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A Signal Processing Approach with a Smooth Empirical Mode Decomposition to Reveal Hidden Trace of Corrosion in Highly Contaminated Guided Wave Signals for Concrete-Covered Pipes Javad Rostami *, Jingming Chen and Peter W. Tse Department of Systems Engineering and Engineering Management, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China; [email protected] (J.C.); [email protected] (P.W.T.) * Correspondence: [email protected] Academic Editors: Dipen N. Sinha and Cristian Pantea Received: 18 December 2016; Accepted: 1 February 2017; Published: 7 February 2017

Abstract: Ultrasonic guided waves have been extensively applied for non-destructive testing of plate-like structures particularly pipes in past two decades. In this regard, if a structure has a simple geometry, obtained guided waves’ signals are easy to explain. However, any small degree of complexity in the geometry such as contacting with other materials may cause an extra amount of complication in the interpretation of guided wave signals. The problem deepens if defects have irregular shapes such as natural corrosion. Signal processing techniques that have been proposed for guided wave signals’ analysis are generally good for simple signals obtained in a highly controlled experimental environment. In fact, guided wave signals in a real situation such as the existence of natural corrosion in wall-covered pipes are much more complicated. Considering pipes in residential buildings that pass through concrete walls, in this paper we introduced Smooth Empirical Mode Decomposition (SEMD) to efficiently separate overlapped guided waves. As empirical mode decomposition (EMD) which is a good candidate for analyzing non-stationary signals, suffers from some shortcomings, wavelet transform was adopted in the sifting stage of EMD to improve its outcome in SEMD. However, selection of mother wavelet that suits best for our purpose plays an important role. Since in guided wave inspection, the incident waves are well known and are usually tone-burst signals, we tailored a complex tone-burst signal to be used as our mother wavelet. In the sifting stage of EMD, wavelet de-noising was applied to eliminate unwanted frequency components from each IMF. SEMD greatly enhances the performance of EMD in guided wave analysis for highly contaminated signals. In our experiment on concrete covered pipes with natural corrosion, this method not only separates the concrete wall indication clearly in time domain signal, a natural corrosion with complex geometry that was hidden and located inside the concrete section was successfully exposed. Keywords: ultrasonic guided wave; NDT; signal processing

1. Introduction Pipes carrying gas into residential buildings are critical infrastructure. Inside the buildings, these pipes pass through the concrete walls. To check the integrity of these pipes, a reliable method must be able to test without having access to the entire geometry of the structure. Ultrasonic guided wave is an effective tool to inspect pipes and has been investigated and improved during past years [1–7]. However, most of the effort in this regard was focused on pipes without any cover or coatings. Existence of coatings around pipes causes limiting inspection range by more attenuation and degrades guided wave test performance. Kwun et al. reported that the coefficients in the coated, buried pipes Sensors 2017, 17, 302; doi:10.3390/s17020302

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were two order of magnitude greater for torsional modes in comparison with bare aboveground pipes [8]. Though conducting the test at low frequencies such as 30 KHz could be a solution to such problems, it will limit the guided wave sensitivity to locate the small defects. Barshinger and Rose calculated attenuation dispersion curves for longitudinal modes in hollow cylinder coated with viscoelastic material. They concluded that by changing the mode and frequency of operation, lower attenuation can be achieved [9]. However, using higher frequency can result in excitation of higher order modes that possibly complicate guided wave signals. Predoi described the wave propagation nature in multilayered pipes by means of SAFE method [10]. For buried pipes, depending on the status of coating and mode type, attenuation could be different. Comparing longitudinal L(0,2) with torsional T(0,1), it was demonstrated that for different status of sands, L(0,2) is less attenuative [11,12]. Apart from guided waves in pipes, corrosion in reinforced bar covered by concrete was studied by Miller et al. [13]. Later on Lu et al. [14] extracted statistical parameters for damage detection in rebar-reinforced concrete beams. It must be noted that unless a structure and its defect have simple geometries, the interpretation of captured signals may not be straightforward for damage detection. This complication is caused by wave reverberation, the dispersion characteristic of guided waves [15] and the existence of multiple modes within a desired working frequency range [16,17]. Although choosing non-dispersive axisymmetric modes may initially facilitate the test, mode conversion at the location of a non-symmetric defect escalates the complexity of obtained signal [2]. To overcome these difficulties, some studies were focused on developing new sensors for pure mode excitation and efficient transduction of guided waves [18–22]. For example, Vinogradov proposed magnetostrictive transduction systems for generation of torsional modes of guided waves in pipes because of their non-dispersive nature [23]. The new transduction techniques greatly improve the quality of signals in terms of suppressing flexural modes. Being highly dispersive, these flexural modes are mostly preferred to be avoided. The velocities of these modes are normally very close to the excitation mode. This will cause the signal to contain multiple overlapping modes that may cover probable defect indications. It must be noted that, although suppression of unwanted modes is possible in transduction stage, they will appear when guided waves reach non-symmetric and irregular defect shapes. To obtain more information about guided wave signals, the most straightforward approach is perhaps to utilize one of the Time-Frequency Representation (TRF) methods. Some of the studies during past years were focused on the improvement of different TFRs for guided wave signals with taking their dispersive characteristic into account [24–26]. Nevertheless, if the frequency contents of two overlapped wave packages are very close to each other or roughly the same, mode separation by means of conventional TFRs may not be feasible. Chen et al. addressed the corrosion detection in submerged aluminum plate with post processing of the acquired signals [27]. In another attempt for pipes, Tse and Wang [28] estimated the axial length of a defect by matching pursuit. Despite efficiency of matching pursuit, it is computationally expensive and very sensitive to noise. In addition, its performance depends on a dictionary in which dispersion of guided waves is neglected. Matching Pursuit is also too sensitive to the background noise that can deteriorate its outcome. Moreover, Chirplet transform was used to characterize the defects in plates and pipes with artificial notches [29,30]. Being an effective method to separate overlapped modes, Chirplet was applied to a guided wave signals in highly controlled environment without being influenced by real noise. In addition, setting different parameters of Chirplet Transform can add to its computational cost together with its mathematical complexity. One of the notable methods for mode separation is the empirical mode decomposition (EMD) that can be applied to wide variety of non-stationary signals [31]. This method effectively separates the overlapping wave packages into intrinsic mode functions (IMFs); however sometimes it may not provide satisfactory results if overlapped modes have the same frequency band. In another word, it may not be able to fully decompose a signal that has multiple overlapping modes. Meanwhile, it suffers from the end effect and redundant IMFs that in some cases might affect the final results [32,33]. Nevertheless, there have been some improvements on EMD method [34–36]. Recently, Yan and

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Lu [37] applied EMD combined with wavelet on a vibration and an electrocardiogram (ECG) signals. In this paper, a similar approach but with a tailored mother wavelet that we call Smooth Empirical Mode Decomposition (SEMD) is adopted to expose a natural corrosion indication hidden in highly overlapped and contaminated signal from a concrete covered pipe. The validation of the proposed method was verified by applying it on different guided wave signals obtained from concrete-covered pipes. To demonstrate the effectiveness of this approach and the amount of improvement it provides, the signals were compared with conventional EMD and Ensemble EMD (EEMD). Meanwhile, for even further validation, we examined the performance of this method by applying it on guided wave signals acquired from field test. Field test data belonged to gas pipes passing through concrete wall in residential buildings. 2. Wavelet Transform (WT) The wavelet transform is a powerful tool to assess signals by decomposing them on a set of basic functions. The basis vectors are acquired through a family of functions that depend on scale coefficient and the translation step. It is based on windowing signals into variable sized regions using broader sized windows in time to observe low frequencies, and shorter sized windows in time to spot high frequencies; required by the Heisenberg uncertainty principle [38]. According to Heisenberg principle time-frequency resolution is limited by the following relationship: σt2 σ2f ≥

1 4

(1)

where σt2 and σ2f are time and frequency variances, respectively, which represent the local resolution of Wavelet. The Wavelet transform is the sum of the whole signal x(t) multiplied by a wavelet function (mother wavelet ψ(t)): +∞   Z 1 t−l dt (2) W= √ x (t)ψ s s −∞

where s and l are scale and shift, respectively and W represents wavelet coefficients. By growing scale, the basis function is dilated; therefore, the corresponding coefficients give information about low frequency components of the signal, and vice versa [39]. It is worthy of emphasis that the success of Wavelet Transform or at least its best result depends on selecting a mother wavelet that maximally matches the shape of the signal that is being analyzed [40]. Considering the right choice of mother wavelet for a particular problem greatly enhances the outcome of the wavelet transform, one can not only choose a mother wavelet among standard wavelet functions but also tailor a function based on prior knowledge about the signal. For example, for guided wave signals a mother wavelet must be chosen or tailored in a way that, it has the maximum resemblance with the excitation signal. For excitation of guided waves in general, narrowband tone-burst signals are used. Tone-burst signal S(t) is simply a sine wave modulated by windows such as Hamming window: 

X (t)excitation





ωt = sin(ωt + θ ) 0.08 + 0.46 1 − cos N

 (3)

where t, ω, θ and N are the time, circular central frequency, phase and number of cycles, respectively. A five-cycle tone-burst signal is depicted in Figure 1.

