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Published in IET Signal Processing

Received on 23rd May 2009

Revised on 4th September 2009

doi: 10.1049/iet-spr.2009.0137

ISSN 1751-9675

Application of joint time–frequencydomain reflectometry for electric powercable diagnostics

J. Wang P.E.C. Stone Y.-J. Shin R.A. Dougal Department of Electrical Engineering, University of South Carolina, 301 South Main Street, Columbia, SC 29208, USA

E-mail: [email protected]

Abstract: The integrity of the electric power cables is vital to the safety of an entire electrical system. To ensure

the health of the cables, a technique is needed for both detecting/locating defects, and predicting hard defects

before they occur. The theory and limitations of the classical wiring diagnostic techniques time domain

reflectometry (TDR) and frequency domain reflectometry (FDR) are discussed. This study then introduces joint

time-frequency domain reflectometry (JTFDR) as a unique solution for the cable diagnostics and prognostics.

By employing an interrogating incident signal and advanced post-processing of the reflected signals, JTFDR is

shown to be capable of overcoming those limitations. JTFDR is experimentally proven to be successful for

detecting and locating both hard and incipient defects. The prognostic capabilities of JTFDR are also

demonstrated via accelerated ageing tests of an electric power cable. In conclusion, by utilising the incident /

reflected signal information in the time and frequency domains simultaneously, JTFDR is proven to be a more

effective diagnostic technique than the classical TDR and FDR. JTFDR can also be used to monitor incipient

defects and better predict hard defects before they occur.

1 Introduction

Wires and cables are often taken for granted in electric power infrastructures, but they are as fundamental as blood vesselsare to the human body. Unfortunately, these cables aresubjected to various stresses including electrical,mechanical, chemical and especially thermal stress. Thethermal stress is often a result of the heat dissipated from a live inner conductor through the insulation into thesurrounding soil. Under these conditions, the cable’schemical composition and physical morphology may change and water treeing may be expedited [1]. Water treeing is a slowly developing degradation phenomenonthat initiates at a defect or impurity where moisture ispresent [2]. Each of these stresses may damage the cablesunder normal operation.

The deregulated electric power utilities are facing thetechnical challenges of detecting and locating faulty cablesfabricated and installed up to a half-century ago.

Additionally, utilities are experiencing premature failuresmuch earlier than the life expectancy originally estimated;some cables have had to be replaced after 10– 15 years,

which is only a fraction of the designed lifetime of 40 years[3–6]. Furthermore, the disputable remaining-lifeestimation that warrants replacement will become a point of contention between the deregulated power utilities andthe government and power industry.

The fault occurrence in cable lines often engenders severeeconomical losses. To prevent electrical outages and to saverepair expenses, a diagnostic technique is needed which candetect and locate both hard (open or short circuit) andincipient defects (small anomalies or defects) accurately before they lead to any kind of damage. Furthermore, theideal scenario is to be able to quantify the degradation of the insulation of a cable to predict the remaining life of thecable. For this purpose, a non-destructive, non-intrusiveprognostic technique is required which can monitor thestatus of the cable so that appropriate corrective actions can

IET Signal Process., pp. 1 – 11 1

doi: 10.1049/iet-spr.2009.0137 & The Institution of Engineering and Technology 2010

Techset Composition Ltd, Salisbury

Doc: {IEE}SPR/Articles/Pagination/SPR59165.3d

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be taken. For these purposes, it is necessary to have a tool with both diagnostic and prognostic capabilities to analyseand monitor installed cables.

There are a variety of cable diagnostic approaches based onmechanical (Elongation-At-Break [7] Compressive Modulus

[8]), chemical (oxidation induction time [9], Fourier transform infrared spectroscopy [10]) and electricaltechniques, but they are either destructive, need to beperformed in the lab, or lack the capability to predict thefuture performance of the cable. The electrical techniquesare the most desirable techniques for effective in situdiagnostics. The commercial market offers a variety of electrical cable testing instruments based on insulationresistance, dielectric loss measurements, voltage withstandtesting, partial discharge (PD) testing, very-low-frequency (VLF) testing and reflectometry techniques such as timedomain reflectometry (TDR) and frequency domain

reflectometry (FDR). PD is a very popular diagnostic toolused to assess the status of power cable insulation,particularly for extruded insulation materials [11–13]. Adisadvantage of PD testing, however, is that it requires that a small current pulse be measured while a relatively high

voltage is applied, and that high voltage may actually aggravate the defects in the insulation. Furthermore, thePDs from the joint, cable branches, contamination andsplice material type are much higher than those from theextruded dielectric cable, and they can complicate theinterpretations [14– 16].

