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DOI: 10.1177/1475921719855915

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Detection of broken wires in elevatorwire ropes with ultrasonic guidedwaves and tone-burst wavelet

Javad Rostami , Peter W Tse and Maodan Yuan

AbstractElevator wire ropes with polymer cores hold and hoist heavy fluctuating loads in a corrosive environment. Such workingcondition causes metal fatigue, which together with abrasion around pulleys leads to progressive loss of the metalliccross section. This can be seen in the forms of a roughened and pitted surface of the ropes, reduction in diameter, andbroken wires. Therefore, their deterioration must be monitored so that any unexpected damage or corrosion can bedetected before it causes a fatal accident. Ultrasonic-guided wave-based inspection, which has proved its capability innondestructive testing of platelike structures such as tubes and pipes, can monitor the cross section of wire ropes intheir entire length from a single point. However, guided waves have drawn less attention for defect detection purposesin wire ropes. This article reports the condition monitoring of a steel wire rope from a hoisting elevator with brokenwires as a result of corrosive environment and fatigue. Finite element analysis was conducted as a baseline to studyguided wave propagation in wire ropes and plot dispersion curves. Guided wave propagation in wire ropes was experi-mentally investigated on a newly built cable stretching machine equipped with a load sensor under different amount oftensile loading. To expose the indication of broken wires, the recorded signals were analyzed by tailor-made continuouswavelet transform called tone burst wavelet.

KeywordsUltrasonic guided wave, elevator wire rope, NDT, defect detection, wavelet

Introduction

Steel wire ropes with a fiber core that hold and hoistheavy loads in different structures such as clamshells,draglines, and elevators work under fluctuating forcesin a corrosive environment. This consequently leads toprogressive loss of the metallic cross section due toabrasion and corrosion, which can be seen in the formsof roughened and pitted surface of the ropes, reductionin diameter, and broken wires. Broken wires, if nottaken care of, can lead to serious incidents and disaster.For example, in 2013, seven people were injured, threecritically, in a lift accident in Hong Kong. All fourcables of the lift—which could hold up to 12 people—broke at the same time.1 Incidents involving elevatorsand escalators each year kill 31 people and seriouslyinjure about 17,000 people in the United States.2

Therefore, regular inspection of wire ropes in order todetect probable defects is of vital importance.

An efficient inspection method must be able todetect and identify defects rather at their early stages so

that appropriate maintenance action can be executed.Ultrasonic-guided wave is an efficient method for long-range inspection of the platelike structures. Thismethod has been also applied to inspect helical wave-guides such as cables and steel strands.3,4 One of theearliest works on wave propagation within a structurewith arbitrary cross section belongs to Onipede andDong5 in which they reported two-dimensional finiteelement method for studying different modes behaviorwithin a pretwisted beam. However, experimental

The Smart Engineering Asset Management Laboratory (SEAM) and the

Croucher Optical Nondestructive Testing Laboratory (CNDT),

Department of Systems Engineering and Engineering Management, City

University of Hong Kong, Hong Kong, China

Corresponding author:

Peter W Tse, The Smart Engineering Asset Management Laboratory

(SEAM) and the Croucher Optical Nondestructive Testing Laboratory

(CNDT), Department of Systems Engineering and Engineering

Management, City University of Hong Kong, Hong Kong, China.

Email: meptse@cityu.edu.hk

investigation of guided waves in twisted structures wasmostly inspired by Kwun et al.6 in which noncontactmagnetostrictive sensors used for the excitation andsensing of guided waves in seven wire steel strand wasintroduced. It was found out that there is a frequencyband in which the guided waves do not tend to effi-ciently propagate. This frequency is called notch fre-quency and it changes by the amount of stress thatstrand undergoes. For defect detection purpose, thisfrequency range must be avoided. Every single wire inthe steel strand contributes to the total energy of pro-pagation. Lanza di Scalea et al.7 used magnetostrictive-based guided wave for stress measurement and defectdetection in a steel strand under the tensile load. Apartfrom narrowband excitation of guided waves in steelstrands, laser-based ultrasonic can be used for broadband excitation.8 Similar to the magnetostrictive sen-sor, the laser is a noncontact method. However, its highcost and bulky equipment make it cumbersome for realapplication. Comparing the propagation of guidedwaves in a single wire and a steel strand, attenuation ishigher in the latter one.