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Figure 1. Hamming windowed, five-cycle tone-burst; tailored as a mother wavelet. Figure 1. Hamming windowed, five-cycle tone-burst; tailored as a mother wavelet.

Among standard wavelet functions Morlet and Gaussian wavelets have a good similarity with Among standard wavelet Morlet and Gaussian wavelets a goodsignal, similarity the five-cycle tone-burst signalfunctions but for different number of cycles in thehave tone-burst theywith may the signal but if for different number in the tone-burst may notfive-cycle be the besttone-burst choice. Meanwhile, this excitation signalofiscycles tailored to be used as asignal, motherthey wavelet, not be the Meanwhile, if thiswave excitation signal is tailored usedofasanalytic a mother wavelet, it will givebest thechoice. best results for guided analysis. In this paper,to a be family tone-burst itsignals will give the best results for guided wave analysis. In this paper, a family of analytic tone-burst with different number of cycles was designed. Moreover, negative frequency components of signals with different number cycles was designed. negativeto frequency components each member of the family wereofdiscarded with the aid ofMoreover, Hilbert Transform build analytic wavelet of each member of the family were discarded with the aid of Hilbert Transform to build analytic functions. Meanwhile, de-noising can be achieved by wavelet shrinkage and thresholding methods wavelet functions. Meanwhile, can be by wavelet shrinkage thresholding [41]. When thresholding is usedde-noising for de-noising, it isachieved evident that the threshold leveland should be higher methods [41]. When thresholding is used for de-noising, it is evident that the threshold level should than the noise level and below the signal level to maintain the critical information of the signal in the be higher than the noise level and below the signal level to maintain the critical information thea first place as well as efficiently remove any contamination. The value of the threshold canofbe signal in the placeofassome wellwell-known as efficientlyparameters remove any The value of the constant or afirst function in contamination. the signals or mother wavelet. Forthreshold example, can be a constant or a function of some well-known parameters in the signals or mother wavelet. for automated inspection systems, the threshold value is advised to be 1.6 to 2.0 times the mean noise For example, for automated inspection systems, the threshold value is advised to be 1.6 to 2.0 times level; which means signal to noise ratio must be greater than 4.0 to 6.0 dB. The acoustic noise can the mean noise level; which means signal to noise must beultrasonic greater than 4.0 to 6.0are dB.not Therelated acoustic result from wave scattering and reverberation of ratio the incident waves that to noise can result from wave scattering and reverberation of the incident ultrasonic waves that are not probable defects. It can be addressed as an uncorrelated Gaussian random variable, with zero mean related probable defects. can be addressed as an uncorrelated Gaussian random and a to band-limited powerItspectral density function [40]. Wavelet transform act variable, as filterswith that zero mean and a band-limited power spectral density function [40]. Wavelet transform act as filters decompose the signals into approximations and details. If the details have very low amplitude, they that signals into approximations and details. If the details veryinformation. low amplitude, can decompose be removedthe which consequently decreases noise level without losinghave critical The they can be removed consequently decreases noise levelwhose without losing critical information. thresholding is basedwhich on discarding all wavelet coefficients modulus is smaller than the The thresholding is based values on discarding all wavelet coefficients whosethe modulus threshold. The remaining are subsequently used to reconstruct signal. is smaller than the threshold. The remaining values are subsequently used to reconstruct the signal. 3. The Empirical Mode Decomposition (EMD) 3. The Empirical Mode Decomposition (EMD) Empirical mode decomposition is an adaptive method introduced to analyze non-linear and Empirical mode decomposition is an adaptive method introduced to analyze non-linear and non-stationary signals such as guided wave signals. It consists in a local and fully data-driven non-stationary signals such as guided wave signals. It consists in a local and fully data-driven separation of signals in fast and slow oscillations. EMD works based on iteratively subtract the local separation of signals in fast and slow oscillations. EMD works based on iteratively subtract the mean from the signal to be decomposed to obtain the zero mean components called intrinsic mode local mean from the signal to be decomposed to obtain the zero mean components called intrinsic functions (IMF). In this method, a signal is decomposed into IMFs that are not necessarily sinusoidal mode functions (IMF). In this method, a signal is decomposed into IMFs that are not necessarily [31]. The summation of all IMFs plus a residue constitutes the original signal x(t): sinusoidal [31]. The summation of all IMFs plus a residue constitutes the original signal x(t): n

n IMF  t   r  t  x t    j n

x (t) =

j 1 I MFj ( t ) + r n ( t ) ∑

(4) (4)

j =1

Every IMF must satisfy two following conditions: Every IMF must satisfy two following conditions: (1) In the whole dataset, the number of extrema and the number of zero-crossings need to be equal onlywhole differdataset, by one. the number of extrema and the number of zero-crossings need to be equal (1) or In the (2) At any point, a mean or only differ by one. value determined by local maxima envelop and local minima envelop is zero. (2) At any point, a mean value determined by local maxima envelop and local minima envelop is zero. Extracting IMFs is an iterative procedure. First, local maxima and local minima in x(t) are identified and by means of a cubic spline all local maxima and local minima are connected,

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Extracting IMFs is an iterative procedure. First, local maxima and local minima in x(t) are identified and by means of a cubic spline all local maxima and local minima are connected, respectively. After that, mean value of upper and lower envelop m1 (t) is calculated and is subtracted from x(t): h1 ( t ) = x ( t ) − m1 ( t )

(5)

If h1 (t) satisfies the two abovementioned conditions, it is the first IMF; otherwise, x(t) is replaced by h1 (t) and the previous process called sifting process is repeated k times until the IMF conditions are satisfied: h1,j+1 (t) = h1,j (t) − m1,j+1 (t), j = 1, 2, . . . , k (6) in which m1,j+1 (t) is the mean of upper and lower envelop for h1,j (t). After finding the first IMF, it is subtracted from the original signal: r1 (t) = x (t) − I MF1 (t)

(7)

where r1 (t) is the residue. Then the residue is treated as new data and the process is repeated to find the remaining IMFs. The process continues until the residue rn (t) becomes too small or a monotonic function from which no more IMFs can be extracted. As EMD suffers from mode mixing problem, it is further on developed into Ensemble Empirical Mode Decomposition (EEMD) by Wu and Huang [42] to alleviate this shortcoming. In the EEMD method, a white noise is initially added to the signal and decomposing the signal into IMFs is carried out afterwards; similar to EMD. As the white noise is random, the process is repeated over a large number with different sets of white noise. The final decomposition result is acquired by finding the mean of each IMF from each signal decomposition process. The amplitude of white noise substantially affects the performance of EEMD so that if it is too small, it may not prevent mode mixing and if it is too large, the number of ensemble averages required might be too high to suppress the noise in the ensemble averaged IMFs. The value is suggested to be 0.1–0.4 of the standard deviation of the original signal. 4. Smooth Empirical Mode Decomposition (SEMD) Being an effective tool to reveal physical meanings of a signal, EMD suffers from multiple shortcomings that were earlier mentioned. One of its major problems is the frequent appearance of mode mixing. Mode mixing means that an IMF consists of signals of widely disparate scales or signals of a similar scales residing in different IMF components. EEMD provide improvement for mode mixing when the analyzed signal contains high frequency intermittent oscillations [43]. Meanwhile, EMD experiences end effects problems and redundant IMFs that in some cases might affect the final results [42]. Yan and Lu [37] presented an improvement on Hilbert-Huang transform to solve the end effect problem for ECG signals. End effects issue is caused as a result of the lack in a number of extrema at both ends of a signal. This lack deteriorates spline curve fitting process and consequently corrupts each IMF with complex frequency components. To reduce this effect, in SEMD the wavelet transform clarified in the earlier section is applied on IMFs during sifting the process by the following equation:

Wj,k =

+∞ Z

I MFi (t)ψj,k (t)dt

(8)

−∞

where Wj,k is the kth wavelet coefficient at the jth level, j, k  Z. And ψj,k (t) is the mother wavelet. Threshold de-noising is then utilized to eliminate unwanted components in every IMF. After de-noising, new wavelet coefficients are estimated and subsequently a new IMF is reconstructed. After that, unlike conventional EMD, this time, the new purified IMF0 is subtracted from the original signal: ri (t) = x (t) − I MF 0 i (t)

(9)