Thus, for non-destructive electrical cable diagnostics,reflectometry is the most desirable technique, if successful.However, current state-of-the-art reflectometry techniquesare successful for detection and location of the hard defects,but they fall short in detection and location of the incipient defects, which would be the essential capability for prognostics. The state-of-the-art technology for reflectometry-based wiring diagnostics and prognostics canbe largely categorised as either time domain analysis(TDR), frequency domain analysis (FDR), or joint time–frequency analysis (JTFDR) [17]. A brief discussion of the

TDR and FDR techniques will be presented in Section 2. JTFDR will be introduced in Section 3 including

fundamental theory, experimental setup and an example of diagnostics as compared to TDR and FDR. To verify thecapability of JTFDR [18, 19] to monitor the status of thecable insulation, accelerated ageing tests are adopted in thispaper. The results and analysis of the thermal acceleratedageing tests will be presented in Section 4. Overallconclusions of this paper are drawn in Section 5.

2 Classical reflectometry:TDR and FDR

Reflectometry is based on the same principle as radar: a pulseof low-voltage energy is transmitted down a wire, and any discontinuity of impedance generates a reflection so that

one can detect and locate a defect [20]. The amplitude of the reflected waveform can be used to measure theimpedance of the defect, and the time delay of the reflected

waveform can be used to locate it. A coaxial cable and itstransmission line model are provided in Fig. 1. The defect on a wire can be described by its impedance, and the

reflection caused by the defect will be characterised by thereflection coefficient and location of the defect

Gd =Z d − Z 0Z d + Z 0

(1)

where Z 0 is the characteristic impedance of the cable and Z dis the impedance of the defect (Z d = 0 for short and Z d = 1for open). In the case of a hard defect, the reflectioncoefficient is 21(short) or 1(open) and [21, 1] are also thelower bound and upper bound of Gd. Thus, they arerelatively easy to detect and locate. Detecting and locating incipient defects before they become hard defects (open or short circuits) is essential for smart wiring systems.

Based on the reflectometry theory, a variation of impedance on a wire will cause a reflection, but in practice,it is difficult to detect and locate the small reflections fromincipient defects. The impedance of a defect is determinedby the insulation properties and the geometricconfiguration of the conductors. Thus, even a successfulanalysis of reflection waveforms produces ambiguous data;it is unclear whether the reflection is due to the wire’s

deformation or its insulation material. As a result, a smalldifference between the faulty and characteristic impedance

will yield a weak and relatively small reflection that may belost in the noise of the measurement. Unfortunately, a similarly small difference may also appear from a merechafing or fray on the wire [21]. However, under thetypical scenarios of cable ageing, the cable’s insulation isexposed to harsh operational environments like moistureintrusion, chemical corrosion, thermal variation, radiationand mechanical vibration. In addition, unlike the chafing or fray, the typical area of ageing or defect is largely spreadover the cable and the permittivity of the insulation may

change dramatically. Nevertheless, even such noticeablereflections are not adequately observed by current state-of-the-art reflectometry techniques: TDR and FDR.

Figure 1 Transmission line model of a defect on a coaxial

cable

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& The Institution of Engineering and Technology 2010 doi: 10.1049/iet-spr.2009.0137

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In TDR, a rectangular step pulse signal is used, whereas inFDR, a sinusoidal signal serves as the incident signal. Fig. 2a shows an example of TDR obtained by employing anarbitrary waveform generator (AWG) to send a DC pulseinto the cable under test. An incipient defect (1 cm long,half of the circumference of the cable insulation and outer

conductor removed, dielectric scraped) is made at 7 m of the 10 m length of an RG-58 coaxial cable. In principle,the patterns and parameters in the reflected signal can beused to detect, locate and measure impedance; however, thereality of TDR, shown in Fig. 2a , is different from idealoperation. Although the beginning and end of the cable aredetected and located relatively easily, it is almost impossibleto detect and to locate the defect located at 7 m.Furthermore, the magnitude of the reflection, supposedly required to measure impedance of the defect, is difficult todetermine accurately.

The reflection waveform from the end of the cable shouldbe an ideal step pulse, but one can see that the waveform isdistorted after the reflection and propagation as shown inFig. 2a . Even an ideal step pulse (the incident signal of

TDR), although it provides excellent time localisation,corresponds to an extremely broad frequency bandwidth inthe frequency domain. In practice, this causes severedistortion in a transmission line.