Lacking theoretical work in wave propagation, semi-analytical finite element (SAFE) method was intro-duced for wave propagation in a wave guide witharbitrary cross section.9 One of the earliest reportedworks concerning theoretical investigation of wave pro-pagation in a helical wave guide belongs to Treyssede.10

In order to overcome the lack of memory in current PCsystems for such simulation, he only discretized thecross section of a helical wire and used periodic bound-ary condition and a translationally invariant mapping.Investigation of elastic modes in steel strands with thesame method was carried out a few years later.11

Baltazar et al.12 were one of the first who used guidedwave for detecting defects in multiwire aluminum cablewith steel cores in which broadband excitation bymeans of conventional ultrasonic transducers at the freeend of the cable was used. It is noted that in the realworld, such excitation technique is not feasible becausethere is no access to the end of the cable. Raisutis etal.13 investigated the propagation of flexural modes inwire ropes with ultrasonic probes together with the pos-sibility of defect detection in their internal sections.Schaal et al.4 investigated damage detection withguided waves in an aluminum seven-wire strand withthe aid of Hilbert transform.

Nonetheless, not a lot of experimental work and sig-nal processing studies were reported on wire rope withpolymer cores. Steel wire ropes with polymer cores havevery complicated structures for the inspection withguided waves. Because of having the polymer coretogether with a high number of helical thin wires, thesignals are highly attenuative, which leads to a smallervalue of the signal to noise ratio in comparison with,

for example, pipe inspection. In addition, guided wavessignals, which are supposed to have a specified fre-quency band that is determined by the excitation signal,contain some unwanted frequency components, in prac-tice. These unwanted frequency components exposethemselves in some unwanted wave packets in the timedomain and may even overlap with the defect signaland mislead the signal interpretation. For narrow-bandexcitation of guided waves, tone-burst signals are highlypopular.14–18 Excited by the tone-burst, the received sig-nal is supposed to have the same frequency band as thetone-burst signal. However, in the real experimentbecause of the existence of different noise sources, theacquired signal has wider frequency band and is con-taminated in the time domain. Continuous wavelettransform (CWT) is an efficient time-frequency tool forcharacterizing dispersive guided wave signals. The suc-cess of the CWT highly depends on the proper selectionof the mother wavelet. The mother wavelet must havethe maximum resemblance with the incident andreflected guided wave signals. Much of the efforts inthis regard were focused on choosing conventional pop-ular mother wavelets. Nonetheless, if the noise level ishigh, small wave packets that are hidden in the noisecannot be detected. In this article, the excitation tone-burst signal was used as a mother wavelet to expose thehidden indication of broken wires in wire ropes. Withthe aid of this tone-burst wavelet hidden reflection ofguided wave signal from the broken wires was exposed.

Wire rope characteristics

Types of wire ropes

Wire ropes are composed of several precise, movingparts. Some wire ropes have more moving parts thanmany complicated structures. A wire rope with eightstrands can consist of more than 200 individual wiresthat work and move with respect to one another. Thesuccessful operation of an elevator wire rope dependsnot only on its design and manufacture, but also on itsmaintenance. They are always manufactured largerthan their nominal diameters. The nominal diameter isthe minimum diameter of which the wire rope will bemanufactured. Wire rope cores can be made of fiber orwires. Figure 1 demonstrates the different types ofcores. The fiber core is made of natural or syntheticfiber, which makes the wire rope very flexible and resis-tant to contact pressure. Meanwhile, the core can storelubrication to reduce the friction between wires (Figure1(a)). The wire strand cores are best suited for hightemperature working environments. They have moremechanical strength at the expense of lower flexibility(Figure 1(b)). In independent wire rope cores, the ten-sile force is reduced in individual wires, which make the

2 Structural Health Monitoring 00(0)

wire rope more resistant to crushing. In addition, theyare more heat resistant than the fiber cores and wirestrand cores (Figure 1(c)).

