagation time, and hence distance, as in classical TDR.
Motivation and Approach
Short circuits in electrical wiring can be both troublesome and dangerous. If an electrical
conductor becomes faulted, there are two consequences. First, if the conductor is
connected to a source of energy, a large current can flow which can damage the wire and
might cause damage to surrounding conductors and possibly a fire. Hence, circuit
breakers are installed in wiring to disconnect the energy source in the event of a short
circuit. Secondly, if the conductor does not have a significant energy source (such as a
instrumentation signal), then the equipment it is connected to might simply misoperate.
Erroneous electrical signals could lead to potentially dangerous situations. Unfortunately,
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the only mechanism for detecting these problems is simply for the flight crew or
maintenance to discover abnormal operation of a connected “end-use” device or system.
Aircraft wiring is subject to both mechanical and electrical stresses during its lifetime in
the vehicle. Mechanical stress and aging insulation can cause failure of the insulation
system, resulting in faults (short circuits) and electromagnetic interference (EMI). When
a conductor’s insulation system fails, arcing can take place between adjacent conductors
if the voltage potential between the conductors is high enough. Arcing will cause
localized areas of high temperature on the wire. As a result, the insulation is further
compromised and ultimately the wire will fail. The high-resistance faults and faults on
non-power conductors will likely remain in service and cause power quality problems
and electrical noise.
Since the average aircraft has been in service three decades or more, electrical problems
have become more and more common. Aircraft are subject to vibration, thermal cycling,
pressurization, and other environmental factors that are not present in many terrestrial
applications. Wiring harnesses are often moved and handled during this process,
connectors replaced, and attach points changed. As a result, maintenance induces many
wiring problems, especially in aircraft that have insulation that has become old and
brittle.
As an example, Figure 1 shows an electrical system from a helicopter that is almost 50
years old. While probably considered “airworthy,” these pictures show the tremendous
difficulty involved in locating degraded wiring, connectors and terminals. The wiring
bundles also pass through bulkheads and clamps, where chafing can occur.
Figure 1. Wiring from a 1957 Sikorsky helicopter. The left image in under the
instrument panel. The right image is the voltage regulator system. Orange arrows show
various connectors and yellow arrows depict areas where wiring bundles pass through
clamps and bulkheads.
Figure 2 shows an aircraft that is nearly 30 years old undergoing an avionics upgrade.
Even many small aircraft are being retrofitted with “glass cockpits.” Unfortunately, these
systems are often “piggybacked” onto existing electrical systems of unknown condition.
While the wiring’s exterior can be sometimes be examined, it is impossible to determine
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the actual condition of the wire, especially when it is part of a large bundle. Therefore,
many aircraft operators are having the old wiring completely removed during upgrades at
great expense.
Figure 2. An avionics retrofit on a 1976 Cessna 177 Cardinal. The left image shows the
original installation with factory wiring harnesses and avionics from 1976. The right
image shows the wiring after the radios have been removed. The yellow arrows highlight
the avionics wiring. The orange arrow shows the power busbar and circuit breakers.
In modern aircraft, there are often single-point-of-failure conditions in the electrical
system. If a wire faults or is otherwise compromised, either a circuit breaker will remove
the conductor from the power system (rendering the device it powers inoperative) or the
device or system connected by the wire can misoperate. Redundancy of all critical
conductors would be very costly and perhaps prohibitive due to space and weight
constraints. If wiring harnesses were built with spare conductors, smart circuit breakers
could be used to monitor the electrical properties of the conductors and switch off a
failing conductor before damage is done. If spare conductors are available with a
switching array, spares could be brought into service automatically, preventing a device
from misoperating or being disabled. Duplication of each conductor would be
statistically unnecessary.
The key to success is detecting wiring anomalies. Hence, we propose a research program
that investigates diagnostics and treatment of the wiring integrity issues in aging aircraft.
For the diagnostics of electrical wiring integrity, an advanced signal processing-based
reflectometry will be investigated for high-precision detection and localization.
Theory of Joint Time-Frequency Domain Reflectometry
The classical TDR uses a DC-type pulse with fixed time duration and compares the
reference and reflected signals in the time domain only. Therefore, TDR cannot analyze
the signal in the frequency domain because an ideal step pulse has its energy spread over
a wide range of frequencies at the time instance of the step. On the other hand, FDR uses
a set of sinusoidal signals with fixed frequency bandwidth and analyzes the change of the
signal in the frequency domain only. Hence, it is difficult to analyze the signal in time
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domain by FDR because a pure sinusoidal signal (which is a reference signal in FDR)
has, in principle, infinite time duration. From the viewpoint of signal processing, each of
these classical reflectometry methodologies wastes valuable information, which limits the
potential resolution and accuracy enhancement. Hence, the JTFDR accounts for the time
and frequency domain information in a joint manner in the design of the reference signals
and the process of the reflected signals.