Fig. 2b shows an example of FDR obtained by using theSite Master from Anritsu. An incipient defect (1 cm long,half of the circumference of the cable insulation and outer

conductor removed, dielectric scraped) is made at 10 m of the 15 m length of an RG-59 coaxial cable. FDR uses a set of stepped-frequency sinusoid signals, thus enabling excellent frequency localisation. Because FDR utilises a smaller frequency bandwidth (400–500 MHz in theexample in Fig. 2b ) than TDR, the distortion of thereflected signal is less than that of TDR. The FDR diagnostics provide the average return loss of the incident signal in dB with respect to space. The experimental result of FDR is presented in Fig. 2b : the beginning and end of the cable are identified, and approximately 40 dB returnloss is observed at around 6 and 10 m. The impedance of

the defect must be exhibited in the impedance spectrum,but the reflection becomes spread over a range of frequencies, so the magnitude of the reflection at any onefrequency is small. The impedance spectrum is convertedfrom the frequency domain to the space domain via theinverse Fourier transform [22].

As a result, as shown in Fig. 2b , the spatial resolution of FDR is poorer than that of TDR, which is a disadvantageof FDR for the defect localisation. Because of the loss of time localisation by utilising sinusoidal signals, themeasured impedance of the defect is not accurate when it ismapped into space. Nevertheless, a notable advantage of FDR is that one can achieve better results by properly selecting the frequency stepping range [22].

It is desirable to consider time localisation and frequency localisation simultaneously in order to efficiently use

reflectometry. The joint use of time and frequency information proposed here allows us to take advantage of both the time localisation of TDR and the frequency localisation of FDR. In the next section, we willinvestigate the efficacy of a new reflectometry techniquethat can simultaneously provide time and frequency domain information for highly improved cable diagnosticsand prognostics.

3 Joint time– frequency domainreflectometry (JTFDR)

3.1 Fundamentals of JTFDR JTFDR captures the advantages of both TDR and FDR while avoiding some of their limitations by employing aninterrogating incident signal that can be customised basedupon the application and advanced post-processing of thereflected signal. The interrogating incident signal islocalised in both the time and frequency domainssimultaneously. This incident signal is composed of a Gaussian envelope applied to a linear chirp signal as below

s (t ) = (a/p )1/4e−a(t −t 0)2/2+ j b (t −t 0)2

/2+ jv 0(t −t 0) (2)

Figure 2 Coaxial cable diagnostic example by a TDRb FDR



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where coefficient a determines the time duration of theincident signal; coefficients a and b determine thebandwidth of the incident signal; and v 0 is the centrefrequency. A distinct advantage of this incident signal is itsconfigurability. The user can properly select the parametersof the incident signal, including centre frequency, frequency

bandwidth and time duration, by considering the frequency characteristics of the wire being tested. After obtaining thesignals reflected by defects in the cable under test, JTFDR uses a predetermined kernel (the Wigner distribution isused in this paper) to find the time–frequency distributionsof the incident signal and the reflected signal. The Wigner distribution of the time signal, s (t ), is obtained by thefollowing transformation

W (t , v ) = 1

2p

1

−1s ∗ t − 1

2t

s t + 1

2t

e− jtv dt (3)

JTFDR computes the time– frequency cross-correlationbetween the incident signal and the reflected signal withthe following equation

C sr (t )= 1

E s E r (t )

t ′=t +T s

t ′=t −T s

1

−1W r (t ′, v )W s(t ′− t , v )dv dt ′

(4)

where

E r

(t )=

t ′=t +T s

t ′=t −T s1

−1W

r

(t ′, v )dv dt ′ (5)

E s =

W s(t , v )dt dv (6)

and where W r (t , v ) is the Wigner distribution of the reflectedsignal; W s(t , v ) is the Wigner distribution of the incident signal; and denominators E r (t ) and E s play the role of normalisation factors so that the time –frequency cross-correlation function is bounded between 0 and 1: the cross-correlation of the time– frequency distribution of thereference signal and the reflected signal,t ′

=t +

T st ′=t −T s1−1W r (t ′, v )W s(t ′− t , v )dv dt ′, will exhibit local

maximum value E r (t ) in the case that the time-frequency distribution of the reflected signal (W r (t , v )) is ‘matched’

with the time–frequency distribution of the reference signal(W s(t , v )). The local maximum value is bounded by theproduct of E s and E r (t ) so that the time–frequency cross-correlation function is bounded between 0 and 1. Thepeaks of the time–frequency cross-correlation are used todetect the defects and determine their locations. Theunique features of the time– frequency cross-correlationfunction 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, which will bediscussed in detail in the next section.