Wire ropes are identified by their construction or thenumber of strands per rope and number of wires ineach strand. For example, 6 3 24 Seale denotes a six-strand rope, with each strand having 25 wires. Seale (S)denotes the design. Other designs include Warringtonand filler wire. Seale wire ropes have thicker outer wiresand consequently higher degree of resistance againstexternal wear. The Warrington wire ropes have thinnerwires in their outer circle in comparison with the Sealewire ropes. This makes for a marked reduction in flex-ural stress. This type of wire ropes has better perfor-mance in fatigue bending tests. The elevator wire ropeswhose diameters are more than 16 mm should bedesigned with filler construction to improve their flexi-bility. If the diameter is less than 10 mm because of theextreme thinness of the wires, Filler construction is notrecommended. Figure 2 demonstrates the differenttypes of the wire ropes.19

Similar weights and breaking strengths make theconstruction to be grouped into wire rope classifica-tions such as the 8 3 19 and 6 3 19 classes. Unlike theearly days on which wire ropes were made of iron, thedominant material for manufacturing most elevatorhoist ropes is steel. A special grade of steel called trac-tion steel was developed to have high tensile strengthtogether with the good resistance to abrasion.

Nature of developed defects

In service, wire ropes must be removed if any of the fol-lowing defects are developed. Broken wires as a resultof fluctuating forces and the corrosive environment areone of the most common defects that can be seen inwire ropes. Construction regulations usually require arope to be replaced if the number of broken wiresreaches 5% of the total number of wires in the rope.20

As a result of corrosion and abrasion between thewire ropes and sheaves in elevators, the diameter of thewire rope can be reduced. If this reduction reaches 10%of the nominal diameter, the wire rope must be dis-carded. In addition, if the surface of the wires is severelyroughened or pitted, the wire rope should be replaced.20

In addition, the British Standard 6570 requires discard-ing of a wire rope whose surface is completely rough-ened or pitted.21

Furthermore, wire ropes can be deformed from theiroriginal shapes. The deformation occurs as a result oftight sheaves, poor fitting, shock loading, and overload-ing and corrosion. Figure 3 illustrates different types ofdeformation occur in wire ropes. The detail explanationabout wire rope defects and the corresponding failuremechanism can be found in Ronald and Lindsey.20

Finite element investigation

Using analytical methods for studying guided waves,guided wave characteristics for different frequencieshave been revealed for structures generally with simplegeometries such as plates, pipes, and bars.22

Nonetheless, explaining guided wave behavior in wireropes with polymer cores based on such methods areextremely complicated. As numerical methods can alsobe used to study wave propagation in different struc-tures,23,24 in this section simulation of guided waveswas carried out based on finite element methods(FEMs). Commercially available finite element soft-ware ABAQUS/EXPLICIT25 was utilized to conductthe study on the wire rope shown in Figure 4. Thesimulated wire rope with the diameter of 16 mm hadsix strands each with 24 single wires. Due to the smallperturbation resulting from the incident wave, the con-nections between the wires are constrained with tie con-straint in ABAQUS, and relative motions betweenwires were neglected.26

The single wires are steel and the core of the wirerope plus the cores of the strands consist of polypropy-lene. The material properties used for FEM are pre-sented in Table 1.

To have suitable spatial and time resolution inresults, certain criteria for mesh size and time incrementmust be met. The element size is determined from thesmallest wavelength (corresponding to the highest

Figure 1. Different types of wire rope cores: (a) fiber core, (b)wire strand core, and (c) independent wire rope core.19

Figure 2. Different types of wire ropes with fiber cores: (a)seale, (b) Warrington, and (c) filler.19

Rostami et al. 3

frequency of the interest). A rigorous condition of 20nodes per wavelength (Le = lmin/20) is recom-mended.27 An eight-node linear brick element (C3D8R)is selected as the element type. The stability limit forthe integration time (time of travel) is Dt = Lmin/CL.

27

The parameters Lmin and CL represent the smallestlength of the smallest finite element and bulk longitudi-nal wave velocity (5875 m/s), respectively. The largesttime step Dt and element size for the model are deter-mined by the maximum frequency of the interest fmax

27

Dt =1

20fmaxð Þ ð1Þ

The excitation of guided waves was implemented byapplying a time-transient displacement along the x axis

Figure 3. Wire rope deformation: (a) waviness, (b) birdcage, (c) loop formation, (d) loose wires, (e) nodes, (f) thinning of the rope,(g) kinks, and (h) flat areas.20

Figure 4. FEM model used for simulation of wave propagationin a 6 3 24 seale wire rope with seven polymer cores.