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The Theabovementioned abovementionedprocess processisisrepeated repeatedininevery everysifting siftingstage stagesosothat thatnew newIMFs IMFsare areextracted extracted from fromthe thesignal. signal.As Aspreviously previouslymentioned, mentioned,for forguided guidedwave wavesignals, signals,incident incidentwaves wavesare arewell wellknown known and consequently it can be inferred that the signals consist of a combination of the incident waves and consequently it can be inferred that the signals consist of a combination of the incident waves plus plusunwanted unwantedreverberations. reverberations.The Thesame sameassumption assumptioncan canbebemade madefor forIMFs IMFsthat thatconsequently consequentlyform form the Therefore, forfor guided wave signals in which the the tone-burst signal is selected for theoriginal originalsignal. signal. Therefore, guided wave signals in which tone-burst signal is selected the excitation, this assumption can be made when dispersion characteristic of guided waves for the excitation, this assumption can be made when dispersion characteristic of guided wavesisis neglected. neglected.As Asa aresult, result,instead insteadofofusing usingstandard standardwell-known well-knownmother motherwavelets, wavelets,ininSEMD SEMDwe wecan cantailor tailor a acomplex tone-burst function as a mother wavelet which best matches the ultrasonic guided wave complex tone-burst function as a mother wavelet which best matches the ultrasonic guided wave signal. i’ are signal.The Thesteps stepsfor forimplementing implementingSEMD SEMDand andfinding findingIMF IMF follows: i ’ areasasfollows: (1) Compute IMFi according to the procedure discussed in Section 3. (1) Compute IMFi according to the procedure discussed in Section 3. (2) Calculate the wavelet coefficients according to the equation described in Section 2 based on tone(2) Calculate the wavelet coefficients according to the equation described in Section 2 based on burst wavelet: tone-burst wavelet: +∞    Z 1= √1 )ψt  tl −  l dt W I MF t ( W IMF  t   s dt s s

s



 −∞





(3) Estimate Estimatede-noised de-noisednew newwavelet waveletcoefficients coefficientsbybypredefined predefinedpositive positivevalue valueofofthreshold thresholdT:T: (3)

d Wd(W)sgn W W|T−T )+ W(W )(| = sgn (4) i’ from the de-noised coefficients through the inverse wavelet transform. (4) Reconstruct ReconstructIMF IMF i ’ from the de-noised coefficients through the inverse wavelet transform. (5) Subtract IMF i’ from x(t) and obtain the residue ri(t) (5) Subtract IMFi ’ from x(t) and obtain the residue ri (t) Replace x(t) with the residue and return to step 1; repeat the iteration process and continue until Replace x(t) with the residue and return to step 1; repeat the iteration process and continue until the residue rn(t) becomes too small or a monotonic function from which no more IMFs can be the residue rn (t) becomes too small or a monotonic function from which no more IMFs can be extracted. extracted. It is worthy of mention that this method is different than some works with a similar names It is worthy of mention that this method is different than some works with a similar names reported reported in [44–47]. in [44–47]. 5. Experimental Validations 5. Experimental Validations 5.1. 5.1.Experimental ExperimentalSetup Setup To Toverify verifythe theapplicability applicabilityofofthe theproposed proposedmethod methodexperiments experimentswere werecarried carriedout outinintwo twostages stages including a laboratory test and a field test. In Stage 1, the experiment was conducted on two 80 cm including a laboratory test and a field test. In Stage 1, the experiment was conducted on two 80 cm long long steel pipes. They were standard pipes delivering natural gas to residential buildings with the steel pipes. They were standard pipes delivering natural gas to residential buildings with the diameter diameter 33 mm and 4 mm wall thickness. One of them was pristine other had a corrosion of 33 mmofand 4 mm wall thickness. One of them was pristine while thewhile otherthe had a corrosion extended extended over 17 cm along the pipe. The corrosions were naturally formed and the pipes over 17 cm along the pipe. The corrosions were naturally formed and the pipes were provided were by the provided by the sole gas supplier in Hong2).Kong (Figure 2). sole gas supplier in Hong Kong (Figure Natural corrosion extended over 17 cm along the pipe

Figure 2. Steel pipe with natural corrosion. Figure 2. Steel pipe with natural corrosion.

Both pipes were partially covered by concrete to simulate real concrete walls at residential Both pipes were partially covered by concrete to simulate real concrete walls at residential buildings (Figure 3a). For the corroded pipe, the defective part was placed inside the 20 cm long buildings (Figure 3a). For the corroded pipe, the defective part was placed inside the 20 cm long concrete wall. Figure 3b illustrates a schematic diagram of our experimental setup. For the corroded concrete wall. Figure 3b illustrates a schematic diagram of our experimental setup. For the corroded pipe the concrete wall is located 48 cm away from one end which is 8 cm different from the normal pipe the concrete wall is located 48 cm away from one end which is 8 cm different from the normal pipe. An array of PZT strips was bonded at one end of the pipes to transmit and receive guide waves

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in mode. The are so in pulse-echo pulse-echo mode. The strips strips are axisymmetrically axisymmetrically distributed, so that that longitudinal modes pipe. An array of PZT strips was bonded at one end of the distributed, pipes to transmit and longitudinal receive guidemodes waves excitation is guaranteed and flexural modes are suppressed. L(0,2) mode in 160 kHz was excitation is guaranteed and flexural modes are suppressed. mode in 160 kHz waspreferred preferred in pulse-echo mode. The strips are axisymmetrically distributed,L(0,2) so that longitudinal modes excitation over the guided wave modes ofofits straightforward attenuation theother other guided wave modes because itsL(0,2) straightforward excitation andits itsless less attenuation isover guaranteed and flexural modes arebecause suppressed. mode in 160excitation kHz was and preferred over the other in comparison with torsional mode T(0,1) [11]. Lower attenuation, makes L(0,2) mode more feasible in comparison with torsional T(0,1) [11]. Lower attenuation, L(0,2) mode feasible guided wave modes because ofmode its straightforward excitation and itsmakes less attenuation inmore comparison to inspect pipes buried in sand or covered by concrete. In this frequency, it is non-dispersive with the to inspect pipes buried in sand covered by concrete. In this frequency, it isfeasible non-dispersive with the with torsional mode T(0,1) [11]. or Lower attenuation, makes L(0,2) mode more to inspect pipes highest group velocity as depicted in the dispersion curves in Figure 4. PCdisp open source MATLAB highestingroup as depicted in the curves in non-dispersive Figure 4. PCdispwith open source MATLAB buried sand velocity or covered by concrete. Indispersion this frequency, it is the highest group toolbox isisbased on Pochhammer-Chree dispersion equation totoplot curves toolboxwhich which based on Pochhammer-Chree dispersion equation isused used plotdispersion dispersion curves velocity as depicted in the dispersion curves in Figure 4. PCdisp open is source MATLAB toolbox which is [48,49]. Meanwhile, with the aid of this toolbox we can observe that this mode has uniform stress [48,49]. Meanwhile, with the aid of this toolbox we can observe that this mode has uniform stress based on Pochhammer-Chree dispersion equation is used to plot dispersion curves [48,49]. Meanwhile, distribution the pipe Figure the filed ofofL(0,2) distribution over the pipewall wall thickness. Figure 5demonstrates demonstrates thestress stress fileddistribution L(0,2)atat160 160kHz. kHz. with the aidover of this toolbox wethickness. can observe that 5this mode has uniform stress over the The uniform stress distribution makes the L(0,2) equally sensitive to any change; regardless ofofstress their The wall uniform stress distribution makes the L(0,2) equally regardless their pipe thickness. Figure 5 demonstrates the stress filedsensitive of L(0,2)toatany 160change; kHz. The uniform radial ininthe the pipes’ wall For the ofofof L(0,2) radialpositions positions the pipes’ wallthicknesses. thicknesses. Forchange; theexcitation excitation L(0,2) modeat atthe theselected selected distribution makes L(0,2) equally sensitive to any regardless theirmode radial positions in the frequency five-cycle tone-burst signal modulated by Hamming window was delivered through an frequency five-cycle tone-burst signal modulated by Hamming window was delivered an pipes’ wall thicknesses. For the excitation of L(0,2) mode at the selected frequency five-cycle through tone-burst arbitrary signal generator and generated by an RITEC 4000 pulser & receiver (RITEC Inc., Warwick, arbitrary signal generator and generated RITEC 4000 pulseran &arbitrary receiver (RITEC Inc., Warwick, signal modulated by Hamming window by wasandelivered through signal generator and RI, RI,USA): USA): by an RITEC 4000 pulser & receiver (RITEC Inc., Warwick, RI, USA): generated     0.08  0.46 1  cos ωt  t t XX(t)texcitation  t    sin    X = sin ωt + θ 0.08 + 0.46 1 − cos ( )   texcitation  t      sin 0.08 0.46 1 cos  excitation   555   







(10) (10) (10)

Figure Figure Concrete covered pipe (a); schematic diagram of experimental setup; concrete covered Figure3.3.Concrete Concretecovered coveredpipe pipe(a); (a);and andschematic schematicdiagram diagramof ofexperimental experimentalsetup; setup;concrete concretecovered covered pipe (b). pipe (b).

(a) (a)

(b) (b)

Figure Phase the Figure4. Phase(a); (a);and andgroup group(b) (b)velocity velocitydispersion dispersioncurves curvesof theexamined examinedpipe. pipe. Figure 4.4.Phase (a); and group (b) velocity dispersion curves ofofthe examined pipe.