3.2 Detection and location by time–frequency cross-correlation function

In order to properly determine the distance to a defect using JTFDR, it is necessary to understand how the referencesignal propagates in time throughout the medium. We will

now explore the effect of the medium upon the time centreof the reference signal as it propagates for a distance, x .Consider the spatial propagation and reflection of thetime– frequency domain reference signal. As the signalpropagates along the medium with spatial variable x , the

waveform will be changed by the transfer function of themedium H (v , x ) [23]. For convenience of calculation, let the time centre of the reference signal be t 0 = 0 without loss of generality. Let u (x , t ) be a waveform that is observedat a distance, x , for a given initial condition,u (x = 0, t ) = s (t ), then, the general solution of the u (x , t ) is

u (x , t ) = 1 2p

√ 1−1

S (v , x )e− jv t dv (7)

where

S (v , x ) = S (v , x = 0) · H (v , x )

= S (v , x = 0)e−(a(v )− jk(v ))x (8)

and where H (v , x ) is the transfer function of the medium which is characterised by the frequency-dependent attenuation a(v ) and wave number k(v ). In the following

we assume linear frequency-dependent attenuation,a(v ) ≃ A v , and dispersion, k(v ) ≃ K v . Assuming suchlinearity, note that both the phase (v /k) and group (∂v /∂k)

velocities are both equal to 1/K and will, henceforth, besimply denoted by v , the velocity of propagation.

Fig. 3 depicts the time– frequency distributions of a reference signal W s(t , v ), a delayed version of the referencesignal W s(t − t d, v ), and the actual propagated signalW u(x )(t , v ) through a lossy medium. The distribution of W s(t − t d, v ) is identical to the distribution of W s(t , v )except for the time delay t d. The actual propagated signalW u (x )(t , v ) will suffer frequency-dependent attenuation.

However, we need to consider the time centre (t u (x )) andfrequency centre (v u (x )) of the signal u (x , t ) with theassumptions that a(v ) ≃ A v and k(v ) ≃ K v . First of all,evaluate frequency centre (v u (x )) of the signal u (x , t ) withthe propagation distance x

v u (x ) =1

−1v |S (x , v )|2dv

=1

−1v |S (v , 0)|2 · |H (v , x )|2dv

= v 0 −a2

+b 2

a Ax

= v 0 − dv (9)



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where

dv = a2 + b 2

2a Ax (10)

The frequency offset dv can be evaluated with a, b ,attenuation function, and propagation distance as shown in(10). Therefore the estimated frequency centre of thereflected signal will be deviated from the centre frequency

of the reference signal. However, measuring the center frequency of the signal v u (x ) accurately is not a simple task.

The attenuation, which is linearly increasing withfrequency, will result in a decrease in SNR of the receivedsignal.

Similarly, the time centre (t u (x )) of the signal u (x , t ) withthe propagation distance x can be evaluated as follows [24]

t u (x ) =1

−1t · |u (x , t )|2dt

= Re1−1

S ∗(v , x ) − 1 j

∂∂v

S (v , x )

dv

= − b

a2 + b 2· dv + Kx (11)

Therefore the estimated time centre t u (x ) is the propagationdelay of the frequency centre v u (x ). For an accurate measureof the propagation delay, the actual delay of the waveformis to be compensated by d t which is determined by thechirp rate parameter b and frequency deviation dv such that

t delay = t u (x ) − t s +dv

b = Dt + d t (12)

where

d t = dv

b (13)

and Dt is defined as t u (x )

−t s where t s is the time centre

of u (x = 0, t ). The actual propagation distance can beevaluated with knowledge of the velocity of propagation, v . For the detection of the fault, the correlation of the time–frequency distribution of the reference signal and reflected signal is utilised.

Considering the attenuation characteristics of the cable,the Wigner distribution of the reference signal W s(t , v )and the Wigner distribution of the reflected signal W r (t , v )can be obtained as follows [23, 25] Q1

W s(t , v ) = 1

p e−a(t −t 0)2−(v −b (t −t 0)−v 0)2

/a (14)

W r (t , v ) = 1p

e−a(t −x /v )2−(v −b (t −x /v )−v 0)2/a · e−2 Ax v (15)

Also, assign the time index, t M x , of the local maximum of

C sr (t ) at distance x , such that

C sr (t ) = 2p

E r (t ) E s

t ′=t +T s

t ′=t −T s

1

−1W r (t ′, w)W s(t ′ − t , v )dv dt ′

= 2p

E r (t ) E s

t ′=t +T s

t ′=t −T s

× 1−1 e−2 Ax

v

·1

p · e−a

(t ′−kx )