Table 1. The parameters used in the finite element method simulation of the wire rope.

Material Density (r) Young’s modulus (E) Poisson ratio (y)

Structural steel 7800 kg/m3 200 GPa 0.3Polypropylene 940 kg/m3 36 GPa 0.42

4 Structural Health Monitoring 00(0)

(Figure 4) that is a broadband excitation at the end ofthe structures

SExcitation tð Þ=� 1� cos 2pfctð Þ½ � cos 2pfctð Þ, 0<t< 1

fc0, otherwise

�

ð2Þ

In the above equation, SExcitation(t), t, and fc denotethe time transient excitation, the time, and the fre-quency of interest, respectively. As the purpose of thissimulation is to study the behavior of guided waves indifferent frequencies, the broadband pulse excitationfacilitates the study of dispersion in a wide frequencyband. It is worthy of mention that narrowband excita-tion can also be used; however, the simulation must berepeated for the different frequencies, which is time-consuming. Therefore, by using the broadband excita-tion, the study for a wide range of frequencies can bedone in only one single computation in the software.Figure 5 illustrates the temporal wave form and itsbroadband spectrum.

The radial displacement as a response to the excita-tion pulse were recorded from several equally spacednodal points (dx = 2 mm) along the structures (xdirection). The recorded data form a matrix m(t, x)whose columns are recorded signals at each nodal pointalong the wire rope.

The two-dimensional Fourier transform was laterused to identify the energy of each guided wave mode inthe frequency range of the above pulse. This transformis in fact a spatially Fourier transform of a temporalFourier transform. By applying the two-dimensional

Fourier transform on the matrix m(t, x), that is intime–space domain, the new matrix M(f,k), which is infrequency(f)–wavenumber(k), domain will be obtained

M f , kð Þ=

ð‘

�‘

ð‘

�‘

m t, xð Þe�i kx + 2pftð Þ ð3Þ

The obtained result M(f,k) can be used to study thedispersive nature of guided waves for different modes.The modes can be identified in the wavenumber–frequency domain. The detailed description can befound in Bartoli et al.28 and Raisutis et al.29 The resultsin the form of frequency–wavenumber dispersioncurves are depicted in Figure 6. The dominant modewith the highest energy is L(0,1) that demonstrates astable pattern with respect to wave number in differentfrequencies. Nonetheless, there is gap-like region in thefrequencies around 100 kHz.

Experimental setup for elevator wire rope

In-service elevator wire ropes are under stretchingloads. In order to have maximum resemblance with thepractical case, the experiment was conducted in cablestretching machine. This machine was designed andbuilt in SEAM lab at the City University of HongKong. The cable stretching machine is an essential toolfor simulating the real experiments in lab scale since inthe real world, the in-service cables in, for example, ele-vators are under the tensile force. Two cables at thesame time can be hosted by the machine. It is equipped

(a) (b)

Figure 5. The time transient force for generating guided waves: (a) the temporal waveform, and (b) its spectrum.

Rostami et al. 5

with a hydraulic pump that provides tensile force morethan 12000 lb. In addition, with installed load cell onthe machine, the varying load on the wire rope can beaccurately measured.

For gripping the wire rope inside the stretchingmachine wire rope clips were used. In this method, wirerope bends over a thimble and pass through the clips.The wire rope is fixed between the U-bolt and the sad-dle by fastening the two nuts. Figure 7 demonstrates agripping mechanism for wire ropes that was used in theexperiment.

In order for wire rope to withstand higher loads,using ferrule instead of clips was also considered(Figure 8). It should be noted that ferrule is muchstronger than clips; however, it is permanently locatedthere which prohibits installing the new sensors if it isneeded after one experiment. Furthermore, installingthe ferrule on a wire rope was not possible in the laband it had to be carried out at some workshops outside.Therefore, it was decided to use ferrule at one end andclips at the other end of the wire rope. In this case, afterpurchasing a wire rope with a ferrule at one end, mag-netostrictive sensor (MsS)30,31 was installed on the wirerope and afterward fixed it on the machine using theclips.