Therefore, instead of traditional TDR and FDR, we propose a new type of reflectometry,
time-frequency domain reflectometry. JTFDR uses a linearly modulated chirp signal with
a Gaussian envelope. The proposed reference signal can be expressed in terms of time
and frequency jointly as follows:
(1)
where α , β , t0 and ω 0 determine the time duration, frequency sweep rate, time center
and frequency center, respectively. The Gaussian envelope localizes the reference signal
in the time and frequency domain while the instantaneous frequency of the signal
increases with time in a linear manner.
Now the problem is to determine the parameters of the reference signal that will fit the
wave propagation characteristics of cable. For example, the frequency-dependent
attenuation characteristics of the military-purpose communication coaxial cable, with a
test distance of 40m and minimum power for measurement of-24dB, one can determine
the center frequency of the parameter as depicted in Figure 3. :
Figure 3. Routines to determine the center frequency of JTFDR
reference signal for RG 142 coaxial cable
After determining the center frequency of JTFDR reference signals, the remaining
parameters can be determined by the specifications of the signal generator. In this paper,
for a reasonable comparison with TDR, time duration and frequency bandwidth are
selected to be 100 ns. and 100 MHz, respectively. Furthermore, the time and frequency
localized information can be utilized for accurate detection and localization by evaluation
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of the time-frequency cross correlation function between reference and reflected signals
[5].
Experimental Setup for JTFDR
The purpose of the preliminary experiment is to verify the feasibility of joint timefrequency domain reflectometry. Furthermore, the performance is to be compared with a
commercial TDR. The “damage” of the coaxial cable is emulated by a failure of the
external shields so that the internal dielectric material is exposed over 1cm. To illustrate
the ability of TFDR to detect and locate the faults in RG 142 type coaxial cable, an
experimental TFDR system is organized as shown in Fig. 4 –(a).
The system consists of a circulator, an arbitrary waveform generator and an oscilloscope
that are connected to a computer for automatic control of the instruments. The computer
controls the arbitrary waveform generator (AWG) to produce the Gaussian envelope
chirp signal, which propagates into the target cable via the circulator. This reference
signal is reflected at the fault location and back to the circulator. The circulator redirects
the reflected signal to the digital oscilloscope. The computer program, provided in Fig. 4(b), controls and synchronizes the arbitrary waveform generator and digital oscilloscope,
calculates the time-frequency distribution of the reference signal and reflected signals,
and executes the time-frequency cross correlation algorithm.
(a)
(b)
Figure 4. Experimental setup for the JTFDR with signal generator and oscilloscope in (a)
and its GUI system control panel (b)
Experimental Comparison
To illustrate some of the limitations of classical TDR and advantages of proposed
JTFDR, we introduce two sets of preliminary experimental results. The first test is to
compare the accuracy comparison between TDR and JTFDR where a “damage” of the
cable is located at 20 m away from the source. For a fair comparison between TDR and
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JTFDR, the same experimental condition is applied and the results of the experiments are
provided in Fig.5-(a) and (b), respectively.
(a)
(b)
Figure 5. Comparisons of fault detection and localization by classical TDR in (a)
and by proposed JTFDR in (b)
Fig. 5-(a) is a screen snapshot of the output of a state-of-the-art commercial TDR
instrument for a faults on a military-purpose coaxial cable (RG-142) located 20 m away
from the source. The reflected TDR signal is observed between 200-250 ns time interval,
however, one can confirm that the reflected signal is severely distorted in comparison
with the reference signal due to the frequency-dependent attenuation of the coaxial cable.
Tracking the time instance of the reflected signal, the location of the fault based on TDR
scheme is evaluated as follows:
(2)
However, the analysis of the reflected signal is quite different in JTFDR schemes: Fig. 5(b) is a preliminary experimental result of the time-frequency domain reflectometry using
the reference signal design and time-frequency cross correlation function, under the same
experimental conditions of TDR. In the top portion of the figure is shown the reference
signal at around 100 ns, and the signals reflected from the faults at 20 m is found in the
time interval between 250 ns and 300 ns. Shown in the lower portion of the figure is the
result of correlating the time-frequency distributions of the reference and reflected signals.
In this case the reflections from all the faults are clearly visible and thus detectable, in
contrast to the TDR result in Fig. 5-(a). The location of the fault based on JTFDR scheme
is evaluated as follows:
(3)
By exploring the joint time and frequency information of the reference signal in JTFDR,
one can detect the existence of the fault on a coaxial cable with its accurate location. Also
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the peak value of the time-frequency cross correlation provides “quantitative”
measurement for the existence of the fault on the coaxial cable.