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Stresses, mode L(0,2), f = 160 kHz Stresses, mode L(0,2), f = 160 kHz

 rr  rr  zz   zz  rz  rz

Radius (mm) Radius (mm)

31.5 31.5 31 31

30.5 30.5 30 30 29.5 29.5 29 -1 29 -1

-0.8 -0.6 -0.4 -0.2 0 0.2 -0.8 -0.6 -0.4 -0.2 Stress 0 0.2 Stress

0.4 0.4

0.6 0.6

0.8 0.8

1

1

Figure 5. Stress field of L(0,2) mode at 160 kHz in a steel pipe. Figure Figure5.5.Stress Stressfield fieldofofL(0,2) L(0,2)mode modeatat160 160kHz kHzinina asteel steelpipe. pipe.

The frequency band of tone-burst signal can be easily changed by altering the number of cycles. Thefrequency frequencyband bandofoftone-burst tone-burst signalcan canbe beeasily easilychanged changed byaltering altering thenumber number ofcycles. cycles. The By increasing the number of cycles insignal the tone-burst signals, theby narrower the band signalsofcan be By increasing the number of cycles in the tone-burst signals, the narrower band signals can be By increasing the 6number in thesignal tone-burst signals, band signals can be obtained. obtained. Figure shows of thecycles excitation together withthe itsnarrower frequency spectrum. obtained. Figure shows thesignal excitation signal together with itsspectrum. frequency spectrum. Figure 6 shows the6excitation together with its frequency

(a) (a)

(b) (b)

Figure 6. Five-cycle tone-burst at 160 kHz center frequency (a) and its spectrum (b) Figure (a)(a) and itsits spectrum (b). Figure6.6.Five-cycle Five-cycletone-burst tone-burstatat160 160kHz kHzcenter centerfrequency frequency and spectrum (b)

In Stage 2, we repeated the experiment on pipes carrying gas to residential buildings in Hong Stage2,2,we we repeatedthe the experimenton onpipes pipescarrying carryinggas gastotoresidential residentialbuildings buildingsininHong Hong InIn Stage Kong. Similar to therepeated experiment experiment conducted in our lab, a strip of PZTs was mounted on a pipe that Kong. Similar to the experiment conducted in our lab, a strip of PZTs was mounted on a pipe that Kong. Similar to the aexperiment conducted in For ourthe lab,pipe a strip PZTs wasrusty mounted on was a pipe that was passing through concrete wall (Figure 7). withofcorrosion, portion started was passing through a concrete wall (Figure 7). For the pipe with corrosion, rusty portion was started was passing through a concrete 7).all Forthe theway pipetowith corrosion, rustythat portion started at the entry of the concrete wallwall and (Figure extended the portion of pipe was was covered by atthe theentry entryof ofthe the concrete concrete wall wall and and extended all the way to the portion ofofpipe that was covered by at extended all the way to the portion pipe that was covered the concrete wall. However, there were two areas in which the corrosion was severe: the entry of the the concrete wall. However, there were two areas in which the corrosion was severe: the entry of the by the concrete wall. were in which thewall. corrosion severe: the entry concrete wall and an However, area rightthere before thetwo endareas of the concrete Figurewas 8 demonstrates the concrete wall wall and and an area right before thethe end ofofthe concrete wall. Figure 88 demonstrates demonstratesthe the of the concrete an area right before end the concrete wall. Figure schematic diagram of our setup with the location of most severe part of the corrosion on the pipe. schematic diagram of our setup with the location of most severe part of the corrosion on the pipe. schematic diagram of our setup with the location of most severe of thewith corrosion pipe. After completing data collection, the in-service corroded pipe waspart replaced a new on andthe normal Aftercompleting completingdata datacollection, collection,the thein-service in-servicecorroded corrodedpipe pipewas wasreplaced replacedwith withaanew newand andnormal normal After pipe. The data collection process was repeated again on this normal pipe for comparison purpose. pipe.The Thedata datacollection collectionprocess processwas wasrepeated repeatedagain againon onthis thisnormal normalpipe pipefor forcomparison comparisonpurpose. purpose. pipe.

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(a) (a)

(b) (b)

Figure 7. The in-service pipe used for the field test: the indoor portion of the pipe with rust starting Figure Thein-service in-servicepipe pipeused usedfor forthe thefield fieldtest: test:the theindoor indoor portion portion of of the the pipe Figure 7.7.The pipe with with rust rust starting startingat at the entry of the concrete wall (a); and the corroded pipe with rusts after dissembled it from the the entry of the concrete wall (a); and the corroded pipe with rusts after dissembled it from the concrete at the entry of the concrete wall (a); and the corroded pipe with rusts after dissembled it from the concrete wall (b). wall (b). concrete wall (b).

12.5 cm 12.5 cm PZT Strip PZT Strip

16.5 cm 16.5 cm Rust Rust

Rust Rust

Wall Wall

Figure 8. Schematic diagram of experimental setup for on-site testing of pipes carrying gas to Figure diagram of of experimental setup forfor on-site testing of ofpipes Figure8.8.Schematic Schematic diagram experimental setup on-site testing pipescarrying carryinggas gastoto residential buildings. residential buildings. residential buildings.

5.2. Results and Discussion 5.2. and Discussion 5.2.Results Results and Discussion After obtaining the guided wave signals for both pipes, in this section, our goal was focused on After obtaining the guided wave signals forfor both pipes, in this section, our goal was was focused on After obtaining wave signals both pipes, in this our goal two main points. First,the theguided location of concrete on the both signals mustsection, be identified. In otherfocused words, two main points. First, the location of concrete on the both signals must be identified. In other words, on two main points. First, the location of concrete on the both signals must be identified. In the signs reflecting the existence of concrete and its position in the signals must be determined.other The the signs reflecting the existence of concrete and its position in the signals must bemust determined. The words, signs reflecting the existence of concrete its position in theofsignals be determined. second the point, which is the most important one is to and answer the question whether there is corrosion second point, which is the most important one is to one answertothe question of whetherof there is corrosion The point, which is the most The important answer the whether there is in thesecond pipe and if yes at what location. prerequisiteisfor such goals is question to identify the group velocity incorrosion the pipe and if yes at what location. The prerequisite for such goals is to identify the group velocity in the pipe and if yes at what location. The prerequisite for such goals is to identify the value by which time of flights for relevant wave packages are calculated. The group velocity (vgroup g) can value by which of flights relevant wave packages are calculated. The groupThe velocity (vvelocity g) can velocity value time by the which time for of flights relevant wave packages are calculated. be pinpointed on dispersion curves for in Figure 4. As an alternative, group velocity cangroup be calculated be(vpinpointed on the dispersion curves in Figure 4.in AsFigure an alternative, group velocity can velocity be calculated can be pinpointed on theon dispersion curves 4. As anpipe: alternative, group can be byg )measuring time of flights a signal that belongs to a normal bycalculated measuring of flights on of a signal to a belongs normal pipe: bytime measuring time flightsthat on abelongs signal that to a normal pipe:

L vg L L vgv g= D DD

(11) (11)(11)

in which L is the twice length of the normal pipe prior covering it with concrete in pulse echo-mode ininwhich whichL Lisisthe thetwice twicelength lengthofofthe thenormal normalpipe pipeprior priorcovering coveringit itwith withconcrete concreteininpulse pulseecho-mode echo-mode and D is the time shift between near and far end signals. The reason for selecting a normal pipe and shiftbetween betweennear nearand and signals. reason for selecting a normal pipe andDDisis the the time shift farfar endend signals. TheThe reason for selecting a normal pipe without without concrete cover for the calculation is the simplicity of guided wave signals without any without concrete cover for the calculation is the simplicity of guided wave signals without any concrete cover for the calculation is the simplicity of guided wave signals without any overlapping overlapping modes. Parameter D can be manually measured but to accurately determine D, cross overlapping modes. Parameter D can be measured manually measured but to accurately D, cross modes. Parameter D can be manually but to accurately determinedetermine D, cross correlation correlation function (CCF) of the two signals of pipe ends is computed. The time shift between the correlation function (CCF) the two of pipe ends is computed. The between time shiftthe between the function (CCF) of the twoofsignals of signals pipe ends is computed. The time shift two signals two signals corresponds to the maximum value of their CCF [50] as shown below: two signals corresponds to the maximum value of [50] theirasCCF [50]below: as shown below: corresponds to the maximum value of their CCF shown

1T   D  max 1 T ZTx  t  y  t    dt  1 max DD =    T x0 xt (ty)y(tt+τ)dt dt max T T  0 

(12) (12)(12)

where T is observation time, and x and y are near0and far end signals, respectively. The group velocity where T is observation time, and x and y are near and far end signals, respectively. The group velocity g cangroup be calculated for ourTexperiment wastime, determined to ybeare 5100 m/s. is worthy of mention that vThe where is observation and x and near andItfar end signals, respectively. velocity for our experiment was determined to be 5100 m/s. It is worthy of mention that vg can be calculated in pitch-catch mode as well; if we install another strip of PZT in a distance L from the first strip. for our experiment was determined to be 5100 m/s. It is worthy of mention that vg can be calculated in pitch-catch mode as well; if we install another strip of PZT in a distance L from the first strip. Table 1 lists theasdifferent time of flights that indicate positions in the In other in pitch-catch mode well; if we install another strip of PZTcritical in a distance L from the pipes. first strip. Table 1 lists the different time of flights that indicate critical positions in the pipes. In other words, we expect to see those positions at calculated time of flights according to Table 1. The time words, we expect to see those positions at calculated time of flights according to Table 1. The time values in Table 1 were calculated by dividing the traveling distance by 5100 m/s which is the group values in Table 1 were calculated by dividing the traveling distance by 5100 m/s which is the group velocity. velocity.