For generating and receiving guided wave signals,solenoid-type MsS were mounted on the wire rope. Aschematic drawing of this sensor is demonstrated inFigure 9. The MsS consists of two main parts that pro-vide static and dynamic magnetic fields. Superpositionof these fields subsequently induces guided waves inwire ropes. Six permanent magnets with three yokeswere used to expose an axisymmetric static magneticfield to wire ropes. The static filed was parallel with theaxis direction of wire ropes so that the MsS can gener-ate longitudinal guided wave modes. The dynamic fieldwas generated by a solenoid that consisted of three sec-tions connected in series. The adjacent sections in thesolenoid had reverse direction with equal length of42 mm that is approximately half a wavelength of theL(0,1) mode at 70 kHz in a single helical wire of a wirerope.

This type of sensor with the optimized configura-tion31 before fixing the clips are mounted on the wirerope. It should be noted that an array of PZT32 is notsuitable for this experiment under varying load condi-tion. Having a much stronger signal to noise ratio,PZT, however, must be replaced every time afterincreasing the tension in the wire rope. MsS, on theother hand, because of its noncontact nature, is physi-cally stable; regardless of the amount of load applied tothe wire rope. Moreover, because of its noncontactnature, it can freely move along the wire rope, whichcould be useful for experimental measurement of wavevelocity. As a result, despite having lower transductionenergy than PZT, MsS is preferable for the experiment.

The excitation signal is usually designed on a com-puter and then delivered to a function generator. Forall experiments, the generated signals are amplified by

Figure 7. Wire rope clips and its fixing method.19

Figure 8. Wire rope fixing with thimble and ferrule.

Figure 6. Frequency–wavenumber dispersion curves for a wirerope.

6 Structural Health Monitoring 00(0)

a RITEC 4000 pulser and receiver (RITEC Inc.,Warwick, RI, USA) before going to the transducer.Excited waveform, after propagating a distance in thestructure is sensed by a receiver. The obtained signalafter passing through RITEC 4000 pulser and receivercan be saved to a computer for further analysis.Figure 10 shows the schematic diagram of the

experimental setup employed for guided wave-baseddamage detection applications.

Ultrasonic-guided wave experiments were implemen-ted in two stages. In the first stage, the experiment wascarried out on a wire rope without any defect that wasunder varying tensile load. In the second stage of theexperiment, the focus was given to the wire rope withbroken wires. The broken wires on the structure weremade by cutting the wires by a hand saw as shown inFigure 11.

Figure 12 shows a schematic position of sensors onthe wire rope. The transmitter and receiver were 20 cmapart from each other.

The excitation was carried out by a five-cycle tone-burst signal modulated by the Hamming window asshown in Figure 13. It is noted that as the number ofthe cycle increases, frequency band becomes narrowerand as a result, the generated guided wave will be lessdispersive.

Experiment on the normal wire rope

Effect of tensile loading

In order to study the effect of the tensile load on guidedwave propagation, a healthy wire rope was mounted onthe cable stretching machine. During the experiment,the position of the transducer and receiver remainedunchanged. Under different loading conditions fromzero to 9425 lb, guided wave propagation was moni-tored for various excitation frequencies. The frequencyof the excitation signal, which was the five-cycle toneburst was swept from 70 kHz to 150 kHz. Every fre-quency step was 5 kHz. It was found out that theamplitude of the direct signal (the first wave packetrecorded by the receiver) alters in every frequency andtensile load. In order to study such observation more

Figure 9. (a) MsS mounted on a wire rope and (b) description of the dynamic coil with three sections each equals to a halfwavelength of the L(0,1) mode at 70 kHz.

Figure 10. Experimental setup for guided wave testing.

Figure 11. Broken wires made by hand saw.