2

−(v −b

(t ′−kx )−v

0)

2/a

× 1

p e−a(t ′−t )2−(w−b (t ′−t )−w0)2

/a

dw dt ′ (16)

where

E r (t ) =t ′=t +T s

t ′=t −T s

1

−1W r (t ′, v )dv dt ′

= e(a2+b 2)/a A 2x 2−2 Ax v 0

= e−2 Ax (v 0

−dv /2)

(17)

and E s = 1, then

C sr (t ) = e−(a2+b 2/2a)(t −kx )2− Ax (a2+b 22a Ax )

= e− Ax ·dv · e−(a2+b 2/2a)(t −Kx )2

(18)

Then the time– frequency cross-correlation function of thereflected signal C sr (t ) is

C sr (t ) = e−(a2+b 2/2a)( Ax )2 · e−(a2+b 2/2a)(t −x /v )2

(19)

Therefore the existence of the reflected signal can bedetected by a quantitative number between 0 and 1. From

Figure 3 Time–frequency descriptions of a reference signal

W s(t,v ), a del ayed versi on of the refer ence sig nal

W s(t 2 t d ,v ) and the actual propagated signal W u(x)(t,v )

through a lossy medium to evaluate time delay via time

offset (d t ) and frequency offset (dv )



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examination of the time– frequency cross-correlationfunction C sr (t ) in (19), it is clear that it will be a maximum (local peak time) at t = x /v , as expected. Thefirst term on the RHS decreases because, as the reflectedsignal travels farther, its high-frequency content will beattenuated more, and thus the reflected signal will be less

correlated with the reference signal. In later sections, thelocal peak time of the time – frequency cross-correlationfunction will be utilised to accurately measure thepropagation delay of the reflected signal, which is then tobe converted into the fault location with knowledge of the

velocity of propagation.

3.3 Design of the reference signal

The cable samples studied for experimental verification of JTFDR are Rockbestos Firewall III XHHW, 14AWG,2 conductors, 600 V cables, which are normally used for control and instrumentation in nuclear reactors where thecables suffer ageing caused by heat and radiation. Theinsulation on each conductor is composed of cross-linedpolyethylene (XLPE) and a neoprene jacket covers thebundle of insulated conductors. The first step of JTFDR isto configure the incident signal to maximise the capability of the technique for the cable under test based on thephysical properties of the cable. The selection of theparameters take the following order:

Step 1. Centre frequency: While choosing the centrefrequency of the reference signal, one must consider a trade

off between the degree of attenuation and spatialresolution. Higher centre frequencies will suffer more severeattenuation, but they allow for the selection of shorter timedurations, which corresponds to higher spatial resolution.Signals having smaller time duration will cover a shorter length of cable while propagating so as to avoid theoverlapping of the transmitted signal and any reflectedsignals. Considering the noise sensitivity of theexperimental setup, we find we can tolerate a round-tripattenuation of 224 dB. The maximum fault distance inthis set of experiments is 40 m.

The selection of the centre frequency for the referencesignal can be interpreted in terms of energy [26]. AssignP rec as the signal power of the reflected signal and P tran asthe signal power of the transmitted signal, which ischaracterised by the attenuation ( A ) and length of the cable(d ). Then

P rec = P tran/ A (20)

In dB scale calculation

[P rec

]=

[P tran

]−

[ A ] (21)

Normalise the power of the reference signal such that

[P tran] = 0 dB. Then, the power of the received signal is

[P rec] = −[ A ]

= −[ A ] × 2d (22)

where A

is attenuation per unit distance. Assume that theminimum required power of the reflected signal at theterminal is 224 dB

[P rec] ≥ −24dB

−[ A ] × 2d ≥ −24dB (23)

where the maximum length of cable under test is 40 m in thisexperiment. Hence

[ A ] ≤ 24dB

80 m = 6 dB/20 m (24)

Referring to the frequency-dependent attenuationcharacteristics provided in Fig. 4 for 26 dB/20 m, thecentre frequency of the reference signal f 0 should beselected such that

f 0 ≤ 125 MHz (25)

In the general case, the procedure used to select the centrefrequency will depend upon the attenuation characteristicsof the system under test, or possibly other RF characteristics of interest.

Step 2. Frequency bandwidth: In (8) and in the conversion of time of flight into fault location, linear phase is assumed tosimplify the calculation. Therefore it is important that thefrequency response of the cable in Fig. 4 confirms that thisapproximation of linear phase is a reasonable assumption

within the frequency bandwidth of the reference signal. So,the frequency bandwidth is chosen to be 50 MHz as shownin Fig. 4. Also, a higher bandwidth will result in a higher resolution of the time–frequency cross-correlation as shownin (19).