The other important issue of TDR is multiple reflections. In practical applications for the
wiring integrity diagnostics, the number of faults on the suspecting cable might be limited
to one while the circuit might have multiple branches and connectors associated with it.
Based on the following preliminary experiment, one can find a technical merit of JTFDR
for the multiple reflection problems.
Fig. 6 –(a) is a screen snapshot of the output of a state-of-the-art commercial TDR
instrument for a set of multiple-faults on a military-purpose coaxial cable (RG-142)
located 10, 20, and 30 m away from the source. As shown in Fig. 3-(a), it is very difficult
to detect and locate the faults at 20 and 30 m, and to measure the fault impedance of the
coaxial cable with high resolution.
Figure 6. Comparisons of fault detection and localization by classical TDR in (a)
and by proposed JTFDR in (b)
However, the problems of TDR can be resolved by use of JTFDR: Fig. 6-(b) is a
preliminary experimental result of the time-frequency domain reflectometry using the
reference signal design and time-frequency cross correlation function. In the top portion
of the figure is shown the reference signal at around 100 nsec, and the signals reflected
from the faults at 10, 20 and 30 m. Shown in the lower portion of the figure is the result
of correlating the time-frequency distributions of the reference and reflected signals. In
this case the reflections from all the faults are clearly visible and thus detectable, in
contrast to the TDR result in Fig. 6-(a).
Even though it is a set of preliminary experimental results for JTFDR, the advantageous
aspects of JTFDR over classical TDR is successfully illustrated. The experiments and
design of reference signal in this paper is limited to the communication coaxial cable,
however, further investigation and experiments are desirable for various types of cables
where the higher accuracy detection and localization schemes are required. We are
currently interested in application of the JTFDR to variety types of wiring integrity
diagnostics in aging aircraft.
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Conclusion
In this paper, we introduce joint time-frequency domain reflectometry which incorporates
may of the advantages of time domain and frequency domain reflectometry. Faults on
wires and cables are located from knowledge of the propagation time and velocity of
propagation as in TDR. However, the use of a chirp signal with a Gaussian envelope
enables one to effectively use a swept frequency reference signal as in FDR. This flexible
design of reference signal in JTFDR enables us to achieve higher accuracy and
customized-solution to a cable of interest. In this paper, the discussion is confined to a
military-purpose communication coaxial cable. However, a similar analysis can be
applied to other types of cables if information related to the wave propagation
characteristics of cable is available.
The use of time-frequency cross correlation function of the respective time-frequency
distributions of the reference and reflected signals has proven to be a sensitive detector of
weak reflected signals. The feasibility and technical merits of JTFDR for high-precision
detection and localization have been verified for the coaxial cables. Therefore, we will
focus on the efficacy of JTFDR in order to extend the application to the variety types of
cable and wires in aging aircraft systems. Also, we are planning to carry out potential
hardware implementation of the JTFDR based wiring diagnostic systems.
Acknowledgement
This research was funded by the Ministry of Commerce, Industry and Energy, Republic
of Korea, Project #00015071, “Smart Wiring Optimal Signal Design and System
Development for Electrical and Electronic Wiring Diagnosis.” The work reported in this
paper was partially supported by the U.S. ONR under Grants N00014-02-1-0623 and
N00014-00-0368. Also, this research is being supported by SC NASA EPSCoR Research
Grant Award 2005.
References
[1] C. Furse, R. Haupt, “Down to the Wire: The Hidden Hazard of Aging Aircraft
Wiring,” IEEE Spectrum, pp.35-39, Feb. 2001.
[2] National Science and Technology Council Committee on Technology, Wire System
Safety Interagency Working Group, “Review of Federal Programs for Wire System
Safety-Final Report,” National Science and Technology Council Committee on
Technology, November, 2000.
[3] NASA Wiring Integrity Research Group, “Wiring Integrity Research (WIRe) Pilot
Study: Design for Safety Initiative,” NASA Document Number A0SP-0001-XB1.
[4] D. Lynch, “NASA Hybrid Reflectometer Project,” 6th Joint FAA/DoD/NASA Aging
Aircraft Conference, 2002.
[5] Yong-June Shin, T. Choe, E. Song, J. Park, J. Yook, and E. J. Powers, "Application of
Time-Frequency Domain Reflectometry for Detection and Localization of a Fault on a
Coaxial Cable," to appear in IEEE Transactions on Instrumentation and Measurement,
2005.
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