Rostami et al. 7

precisely, the energy of every recorded signal S(t) fordifferent loading and frequency was calculated asfollows

E =

ð‘

�‘

S tð Þj j2dt ð4Þ

Figure 14 demonstrates the variation of signal energyin different frequencies. It is worthy of mention that forultrasonic sensors, the energy of the signal has a maxi-mum point for a specific value of the frequency. If thefrequency increases or decreases, the corresponding sig-nal’s energy will decrease. Noting this fact, it can beobserved that the variation of signal energy follows adifferent pattern. As the frequency increases, the signalenergy initially drops and then rises. If the frequencyfurther increases, the signal energy starts to declineagain.

Regardless of the amount of tensile loading, suchphenomenon follows the same pattern. The only differ-ence is that for the higher amounts of loading energy ofthe signal is generally higher. Meanwhile, the locationof minimum signal energy, which was initially at90 kHz for zero loading moves toward higher frequen-cies such as 95 kHz for 6525 lb. This change in thelocation of minimum signal energy can be used forstress measurement. Figure 15 demonstrates the varia-tion of signal energy by increasing the tensile load inthree frequencies. Three excitation frequencies includ-ing 70, 95 and 120 kHz represent a different region ofthe diagram in Figure 14. As can be seen in Figure 14,if the larger tensile load is applied to the wire rope, theenergy of the signal will increase. This rising in the sig-nal energy is sharper when the frequency is 70 kHz;

Figure 12. Schematic diagram of the wire rope with mounted transducer and receiver.

Figure 13. (a) Five-cycle tone-burst at 150 kHz center frequency and (b) its spectrum.

Figure 14. Variation of direct signal energy coming from thetransducer and received after propagation of 200 mm on thewire rope under different amounts of loading.

8 Structural Health Monitoring 00(0)

that is the central frequency of the MsS. For the excita-tion frequency of 120 kHz, such growth is slower. Onthe other hand, for the frequency of 95 kHz, which rep-resents the valley in Figure 14, a variation of the tensileloading has very little effect on the signal energy. Thisphenomenon is likely due to the complicated helicalstructure of the wire rope and the interwire contactbecause of which the energy of guided waves leaksbetween neighboring wires.33

Notch frequency

If the observations in Figures 14 and 15 are integrated,three-dimensional representation of the effect of tensileload on the signal energy under different excitation fre-quencies can be obtained. Such representation isdepicted in Figure 16. In this figure, x and y axesdemonstrate frequency and tensile loading; respectively.The color bar illustrates the scale for representation ofthe signal energy. In order to obtain high-resolutionimage, linear interpolation was applied to the data inFigures 14 and 15.

As it is demonstrated in Figure 16, there is a gap inthe signal energy around 95 kHz. The remarkable dropin signal energy around this frequency is consistent withthe FEM result presented in Figure 6. The dashed linein Figure 6 demonstrates the subtle growth in this miss-ing frequency band by applying more loads. It lookssimilar to the notch frequency region whose existencewas reported for steel strands.6 For the steel strand,similar phenomenon happens because of the radial dis-placement constraint, which is imposed on helical wiresby the core in the interwire contact region. It corre-sponds to a veering in the L(0,1) mode and increasesunder tensile loads, that is, mainly due to interwire con-tact mechanisms.34 This growth is in agreement withthe work reported by Treyssede et al.,35 in which theincrease in the notch frequency of steel strands undertensile load happens as a result of the increase in theinterwire contact. The theoretical explanation aboutcurve veering can be found in Treyssede34 and Perkinsand Mote.36

A closer look at the recorded waveform in the timedomain in Figure 17 reveals that the tone burst signalat the receiving point in notch frequency region is dis-torted. Meanwhile, fast Fourier transform (FFT) of thesignal in this region shows significant distortion. Suchdistortion appears with the branching of the originalexcitation signal. Addressing the notch frequency inwire ropes, it should be noted that for damage detec-tion purpose, this frequency region must be avoided.

Detecting defects in wire ropes

Noting that for nondestructive testing of the wire rope,the notch frequency must be avoided, the experimentwas conducted on a normal wire rope and a wire ropewith seven broken wires. The broken wires are less than5% of the total wires in the 6 3 24 wire rope.According to Figure 14 as the 70 kHz excitation fre-quency grants the maximum obtained signal energy,this frequency was chosen to inspect the wire rope fordamage detection. The measured signals are demon-strated in Figure 18. To increase the chance of spotting

Figure 16. Representation of direct signal energy coming fromthe transducer and received after propagation of 200 mm onthe wire rope under different amounts of loading in differentfrequencies.