Figure 4 Bode plot of Rockbestos Firewall III XLPE insulated

cable



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Step 3. Time duration: The performance of the signalgenerator in terms of rise/fall time and frequency sweepcapacity limit is 25 ns. In order to meet the selectedparameters (centre frequency and frequency bandwidth)selected above, the time duration of the reference signal isselected to be 30 ns.

In summary, the following parameters of the chirp signal(2) will be applied to the cable sample as a reference signal:

† centre frequency: v 0/2p = 125MHz;

† time duration of chirp: 1/ 2a

√ = 30ns;

† frequency bandwidth: a2 + b 2/2a

= 50 MHz

(100 MHz 150 MHz); and

† Frequency sweep rate: linearly increasing

(b /2p = 50 MHz /30ns)

In this section, the design of the reference signal iscustomised for a cable up to 40 m in length. However, for longer distance testing, the time duration of the signal is tobe increased whereas the centre frequency is to bedecreased so that the reference signal suffers lessattenuation by the wire or cable under test. The flexibility in designing the reference signal in JTFDR also allows oneto minimise frequency-dependent distortion of the reflectedsignal by assigning a relatively narrower frequency bandwidth.

3.4 Experimental setup

Fig. 5 is the system function diagram that describes theconfiguration and function of the experimental devices of the JTFDR wiring test bed. The computer (PC) instructsthe AWG to produce the Gaussian-chirp incident signaldesigned based upon the input center frequency,bandwidth, and time duration. The incident signalpropagates into the target cable via the circulator, isreflected at the fault location and travels back to thecirculator. The circulator redirects the reflected signal to thedigital oscilloscope. The computer program acquires both

the incident and reflected signals from the oscilloscope,calculates the time–frequency distributions of the incident

and reflected signals, and executes the time– frequency cross-correlation algorithm to detect, locate, and assess any defects on the cable. Fig. 6a shows the JTFDR wiring test bed which is composed of a signal generator, a digitaloscilloscope, a circulator, and a control PC. The heat chamber used for accelerated thermal ageing is shown in

Fig. 6b .

3.5 Detection and location of defects

For experimentation, a defect corresponding to the removalof 0.635 cm of the outer neoprene jacket insulation aroundhalf the circumference and 0.635 cm of the XLPEinsulation on one of the conductors around half itscircumference is created at 5.5 m from the beginning of thecable on a 10 m long cable sample described in Section 3.3.

The designed reference signal, which has a 125 MHz centre frequency, a 50 MHz bandwidth, and 30 ns time

duration, is transmitted down this cable. The JTFDR experimental results are given in Fig. 7. Fig. 7a shows theincident and reflected waveforms in the time domain. The

waveforms in Fig. 7a and the plot in Fig. 7b are allfunctions of time. For convenience, the time axis isconverted to distance by multiplying the time by the speedof propagation of the signal in the cable. The speed of propagation in the cable can be obtained by the speed of light (c ) and permittivity of XLPE (1r = 2.3) as follows

v = c

1r

√ = 3 × 108 2.3

√ = 1.98 × 108 ms−1 (26)

The first portion of the waveform located at 0 m is theincident waveform. The second portion of the waveformlocated at 10 m is the reflection from the open end of thecable. The reflection from the defect (located at 5.5 m) isalmost invisible in Fig. 7a . These incident and reflected

waveforms are acquired by the oscilloscope and saved to thePC. The corresponding Wigner distributions (W r and W s)and joint time–frequency cross-correlation function (C sr (t ))of the incident and reflected waveforms are calculated with(3) and (4). The plot of the time–frequency cross-correlation function (Fig. 7b ) shows a peak at thebeginning of the cable which corresponds to the cross-

correlation of the incident waveform with itself; this is alsoknown as the auto-correlation. Fig. 7b also shows an

Figure 5 JTFDR system function diagram



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obvious peak at the end of the cable which corresponds to thereflection from the open end. The smaller peak in betweenthose two corresponds to the reflection from the defect. Soeven if the reflection from an incipient defect is very minor in the time domain and potentially covered by the noise, if the time–frequency signature of the reflection is similar tothose of the transmitted signal, the time-frequency cross-correlation can exemplify this similarity.