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Table 1 lists the different time of flights that indicate critical positions in the pipes. In other words, we expect to see those positions at calculated time of flights according to Table 1. The time values in Table 1 were calculated by dividing the traveling distance by 5100 m/s which is the group velocity. Sensors 2017, 17, 302

Table 1. Calculated time of flights for critical positions in the concrete-covered pipes.

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Table 1. Calculated time of flights for critical positions in the concrete-covered pipes. Time of Flight (ms) of Flight (ms) t1 (Start of Concrete Wall) Time t2 (End of Concrete Wall) t4 (Pipe End) t1 (Start of Concrete Wall) t2 (End of Concrete Wall) t4 (Pipe End) 0.15 0.23 0.31 0.15 0.23 0.31 0.18 0.26 0.31 0.18 0.26 0.31

Group Velocity 5100 (m/s) Group Velocity 5100 (m/s) Normal Pipe Normal Pipe withPipe Corrosion Pipe with Corrosion

Figure 99 demonstrates demonstrates the the signals signals obtained obtained from from the the concrete concrete covered covered pipes. pipes. As Ascan canbe beseen, seen,the the Figure time domain signals are too complicated to locate concrete section and the corrosion. Although the time domain signals are too complicated to locate concrete section and the corrosion. Although the critical positions positions were were identified identified according critical according to to Table Table1,1,distinguishing distinguishingthem themininthe thesignals signalsininFigure Figure9 9is not spectrum of of both both is notstraightforward straightforwardand andalmost almostimpossible. impossible.Meanwhile, Meanwhile, looking looking at at the the frequency frequency spectrum signals, one can see that they are distorted from the original FFT in Figure 6b and they contain some signals, one can see that they are distorted from the original FFT in Figure 6b and they contain some other frequency frequency components. components. Comparing Comparing these these two two signals, signals, the the signal signal of ofthe thecorroded corrodedpipe pipehas hashigher higher other energy reflected from the concrete section. Having higher reflection energy although could be sign energy reflected from the concrete section. Having higher reflection energy although could be aa sign of corrosion; it may not enough to assure such conclusion. This is because rough surface of the rusty of corrosion; it may not enough to assure such conclusion. This is because rough surface of the rusty part in in concrete concrete wall wall facilities facilities the the coupling coupling of oftwo twomaterials materialsso sothat thatthey theyare arestrongly stronglybonded bondedtogether together part and signal energy eventually may fade away inside the concrete wall without having much of it it left to and signal energy eventually may fade away inside the concrete wall without having much of left reflect back. Meanwhile, in real situation since the walls have very big lengths, we may not see the to reflect back. Meanwhile, in real situation since the walls have very big lengths, we may not see the reflection of of guided guided waves waves once once they they leak leak into into the the concrete. concrete. Such Such issues issues dictate dictate the the necessity necessity of of using using reflection an advanced signal processing technique to provide an insight into the real situation of the pipes. an advanced signal processing technique to provide an insight into the real situation of the pipes.

Figure wave signals signals measured measuredatat160 160kHz kHzforfor concrete covered pristine pipe (a) with its Figure 9. 9. Guided Guided wave concrete covered pristine pipe (a) with its FFT FFT (b); and concrete covered corroded pipe (c) with its FFT (d). (b); and concrete covered corroded pipe (c) with its FFT (d).

To find the localized frequency components of the signals, wavelet was used to draw their timeTo find the localized frequency components of the signals, wavelet was used to draw their frequency representations (TFRs). Figure 10 demonstrates continuous wavelet transform of the time-frequency representations (TFRs). Figure 10 demonstrates continuous wavelet transform of the signals in Figure 9 by adopting complex tone-burst wavelet. As can be seen in Figure 10, the two TFRs signals in Figure 9 by adopting complex tone-burst wavelet. As can be seen in Figure 10, the two look very similar and not only cannot we locate the concrete wall but there is large amount of TFRs look very similar and not only cannot we locate the concrete wall but there is large amount of ambiguity about the existence of the defect. This problem occurs because of many overlapping modes ambiguity about the existence of the defect. This problem occurs because of many overlapping modes coming with the environmental contamination. Nevertheless, despite the difficulty in extracting the coming with the environmental contamination. Nevertheless, despite the difficulty in extracting the critical information, detecting the pipe ends at 0.31 ms is possible. The simplicity in detecting the end critical information, detecting the pipe ends at 0.31 ms is possible. The simplicity in detecting the is because of the fact that the end acts as a block that reflects all the energy back towards the incident end is because of the fact that the end acts as a block that reflects all the energy back towards the point. incident point.

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Figure 10. Continuous wavelets transform of the pristine pipe (a); and the pipe with corrosion (b). Figure 10. Continuous wavelets transform of the pristine pipe (a); and the pipe with corrosion (b). Figure 10. Continuous wavelets transform of the pristine pipe (a); and the pipe with corrosion (b).

As a good candidate to decompose a non-stationary signal into its intrinsic mode functions, we a good candidate to decompose a non-stationary signal its intrinsic mode functions, we firstlyAsadopted conventional EMD for our recorded signals. Theinto signals obtained in Figure 9 were firstly adopted conventional EMD for our recorded signals. The signals obtained in Figure 9 were decomposed into different IMFs according to the algorithm that was explained in the earlier section. decomposed into different IMFs according earlier section. section. to thepipes algorithm thatwith was their explained earlier The original signals of the pristine and corroded together IMFs in arethe demonstrated in The original signals of the pristine and corroded pipes together with their IMFs are demonstrated in Figure 11a,b, respectively. Two vertical dashed lines passing through all IMFs indicate the location Figure 11a,b, respectively. Two vertical dashed lines passing through all IMFs indicate the location of 11a,b, respectively. Two verticaltodashed lines passing through all IMFs indicate the location of concrete wall on time axis according Table 1. concrete wall on on time axisaxis according to Table 1. 1. of concrete wall time according to Table

Figure 11. Decomposition of signals into their IMFs by EMD for the pristine pipe (a); and the pipe Figure 11. Decomposition Decomposition signalsinto intotheir their IMFs EMD pristine (a); the andpipe the with pipe 11. ofofsignals IMFs byby EMD for for the the pristine pipepipe (a); and with a natural corrosion (b). a natural corrosion awith natural corrosion (b). (b).

Only first four IMFs are illustrated in Figure 11. The higher order IMFs, due to having very low Only first four IMFs IMFs are illustrated illustrated inthe Figure 11. The The higher order order IMFs, due to to having having very low energy andfirst frequency inconsistency within excitation frequency bandIMFs, are neglected. To find which Only four are Figure 11. higher due very low energy and frequency inconsistency with the excitation frequency band are neglected. To find which IMF contains the mostinconsistency relevant information, correlation of the original signals and theirwhich IMFs energy and frequency with the cross excitation frequency band are neglected. To find IMF contains contains theCross most correlation relevant information, information, cross correlation correlation of the the original original signals and their their IMFs were calculated. is a tool of measuring the similarity between two signals which in IMF the most relevant cross of signals and IMFs were calculated. Cross correlation is a tool of measuring the similarity between two signals which in our case are an original guided wave signal x(t) and a corresponding IMF [51,52]: were calculated. Cross correlation is a tool of measuring the similarity between two signals which in our case are an original guided wave signal x(t) and a corresponding IMF [51,52]: T and a corresponding IMF [51,52]: our case are an original guided wave signal x(t)

1 R    1 T x  t  IMF  t    dt R    T 0 x  t  IMF  t    dt T 0

(13) (13)

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R(τ ) =

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1 T

ZT

x (t) I MF (t + τ )dt

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0

TheThe normalized value of cross-correlation is aisnumber between −1 − and 1. The bigger absolute normalized value of cross-correlation a number between 1 and 1. The bigger absolute value of cross-correlation, indicate more similarity between two signals (Figure 12). value of cross-correlation, indicate more similarity between two signals (Figure 12). 0.9 Correlation Coefficient

0.8 0.7 0.6 0.5 0.4

Normal Pipe

0.3

Corroded Pipe

0.2 0.1 0

Figure Absolute cross correlationofofguided guidedwave wave signals signals from IMFs Figure 12. 12. Absolute cross correlation from pipes pipeswith withtheir theircorresponding corresponding obtained from EMD. IMFs obtained from EMD.