Figure 15. Effect of increasing tensile load on the energy ofthe waveform arriving from the transducer after propagating a200 mm distance on the wire rope at frequencies of 70 kHz,95 kHz, and 120 kHz.

Rostami et al. 9

the reflection from the defect, the input gain of the sig-nal was increased. The first wave packet that can beobserved for both wire ropes is the direct signalreceived by the receiver after propagating a 360 mmdistance that is measured from the middle point of thetransducer to the middle point of the receiver. As thesignals are noisy, it can be observed that there is nosign of a defect in the signal belonging to the wire ropewith broken wires.

Tone-burst wavelet

The wavelet transform is a powerful tool for analyzingand processing nonstationary signals such as guidedwave signals. Unlike the short-time Fourier transform,which gives general local feature information of a defectsignal in fixed windows, CWT has more choices of basisfunction to match a defect signal. Localizing time-frequency atoms and de-noising with some modifica-tions can facilitate signal interpretation for

Figure 17. Changing in the waveform in time and frequency domains arriving from the transducer after propagating a 200 mmdistance on the wire rope at frequencies of (a) 70 kHz, (b)90 kHz, and (c) 110 kHz.

Figure 18. Signals obtained from wire ropes and their spectrums: (a) temporal waveform of the normal wire rope, (b) spectrum ofthe waveform from the normal wire rope, (c) temporal waveform of the wire rope with broken wires, and (d) spectrum of thewaveform from wire rope with broken wires spectrum.

10 Structural Health Monitoring 00(0)

nondestructive testing (NDT) purpose.37,38 The wavelettransform is a powerful tool that decomposes signalswith respect to their frequency components. Thedecomposition of a signal S(t) is implemented by find-ing the signal correlation with the mother wavelet c(t)

WTC a, bð Þ=1ffiffiffiap

ð‘

�‘

S tð ÞC� t � b

a

� �dt ð5Þ

where c*(t) indicates the complex conjugate of themother wavelet c(t), a is the dilation parameter (scale)and b is the translation. According to the above equa-tion, the larger values of the wavelet coefficient, WT, isobtained when there is more similarity between the sig-nal and the mother wavelet. Therefore, the motherwavelet must be chosen such that it has the maximumresemblance with the excitation signal. In doing so, allthe wave packets, that are consistent in shape and fre-quency with the excitation signal will have larger wave-let coefficients. Tone-burst signals are sine wavesmodulated by windows such as the Hamming window

S tð Þexcitation = sin vt + uð Þ 0:08 + 0:46 1� cosvt

N

� �� �� �

ð6Þ

where t, v, u, and N are the time, circular central fre-quency, phase, and number of cycles, respectively. Thefrequency band can be easily altered by changing thenumber of cycles. The narrower band signals can beobtained by increasing the number of cycles in thetone-burst signals. In this case, if the excitation signal isa five-cycle tone-burst, for example, the Morlet waveletcould be a good choice. However, this resemblancedecreases if the number of cycles in the excitation tone-burst signal is altered. Figure 19 demonstrates how dif-ferent the five-cycle tone-burst signal and Morlet wave-let waveform are. In the real world, an unsuitableselection of the mother wavelet will affect the accuracy

of CWT in extracting defect-related information fromthe measured signals.

Addressing this problem, the aim is to find a waveletfunction that best matches the excitation tone-burst sig-nals. In doing so, the excitation signal itself can be tai-lored as a mother wavelet.32 In this case, CWT canhelp decompose the reflected signals with regard totheir frequency components in a much more efficientway. The decomposition is implemented by finding asignal correlation with the selected mother wavelet. Theexcitation tone-burst signal that is used as a motherwavelet is called the tone-burst wavelet. By applyingthis wavelet on a very contaminated guided wave sig-nal, the wave packets that have a similar shape to theexcitation signal (with a high correlation value with themother wavelet of CWT) could be extracted from thereceived and defect-related signals. Any noise andundesired components that did not have a shape similarto the shape of the mother wavelet (with a low correla-tion value with the mother wavelet of CWT) can beremoved from the raw measured signals. Hence, thelargest value of the wavelet coefficients facilitated theexposure of a probable small defect signal in a highlycontaminated signal.