After localising the defect from the time– frequency cross-correlation function, the four time and frequency moments(the time centre (t s), the time duration (T s), the frequency

centre (v s) and the bandwidth (B s)) of the localisedreference signal and reflected signal can be obtained by marginal distributions and are summarised in Table 1. TheT s, v s and B s of the reflected signal are all smaller thanthat of the reference signal because of the frequency-dependent attenuation. With the evaluated time andfrequency moments in Table 1, the accurate location of thedefect (d f ) can be calculated as follows:

† Estimated time delay: the estimated time delay of thereflected signal can be obtained from the time centres of

the localised signals

Dt r = t r − t s = 54.26 ns (27)

† Compensation time: the time delay caused by the distortionof the reflected signal needs to be compensated as follows

d t r =d f r

b = 125.45 × 106 − 122.03 × 106

2p 1.67 × 1015 = 0.32ns (28)

† Total time delay:

t delay

=Dt r

+d t r

=54.58 ns (29)

† Location of defect:

d f =vt delay

2 = (1.98 × 108)54.58 × 10−9

2 = 5.40 m (30)

This is 0.1 m from the actual fault distance whichcorresponds to only 1.8% error according to the entire fault distance. These experimental results show that JTFDR canaccurately detect and locate incipient defects on these

XLPE-insulated cables. Based on the theory andpreliminary results of JTFDR, in the next section we will

discuss the applications of JTFDR for prognostics of cables.

Table 1 Time and frequency center and bandwidth for

reference and reflected signals

Reference

signal

Reflected

signal

time centre t s (ns) 283.75 338.01

time duration t s (ns) 26.55 22.13

frequency centre f s (ns)

(MHz)

125.45 122.03

frequency bandwidth Bs

(ns) (MHz)48.64 43.78

Figure 6

a Experimental JTFDR cable test bed setupb Heat chamber for accelerated ageing test Q2

Figure 7Q2a Incident and reflected waveforms in the time domainb Corresponding time–frequency cross-correlation



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4 Condition monitoring viaaccelerated thermal ageing testing As defined by IEEE 1064 standard, the ageing is theoccurrence of irreversible deleterious changes that critically affect performance and shorten useful life [27]. Theaccelerated thermal ageing tests in this paper will apply higher stress levels than normal operation values to quickly induce age-related degradation of a cable and enable thestudy of the ageing process of the cable in a relatively short time period.

The well-known Arrhenius model is used to determine theageing test parameters such as thermal stress and timeduration. The Arrhenius model is based on chemical ratetheory and has been verified to be effective for many solidmaterials. The equation of the Arrhenius model describesthe relationship between the reaction rate and the

temperature of a chemical reaction [28]. The modified Arrhenius equation for an accelerated ageing test is statedbelow

t ct a

= e[ E a /B (1/T c−1/T a )] (31)

where T c is the service temperature; T a is the acceleratedageing temperature; t c is the ageing time at servicetemperature; t a is the ageing time at accelerationtemperature; E a is the activation energy of the material;B is the Boltzmann’s constant (given below)

B = 8.617 × 10−5 (eV /K) (32)

This equation equates the heating of a material at temperature T a for time t a to the ageing of the material at the service temperature T c over a time t c.

During the accelerated ageing test, JTFDR is employed toassess the various states of the cable during the ageing process. Before any external stresses are applied, the

waveforms are acquired and processed for the cable sampleto obtain the time–frequency cross-correlation baseline for future comparison. Then, the intended ‘hot spot’ of the

sample is put into the heat chamber (which is preheated toa specific temperature) for a certain number of hours (t a ),depending on how long (t c) the cable is to be aged. During the ageing process, the waveforms are acquired andprocessed after each hour to obtain an updated time–frequency cross-correlation plot. To achieve authentic andscientific results, this procedure is performed three timesafter each hour.

For XLPE insulation, the higher temperature will hastenthe chemical reaction rate and enhance the degree of other thermally activated processes. At temperatures greater than

908C, the crystalline regions melt and further oxidationoccurs [28]. The same Rockbestos Firewall III cable type

that was analysed in Section 3.5 will be used for this

accelerated ageing test. The length of the sample is again10 m, and the segment to be tested is located from 5 to6 m; thus, the length of the ‘hot spot’ is 1 m. The sameincident waveform (125 MHz centre frequency, 50 MHz bandwidth, 30 ns time duration) is applied to the cablesample. To simulate exposure to a service temperature of

508C for a duration of 60 years, the cable needs to beheated in the chamber at 1408C for 16 h. These parametersare determined by the Arrhenius equation with anactivation energy of 1.33 eV [29].