As As illustrated in Figure 1111 wewe may only partially illustrated in Figure may only partiallyachieve achieveour ourgoals goalsininexposing exposingcritical criticalfeatures features of of the IMFs have have the thegreatest greatestportion portionofofthe thesignals’ signals’energy. energy. Meanwhile they both the pipes. First two IMFs Meanwhile they both have have maximum similarity the original signal as their absolute for cross-correlation thethe maximum similarity withwith the original signal as their absolute valuesvalues for cross-correlation are much arebigger much than bigger thanIMFs other IMFs (Figure 12) However has theabsolute largest absolute correlation and is other (Figure 12) However IMF1 hasIMF1 the largest correlation and therefore, therefore, of more importance. Weabsolute take the absolute cross-correlation as a criterion an IMF of moreisimportance. We take the cross-correlation as a criterion to select to anselect IMF for further for analysis. further analysis. The other on physical of the original is neglected The effect ofeffect other of IMFs onIMFs physical meaningmeaning of the original signal issignal neglected because of because of the lowerfor values for cross-correlation. Now with aidpositions of EMD positions ofare thevery endsevident are the lower values cross-correlation. Now with the aid ofthe EMD of the ends very evident for especially for the pipeinasIMF1 exposed inboth IMF1 for the bothbepipes. It must bethe especially the pristine pipepristine as exposed for the pipes. It must mentioned that mentioned that the pristine pipe is slightly longer and as a result the location of pipe end reflection pristine pipe is slightly longer and as a result the location of pipe end reflection happens with a few happens with a few microseconds that,section, for the concrete section, one can see visible that it in microseconds delay. Apart fromdelay. that, Apart for thefrom concrete one can see that it is almost is almost visible in IMF1 for both pipes; IMF1s highly noisyThis andoccurrence contaminated. This of IMF1 for both pipes; although IMF1s arealthough highly noisy andare contaminated. is because occurrence is because of signal reverberation and generation of unwanted modes and contamination signal reverberation and generation of unwanted modes and contamination when guided waves reach when guided waves reach the concrete Therefore, bothreverberation groups of IMFs other be the concrete wall. Therefore, both groups wall. of IMFs include other signalsinclude which might reverberation signals which might be difficult to interpret. Being better than EMD, EEMD was later 9. difficult to interpret. Being better than EMD, EEMD was later applied on the same signals in Figure applied on theobtained same signals Figureare 9. depicted The results obtained The results fromin EEMD in Figure 13.from EEMD are depicted in Figure 13. Similar to EMD, cross correlation waswas used to find which IMFs for for both pipes contain thethe critical Similar to EMD, cross correlation used to find which IMFs both pipes contain critical information. As can be observed in Figure 13, comparable to the results of EMD, IMF1s include much information. As can be observed in Figure 13, comparable to the results of EMD, IMF1s include much information about thethe critical features of the pipes as their features cancan be be somehow spotted in the information about critical features of the pipes as their features somehow spotted in the firstfirst IMFs. This is inisan with thethe correlation results in Figure 14 which means IMF1s have IMFs. This in agreement an agreement with correlation results in Figure 14 which means IMF1s have thethe most relevant embedded information. The reflections from the far end for both pipes are exposed most relevant embedded information. The reflections from the far end for both pipes are exposed in IMF1s. In addition, while thethe concrete wall is separated for for thethe corroded pipe, in the normal pipe in IMF1s. In addition, while concrete wall is separated corroded pipe, in the normal pipe IMF1 still have many overlapped components. Meanwhile, for corrosion detection, comparison study IMF1 still have many overlapped components. Meanwhile, for corrosion detection, comparison study between thethe second IMFs does notnot provide useful and clear information. between second IMFs does provide useful and clear information.

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Figure 13. Decomposition of signals into their IMFs by EEMD for the pristine pipe (a); and the pipe Figure13. 13.Decomposition Decomposition of of signals signals into pipe (a);(a); and thethe pipe Figure into their their IMFs IMFsby byEEMD EEMDfor forthe thepristine pristine pipe and pipe with a natural corrosion (b). with a naturalcorrosion corrosion(b). (b). with a natural

0.8 0.8 Correlarion CorrelarionCoefficient Coefficient

0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3

Normal Pipe Normal Pipe Corroded Pipe Corroded Pipe

0.2 0.2 0.1 0.1 0 0

Figure 14.14. Absolute cross correlation of guided wave signals from pipes with theirtheir corresponding IMFs Figure Absolute cross correlation of guided wave signals from pipes with corresponding Figure 14. Absolute cross correlation of guided wave signals from pipes with their corresponding obtained from EEMD. IMFs obtained from EEMD. IMFs obtained from EEMD.

Furthermore, to overcomethe the shortcomings of of conventional EMD, we utilized the SEMD Furthermore, conventionalEMD, EMD,we weutilized utilized SEMD Furthermore,toto overcome overcome the shortcomings shortcomings of conventional thethe SEMD whose theory was already discussed in a former section in this paper. The main point is that not whose former section sectionininthis thispaper. paper.The Themain main point is that whosetheory theorywas wasalready alreadydiscussed discussed in a former point is that notnot only guided wave signals may contain many contaminations; each IMF may also include some only many contaminations; contaminations;each eachIMF IMFmay may also include some onlyguided guidedwave wavesignals signals may may contain contain many also include some unwanted components. Thus, with the aid of wavelet transform on IMFs in sifting process unwanted components. Thus, with aidwavelet of wavelet transform on in IMFs in process sifting process unwanted components. Thus, with the the aid of transform on IMFs sifting unwanted unwanted reverberations can be discarded from their wavelet coefficients. For wavelet transform, unwanted reverberations can be from discarded theircoefficients. wavelet coefficients. For wavelet transform, reverberations can be discarded theirfrom wavelet For wavelet transform, complex complex tone-burst wavelet was used as a mother wavelet whose design was already explained. complex tone-burst wavelet as awavelet motherwhose wavelet whosewas design was explained. already explained. tone-burst wavelet was used was as a used mother design already Figure 15 Figure 15 demonstrates the signal from the pristine and corroded pipe together with their IMFs. Figure 15 demonstrates the signal from the pristine and pipe corroded pipe with together with theirSimilar IMFs. to demonstrates the signal from pristine and corroded together their IMFs. Similar to previous results, in the SEMD only four IMFs are depicted as the rest have very low energy in Similar to previous results, in SEMD only four IMFs are depicted as the rest have very low energy in previous results,with in SEMD only four IMFsAs are is depicted the rest16, have very have low energy in comparison comparison the original signal. clear inasFigure IMF1s the most relevant comparison with the original signal. As is16,clear in have Figure IMF1s have information the most relevant with the original signal. As is clear in Figure IMF1s the16, most relevant about the

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original signals for both the normal pipe with corrosion. thecorrosion. first IMFs were the taken information about the original original signals forand bothpipe the normal normal pipe and and Hence, pipe with with corrosion. Hence, the information about the signals for both the pipe pipe Hence, into account for further analysis. Selecting first IMFs can be verified through the comparison of first IMFs were taken into account for further analysis. Selecting first IMFs can be verified through first IMFs were taken into account for further analysis. Selecting first IMFs can be verified throughthe the comparison comparison ofand the correlation correlation of IMFs IMFs and original signals in in Figure Figure 16. 16. correlation of IMFs original signals in and Figure 16. signals the of the of original

Figure 15. Decompositionof ofsignals signals into into their their IMFs IMFs by SEMD for the pristine pipe (a); and thethe pipe Figure Decomposition of signals pipe (a); and the pipe Figure 15.15. Decomposition their IMFsby bySEMD SEMDfor forthe thepristine pristine pipe (a); and pipe with a natural corrosion (b). with a natural corrosion (b). with a natural corrosion (b).

0.8 0.8 Correlation CorrelationCoefficient Coefficient

0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3

Normal Pipe Pipe Normal Corroded Pipe Pipe Corroded

0.2 0.2 0.1 0.1 00

Figure 16. Absolute cross correlation of guided wave signals from pipes with their corresponding IMFs Figure 16. 16. Absolute Absolute cross cross correlation correlation of of guided guided wave wave signals signals from from pipes pipes with with their their corresponding corresponding Figure obtained from SEMD. IMFs obtained from SEMD. IMFs obtained from SEMD.