Detecting of broken wires

As it was demonstrated in Figure 18, the broken wiresare not detectable in the measured signal. The defecthas 4.6 % of the whole cross section of the wire rope.In this section, the tailor designed tone-burst waveletwas used for analyzing the signals. The signal acquiredfrom the normal wire rope was represented by Morletand tone-burst wavelets in Figure 20(a) and (b), respec-tively. After that, Morlet and tone-burst wavelets wereapplied on the signal obtained from the wire rope withbroken wires. The results are depicted in Figure 20(c)and (d). As can be seen, Morlet Wavelet was unable todetect the defect. However, when the signal undergoesthe tone-burst wavelet, the representation highlight

(a) (b)

Figure 19. Mother wavelets used for CWT: (a) five-cycle tone-burst and (b) Morlet.

Rostami et al. 11

something extra and a clear distinction can be seenbetween the representations of normal and defectivewire ropes.

The result in Figure 20(d) shows that around0.23 ms there is a wave packet that corresponds to70 kHz. This wave packet is, in fact, the reflection ofthe incident signal from the defect, that is, received bythe receiver after traveling 640 mm from the locationof broken wires to the center of receiver. It can be con-cluded that in the presence of the noise when the defectindication is buried in it, the obtained signal must befurther processed by advanced signal processing tech-niques. In this regard, the tailor-designed tone burstwave is a practical tool that facilitates signal interpreta-tion. Meanwhile, it is a helpful tool in checking thestructural integrity of different structures including wireropes.

Conclusion

In this article, the propagation of guided waves in ele-vator wire ropes with polymer cores was numericallyand experimentally investigated. To simulate the realworking condition, the wire rope was mounted on acable stretching machine, which was designed and built

at our lab at the City University of Hong Kong. Thesignal energy was calculated for a different number ofloads and excitation frequency. It was found out that,in some frequencies called the notch frequency, theenergy of the received signal is very low. Meanwhile, innotch frequency region, FFT of the received wavepacket exhibit severe branching and subsequently, itsfrequency characteristics differ from the incident signal.Identifying notch frequency region is of great impor-tance for nondestructive testing of the wire ropes todetect broken wires. As the signal energy and its spec-trum changes within this area, such region should beavoided.

Addressing the notch frequency and its location, afrequency with energy response was chosen to inspectthe wire rope with broken wires. As the defect con-tained only few broken wires (less than 5% of the crosssection of the wire rope) and as a result, a small defect,its indication in the signal was not detectable. In orderto spot the broken wires in the signal, the tailor-madetone-burst wavelet was used for time–frequency repre-sentation of the signal. As the mother wavelet in thetone-burst wavelet has the maximum resemblance withthe excitation signal, it generates larger wavelet coeffi-cients in comparison with other types of wavelets such

Figure 20. CWTof the signals obtained from the wire ropes: (a) Morlet wavelet from the normal wire rope, (b) tone-burst waveletfrom the normal wire rope, (c) Morlet wavelet from the wire rope with broken wires, and (d) tone-burst wavelet from the wirerope with broken wires.

12 Structural Health Monitoring 00(0)

as Morlet. As a result, the indication of broken wiresthat was buried in the noise in the original measuredsignal was spotted by using tone-burst wavelet.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest withrespect to the research, authorship, and/or publication of thisarticle.

Funding

The author(s) disclosed receipt of the following financial sup-port for the research, authorship, and/or publication of thisarticle: the work described in this article was fully supportedby a grant from City University of Hong Kong (Project No.7004905) and a grant from the Innovation and TechnologyCommission (ITC; Project No. ITS/061/14FP) of theGovernment of the Hong Kong Special AdministrativeRegion (HKSAR), China. Any opinions, findings, conclu-sions, or recommendations expressed in this material (or bymembers of the project team) do not reflect the views of theGovernment of the HKSAR, ITC, or Panel of the Assessorsfor the Innovation and Technology Support Programme ofthe Innovation and Technology Fund.

ORCID iD

Javad Rostami https://orcid.org/0000-0001-9943-8587

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