Fig. 8 presents the time–frequency cross-correlationfunction after 1, 10 and 14 h of thermal ageing. The peaksof the time –frequency cross-correlation function at theorigin and at the open-end of the cable show a peak valueclose to 1; these values do not change much with thermalageing. However, the time–frequency cross-correlationfunctions at each time exhibit differing reflections from the

‘hot spot’ located 5– 6 m away from the beginning of the cable. Notably, the time– frequency cross-correlationpeak value increases from less than 0.1 after 1 h up to 0.3after 14 h.

Fig. 9 is the monitored local peak value. The local peak value increases slowly from the beginning up to the 13thhour (48 simulated service years) and increases abruptly at the 14th hour (51 simulated service years). The increased

values are maintained for the 15th and 16th hours. Thisindicates that the quality of the cable under test ismoderately degraded from the beginning to 48 simulated

service years and is seriously degraded during 48 and 51simulated service years. The manner of this ageing processmay imply that electrical treeing was initiated during 48and 51 simulated service years. Electrical treeing is a rapid-degradation phenomenon that initiates at an imperfection[2]. The cable was removed from the chamber and twoadditional tests were conducted after the 16 hours of accelerated ageing. The local peak maintains the same highlevel as in the 14th–16th hours, which means the damageinitiated by accelerating ageing is irreversible.

Figure 8 Time– frequency cross-correlation at various times

during the ageing test for XLPE cable



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The experimental results show that the local peak hassuccessfully monitored the health status of the XLPE-insulated cable, demonstrating that JTFDR is an efficient

and non-destructive diagnostic and prognostic technique.Because the accelerated ageing tests in this paper areconducted over a preset time range, additional ‘time tobreakdown’ accelerated ageing tests need to be done tocomplete the ageing process. The local peak may then beused to predict the remaining life of the cable.

5 ConclusionsIn this paper, the theory and limitations of the classical wiring diagnostic techniques TDR and FDR were discussed. It was

shown that both techniques have good resolution in onedomain by sacrificing resolution in another domain. Incomparison, JTFDR was introduced which employs aninterrogating Gaussian-chirp incident signal to obtain bothtime localisation and frequency localisation. Theinterrogating incident signal may also have its centrefrequency, bandwidth and time duration customisedaccording to the cable under test to obtain a most-effective

wiring diagnostic/prognostic solution. In addition, the post-processing of the reflected signal can provide very sensitiveand accurate detection and location of the incipient defects.

The experimental test bed of JTFDR was introduced andthe process of determining the most effective reference

signal parameters for an electric power cable such asRockbestos Firewall III, XLPE-insulated cable wasexamined in detail. JTFDR was then used to successfully detect and locate an incipient defect with a minimal error of 1.8%, proving it to be the most promising diagnostictool of the three examined reflectometry techniques.

To further prove the capability of JTFDR as a prognostictool, accelerated ageing tests were applied to the same

XLPE-insulated cable type. The reputable Arrheniusequation provided the proper accelerated service time andtemperature for a desired simulated time and temperature.

The local peak of the time– frequency cross-correlationfunction was successfully used as an observer to monitor the status of the ageing cable after every hour of accelerated

ageing. The results showed that JTFDR possesses thesensitivity and localisation capabilities necessary for locating and monitoring age-related degradations within an XLPE-insulated cable.

JTFDR as an effective diagnostic and prognostic technique

can be applied to the health monitoring of electric cables where the access to the cable is limited but safety isrequired such as nuclear power plants and undergroundpower systems. Furthermore, if appropriate sensors areincorporated with the JTFDR technique described in thispaper, JTFDR can be applied in structural healthmonitoring to detect cracks in both pipelines and to thebodies of aircraft in the future.

6 Acknowledgments This work was supported by National Science Foundationgrants #0747681, ‘CAREER: Diagnostics and Prognosticsof Electric Cables in Aging Power Infrastructure,’ and theUS Office of Naval Research (ONR) under grantsN00014-02-1-0623 and N00014-03-1-0434 ‘Electric ShipResearch and Development Consortium.’ Author appreciatereal-world cable samples and FDR equipment from NavalResearch Laboratory (NRL).

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during the ageing test for XLPE cable



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SPR59165 Author Queries

J. Wang, P.E.C. Stone, Y.-J. Shin, R.A. Dougal

Q1 References [25, 26] are renumber to maintain sequence order. Please check.Q2 Please provide main caption for Figures 6 and 7.

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Prof. Yong-June ShinElectrical Engineering

University of South Carolin

301 S Main St.

Columbia South Carolina

United States

Reference: Item Number 0137S Ref. Id: SPR-2009-0137

SPECIAL ISSUE RADAR: Application of Joint Time-Frequency Domain Reflectometry

for Electric Power Cable

Diagnostics

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