The firstIMFs IMFshave havethe themaximum maximum similarity similarity with with the original signal because ofof their biggest The first with the theoriginal originalsignal signalbecause because their biggest The first IMFs have the maximum similarity of their biggest values of absolutecross crosscorrelation correlation in in Figure Figure 16. 16. As As can be seen, all critical information about this values ofof absolute As can canbe beseen, seen,all allcritical criticalinformation information about this values absolute cross correlation in Figure about this pipe is clearly exposedinin inIMF1. IMF1.The The locations locations of of concrete wall plus the pipe end inin time axis cancan be be pipe clearly exposed IMF1. The locations end in time axis can be pipe is is clearly exposed of concrete concretewall wallplus plusthe thepipe pipe end time axis easily verified accordingtoto toTable Table1.1. 1.Since Since the the reflection reflection of of guided wave from the end has much higher easily verified according Table Since end has much higher easily verified according reflection ofguided guidedwave wavefrom fromthe the end has much higher energy, it can be observed in IMF2 as well. In IMF1 between the start and end of concrete wall, signal energy, it can observedininIMF2 IMF2as aswell. well. In IMF1 ofof concrete wall, signal energy, it can bebeobserved IMF1 between betweenthe thestart startand andend end concrete wall, signal

is very clear and there is no implication of any defect. It should be noted that the first wave packet in IMF1 which can also be seen in the original signal, is the reflection from the position of a PZT ring that had initially been installed there to measure the group velocity in pitch-catch mode. In addition, the first wave packet in IMF2 is the reflection of guided wave from the near end (close to PZT ring in Figure Figure 15b demonstrates the signal for the corroded pipe in conjunction with15its Sensors 2017,3). 17,Moreover, 302 of 21 IMFs. Similar to the first IMF for the pristine pipe, location of the concrete wall and the pipe end are evident in the IMF1 and can be verified again according to Table 1. Nonetheless, inside the concrete is very clear and is there is no implication of any defect. It complexity should be noted first wave packet in wall the signal chaotic with many reverberations. This in thisthat partthe of the signal indicates IMF1 which can also be seen in the original signal, is the reflection from the position of a PZT ring the natural corrosion with an irregular geometry that is extending over 17 cm in the pipe (Figure 2). that had initially installed thereearlier, to measure thecorrosion group velocity in pitch-catch mode. In addition, Meanwhile, as been it was mentioned all the was placed inside the concrete wall. such wave packets inside theofwall is notwave unexpected. Innear addition, unliketo thePZT IMF2 theTherefore, first waveseeing packet in IMF2 is the reflection guided from the end (close ring for pristine pipe, the reflection from the pipe endthe does not appear the second IMF. This is because in Figure 3). Moreover, Figure 15b demonstrates signal for thein corroded pipe in conjunction with signal energy reflected back towards the PZT ring as aconcrete result of wall the guided wave its much IMFs.ofSimilar to thewas firstalready IMF for the pristine pipe, location of the and the pipe hitting the corrosion. The higher order for both pristine pipe and the corroded pipeinside do notthe end are evident in the IMF1 and can be IMFs verified againthe according to Table 1. Nonetheless, have meaningful information themany signalreverberations. energy becomes low andintheir absolute concrete wall the signal is chaoticas with Thisvery complexity this part of thecross signal correlation is close to zero. indicates the natural corrosion with an irregular geometry that is extending over 17 cm in the pipe data obtainedasinitthe Stage 2 from normal concrete-wall pipesinside in thethe field test, (FigureThe 2). Meanwhile, was mentioned earlier,and all the corrosion covered was placed concrete as per Stage 1, the conventional EMD, EEMD and finally SEMD were used for the signal analysis. wall. Therefore, seeing such wave packets inside the wall is not unexpected. In addition, unlike the Figure 17 depicts the original signals obtained from normal and rusty pipe in field test together with IMF2 for pristine pipe, the reflection from the pipe end does not appear in the second IMF. This is their IMFs from EMD. because much of signal energy was already reflected back towards the PZT ring as a result of the Although because of the severe corrosion, the higher reflection energy of the original signals guided wave hitting the corrosion. The higher order IMFs for both the pristine pipe and the corroded in Figure 17 can address a defect, the signals are highly contaminated that could be taken as source pipe do not have meaningful information as the signal energy becomes very low and their absolute of ambiguity. Cross correlation of IMFs of the EMD with the original signals are demonstrated in cross correlation is close to zero. Figure 18. In IMF1 for the pristine pipe, within the concrete wall there are two main wave-packets. The data obtained in Stage as 2 from normal concrete-wall coveredwall, pipes inexistence the field of test, While the first one couldthe be taken the sign of theand beginning of the concrete the as the persecond Stage 1, the conventional EMD, EEMD and finally SEMD were used for the signal analysis. wave-packet remains unanswered. For the pipe with the two corrosion areas, IMF1 shows Figure 17energy depictsreflecting the original obtained from normal and rusty in field test together with larger backsignals from the concrete wall. However, it is pipe not much different from the their IMFs from EMD. original signal.

Figure Decompositionofoffield fieldtest testsignals signals into into their their IMFs (a); and thethe Figure 17.17. Decomposition IMFs by byEMD EMDfor forthe thepristine pristinepipe pipe (a); and pipe with a natural corrosion (b). pipe with a natural corrosion (b).

Although because of the severe corrosion, the higher reflection energy of the original signals in Figure 17 can address a defect, the signals are highly contaminated that could be taken as source of ambiguity. Cross correlation of IMFs of the EMD with the original signals are demonstrated in Figure 18. In IMF1 for the pristine pipe, within the concrete wall there are two main wave-packets. While the first one could be taken as the sign of the beginning of the concrete wall, the existence of the second wave-packet remains unanswered. For the pipe with the two corrosion areas, IMF1 shows larger energy reflecting back from the concrete wall. However, it is not much different from the original signal.

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0.9 0.7 0.8

Correletion Coefficient

Correletion Coefficient

0.8 0.9 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2

Normal Pipe Normal PipePipe Corroded Corroded Pipe

0.2 0.1 0.1 0 0

Figure 18. Absolute Absolute cross cross correlation correlation of guided wave signals signals from the pipes in residential building Figure 18. Absolute cross correlation of guided wave signals from the pipes in residential building with their corresponding IMFs obtained from from EMD. EMD. with their corresponding IMFs obtained from EMD.

Figure 19 illustrates the same signals decomposed by EEMD. Similar the previous sections sections Figure decomposedby byEEMD. EEMD.Similar Similartoto to the previous Figure1919illustrates illustratesthe the same same signals signals decomposed the previous sections only four IMFs are shown in the figure. The remaining IMFs whose energies approach to zero were only four remainingIMFs IMFswhose whoseenergies energies approach zero were only fourIMFs IMFsare areshown shownin inthe the figure. figure. The remaining approach to to zero were neglected. Cross correlations of the IMFs with the original signals are depicted in Figure 19. For neglected. with the the original originalsignals signalsare aredepicted depicted Figure the neglected.Cross Crosscorrelations correlations of of the the IMFs with inin Figure 19.19. ForFor thethe pristine pipe, IMF1 has the maximum similarity according to Figure 19. Compared to IMF1 from pristine pipe, IMF1 maximum similarity according to Figure Compared to IMF1 from pristine pipe, IMF1 hashas thethe maximum similarity according to Figure 19. 19. Compared to IMF1 from EMD, EMD, EEMD aabetter as there isone onlywave-packet onewave-packet wave-packet the beginning the concrete EMD, EEMDprovides provides betterresult result as is there only one ininbeginning the beginning of of the concrete EEMD provides a better result as there onlyis in the of the concrete wall wall that indicates the of the For corroded thecorroded corroded pipe, unlike the normal pipe, IMF2 wall that indicates thestart startpoint point ofwall. the wall. wall. For the pipe, unlike normal pipe, IMF2 hashas that indicates the start point of the For the pipe, unlike thethe normal pipe, IMF2 has the the maximum correlation coefficient as canseen be seen seen inFigure Figure full mode reverberations the maximum correlation coefficient and as can be in isisfull ofof mode reverberations maximum correlation coefficient andand as can be in Figure 20 is2020 full of mode reverberations very very Meanwhile, looking atthe theresults results from EMD and EEMD, verysimilar similar tothe theoriginal original signal. Meanwhile, looking from EMD and EEMD, thethe similar to theto original signal.signal. Meanwhile, looking at the at results from EMD and EEMD, the concrete concrete wall cannot be separated from the rest of the signal as it was clearer in our experiment concrete wall cannot be separated from rest of the signal as it was clearer in our experiment wall cannot be separated from the rest of the signal as it was clearer in our experiment in Stagein1 in in Stage 1 in thelab. lab. Stage 1 in the the lab.

Figure 19. Decomposition of field test signals into their IMFs by EEMD for the pristine pipe (a); and the pipe with a natural corrosion (b). signals into their IMFs by EEMD for the pristine pipe (a); and Figure Figure 19. 19. Decomposition Decomposition of of field field test test signals into their IMFs by EEMD for the pristine pipe (a); and the (b). the pipe pipe with with aa natural natural corrosion corrosion (b).

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Correlation Coefficient Correlation Coefficient

0.8 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2

NormalPipe Pipe Normal CorrodedPipe Pipe Corroded

0.1 0.1 00

Figure 20. Absolute cross correlation of guided wave signals from the pipes in residential building Figure Absolutecross crosscorrelation correlationofofguided guided wave wave signals signals from the pipes Figure 20.20. Absolute pipes in in residential residentialbuilding building with their corresponding IMFs obtained from EEMD. with their correspondingIMFs IMFsobtained obtainedfrom fromEEMD. EEMD. with their corresponding

In our next step, weapplied applied SEMD to acquire much clearer and easier to interpret ournext nextstep, step,we we applied SEMD toacquire acquire much clearer and to results. The InIn our SEMD to much clearer and easier easier to interpret interpret results.results. The The original signal from our field test together with IMFs obtained by SEMD are shown in Figure original signal from our field test together with IMFs obtained by SEMD are shown in Figure 21. original signal from our field test together with IMFs obtained by SEMD are shown in Figure 21.As As21. As one can see from this figure, unlike the results in the lab, we do not have pipe end as the pipes one can see from this figure, unlike the results in the lab, we do not have pipe end as the pipes one can see from this figure, unlike the results in the lab, we do not have pipe end as the pipes connected totoaaanetwork network with elbows.Therefore, Therefore, since there is no blockage for wave propagation connectedto networkwith withelbows. elbows. Therefore, since there is no no blockage for propagation asas connected since there is blockage for wave wave propagation well as high attenuation within the concrete wall section, it is very difficult to locate the pipe elbows. as well as high attenuation within the concrete wall section, it is very difficult to locate the pipe well as high attenuation within the concrete wall section, it is very difficult to locate the pipe elbows. According to the calculation of time of flight for L(0,2) mode that propagates with 5100 m/s velocity elbows. According to the calculation of time of flight for L(0,2) mode that propagates with 5100 m/s According to the calculation of time of flight for L(0,2) mode that propagates with 5100 m/s velocity and considering the distance of concrete wall from PZT strips in Figure 8, we expect to see the velocity and considering the distance of concrete wall from PZT strips in Figure 8, we expect the and considering the distance of concrete wall from PZT strips in Figure 8, we expect to to seesee the beginning and endofofthe theconcrete concretewall wallatat0.49 0.49and and1.11 1.11ms. ms.However, However, unlike unlike the the signals signals in obtained beginning and end in obtained beginning and end of the concrete wall at 0.49 and 1.11 ms. However, unlike the signals in obtainedin inlab, our the lab,end the of end ofconcrete the concrete wall remains hidden. This is because, in field testwall the wallinfinite has our wallwall remains hidden. This This is because, in field in our lab, the endthe of the concrete remains hidden. is because, in test fieldthe test thehas wall has infinite length and when guided waves propagate and leaks into the wall, it attenuates inside thewe length when guided propagate and leaksand intoleaks the wall, attenuates inside the wall and infiniteand length and whenwaves guided waves propagate intoitthe wall, it attenuates inside the wall and we cannot see its reflection. Nevertheless, the two corrosion spots were clearly extracted cannot see its reflection. Nevertheless, the two corrosion spots were clearly extracted from the signal wall and we cannot see its reflection. Nevertheless, the two corrosion spots were clearly extracted from the signal and can be easily located in IMF1. and easily located IMF1.located in IMF1. fromcan thebe signal and can beineasily

Figure 21. Decomposition of signals into their IMFs by SEMD for the pristine pipe (a); and the pipe with natural corrosion (b).signals into their IMFs by SEMD for the pristine pipe (a); and the pipe Figure a21. 21. Decomposition Figure Decompositionof of signals into their IMFs by SEMD for the pristine pipe (a); and the pipe with aa natural natural corrosion with corrosion (b). (b).

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Analogous to SEMD result from the lab test, the first IMF has the most relevant information about Analogous to be SEMD result the lab test, the first IMF of hascross the most relevantofinformation two pipes. This can proved byfrom comparing absolute values correlation the IMFs with the about two pipes. This can be proved by comparing absolute values of cross correlation of the IMFs original signals. As can be seen in Figure 22, for the two signals, IMF1 has the largest value among with the original signals. As can be seen in Figure 22, for the two signals, IMF1 has the largest value the other IMFs meaning it has maximum similarity with the original signal. In other words, Figure 22 among the other IMFs meaning it has maximum similarity with the original signal. In other words, provides abouta the IMFs toIMFs be taken Figure a22clue provides cluemost aboutimportant the most important to be into takenconsideration. into consideration. 0.8

Correlation Coefficient

0.7 0.6 0.5 0.4 0.3

Normal Pipe Corroded Pipe

0.2 0.1 0

Figure Absolutecross cross correlation wave signals fromfrom the pipes in residential building building Figure 22.22. Absolute correlationofofguided guided wave signals the pipes in residential with their corresponding IMFs obtained from SEMD. with their corresponding IMFs obtained from SEMD.

6. Conclusions

6. Conclusions

In this paper we focused on the separation of overlapped modes in concrete-wall covered pipes In this paper weprocessing focused on the separation of overlapped modes concrete-wall pipes using a new signal technique. The study was carried out on a in pristine pipe and acovered pipe using a new signal processing technique. Thetostudy carriedguided out onwaves a pristine pipe and a pipe with with a natural corrosion. A PZT ring was used excite was and receive in pulse-echo mode and both pipes wereApartially covered concrete. Guided wave signals obtained in such were mode a natural corrosion. PZT ring wasby used to excite and receive guided waves inpipes pulse-echo because of the existence the overlapped modes andsignals wave reverberations. Initially andvery bothcomplicated pipes were partially covered byofconcrete. Guided wave obtained in such pipes were wavelet transform was used to study localized frequency components in the signal. Afterwards, very complicated because of the existence of the overlapped modes and wave reverberations. Initially conventional EMD and later EEMD were applied on the signals. The two methods did not perform wavelet transform was used to study localized frequency components in the signal. Afterwards, well for interpretation of the signals, and the best results were obtained utilizing SEMD which is the conventional EMD and later EEMD were applied on the signals. The two methods did not perform integration of the tailored wavelet and EMD. Cross Correlation was used to select the IMF best wellmatches for interpretation of thesignals. signals, the best results were obtained SEMD is the with the original Forand SEMD, a novel mother wavelet was utilizing tailored based onwhich the integration of the tailored wavelet and EMD. Cross Correlation was used to select the IMF best matches information about incident waves which was the tone-burst signal. Wavelet transform then was used tothe purify the IMFs in the sifting process. This is mother because not only raw are based contaminated with original signals. For SEMD, a novel wavelet wassignals tailored on thewith information unwanted components and wave reverberations, IMFs may also suffer from the was sameused issue.to purify about incident waves which was the tone-bursttheir signal. Wavelet transform then de-noising tool This substantially enhanced theraw performance this signal processing the Thus, IMFs wavelet in the sifting process. is because not only signals areofcontaminated with unwanted technique for guided waves in wall covered pipes. The positions of the concrete wall, pipe end and components and wave reverberations, their IMFs may also suffer from the same issue. Thus, wavelet defect in time axis were distinctly exposed. These locations were verified by calculating the time of de-noising tool substantially enhanced the performance of this signal processing technique for guided flight of L(0,2) mode traveling the well-known distances on our pipes. The defect signal was not a waves in wave wall packet covered Theofpositions of the concrete pipe end and defect single andpipes. consisted multiple small waves. This wall, was because of irregular shapeinoftime axis were distinctly exposed. These locations were verified by calculating the time of flight of L(0,2) mode corrosion and its extension inside the concrete wall. For further validation, the experiment conducted traveling the well-known distances on our pipes. The defect signal was not a single wave packet and in a residential building on pipes carrying gas. The irregular shape corrosion was successfully revealed separated from the rest of the and of confirmed theshape additivity of this method consisted ofand multiple small waves. This wassignal because irregular of corrosion and itsforextension applying highly contaminated guided validation, wave signals.the experiment conducted in a residential building inside the concrete wall. For further

on pipes carrying gas. The irregular shape corrosion was successfully revealed and separated from Acknowledgment: The work described in this paper was fully supported by the Research Grants Council the (Project rest ofNo. theCityU signal and the confirmed this method for applying highly contaminated 122513), Innovationthe andadditivity Technology of Commission (ITC) (Project No. ITS/061/14FP) of the Government of the Hong Kong Special Administrative Region (HKSAR), China. Any opinions, findings, guided wave signals. Acknowledgments: The work described in this paper was fully supported by the Research Grants Council (Project No. CityU 122513), the Innovation and Technology Commission (ITC) (Project No. ITS/061/14FP) of the Government of the Hong Kong Special Administrative Region (HKSAR), China. Any opinions, findings, conclusions or recommendations expressed in this material/event (or by members of the project team) do not

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reflect the views of the Government of the HKSAR, the ITC or the Panel of Assessors for the Innovation and Technology Support Program of the Innovation and Technology Fund. Author Contributions: J.R. and P.T. proposed the idea; P.T. designed and led the field tests. P.T. and J.C. performed experiments; J.R. contributed to writing and editing the manuscript. P.T. guided the research with critical revisions of the manuscript; J.R. and P.T. analyzed the results. Conflicts of Interest: The authors declare no conflict of interest.

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