Strojniški vestnik - Journal of Mechanical Engineering 60(2014)5, 298-306 © 2014 Journal of Mechanical Engineering. All rights reserved. D0l:10.5545/sv-jme.2014.1830 Special Issue, Original Scientific Paper Received for review: 2013-10-19 Received revised form: 2014-02-14 Accepted for publication: 2014-04-01 Measurement of Wave Attenuation in Buried Plastic Water Distribution Pipes Fabrício César Lobato de Almeida1* - Michael John Brennan1 - Phillip Frederick Joseph2 -Simon Dray3 - Stuart Whitfield4 - Amarildo Tabone Paschoalini1 1 University Estadual Paulista, Department of Mechanical Engineering, Brazil 2 University of Southampton, Institute of Sound and Vibration Research, United Kingdom 3 Hydrosave, United Kingdom 4 South Staffs Water, United Kingdom Leaks in pipes are a common issue encountered in the water industry. Acoustic methods are generally successful in finding and locating leaks in metallic pipes, however, they are less effective when applied to plastic pipes. This is because leak-noise signals are heavily attenuated due to high damping in the pipe-wall and sound radiation into the soil. As result, high frequency leak noise does not travel long distances. To determine how far leak noise may travel in a pipe at any frequency, the attenuation of the wave responsible for leak noise propagation should be known. In this paper a new method to estimate this is described. The method is then applied to some measurements made on a bespoke pipe-test rig in the UK, and the results are compared with theoretical predictions. Keywords: leak detection, wave attenuation, water industry, plastic pipes 0 INTRODUCTION Water distributions systems are susceptible to leakage, which results in a substantial wastage of water. The social and environmental effects due to leakage problems are also a matter of concern. Recently, a survey about the costs of installation/repair work of buried infrastructure in the UK has estimated that street works cost about £7bn in losses for the government annually; Social costs account for about £5.5bn and damage costs are about £1.5bn [1]. Water loss in distribution systems can typically reach between 20 and 30% of the total water production [2], but in some extreme cases this figure can rise up to 50% [3]. Leakage is the main issue responsible for such loss. Energy to supply water is one of major costs in developing countries, and it may easily consume 50% of a municipality's budget in the developing world [4]. Hence, reducing wastage of water through leaks directy affects the cost of water distribution. Furthermore, it is estimated that between 2 and 3% of the world's energy consumption is used to pump and treat water for urban and industrial purposes [4]. Approximately 30 to 50% of water is lost globally due to water leakage. The noise from a leak in a buried plastic pipe generally has low frequency content, occurring well below the pipe ring frequency [5]. In this frequency region, only four types of waves are, in general, responsible for most of the energy transfer in a pipe [6] and [7]. However, in buried plastic water pipes leak noise propagates in an axis-symmetric wave that is predominantly a fluid wave, but is strongly coupled to the pipe-wall, such that there is significant radial motion [5] and [7]. This strong coupling means that leak noise energy is dissipated within the pipe-wall and also radiates as sound into the ground [8] and [9]. The result is that the pipe acts as a low-pass filter [10], and hence measured leak noise tends to be below about 200 Hz. There are different ways of estimating the wave attenuation in pipes. Muggleton et al. [5], [8] and [11] have derived analytical expressions to predict the wavenumber in buried and submerged pipes for leak detection problems. The wavenumber is a frequency dependent complex quantity, the real part of which is related to the wavespeed, and imaginary part is related to the attenuation factor, which determines how far a wave can propagate along the pipe at any particular frequency. Hence, if the wavenumber can be predicted then the wave attenuation factor can be estimated. Measurements have also been carried out to determine the wavenumber in buried pipes [9], [12] and [13]. The aim of this paper is to investigate a new technique to estimate the wave attenuation factor in-situ, in buried pipes. This technique is based on the envelope of the cross-correlation function between two vibration signals measured on the pipe, either side of the leak. An advantage of the method is that it can also be used in the presence of a leak, which could potentially affect the estimate of wave attenuation. Following a description of the method in the next section, and some simulations in Section 2, some experiments on a bespoke test rig are reported in Section 3 to validate the proposed method. 298 *Corr. Author's Address: UNESP, Av. Brasil centro, 56, Ilha Solteira, Brazil, fabricio_cesar@dem.feis.unesp.br Strojniski vestnik - Journal of Mechanical Engineering 60(2014)5, 298-306 1 THEORETICAL DEVELOPMENT Fig. 1 shows a schematic of a pipe with a leak between measurement Positions 1 and 2, together with actuators and sensors attached to each measurement position. The measurement positions are at convenient access points. Leak position Fig. 1. Schematic of a buried pipe showing the sensors and actuators mounted at measurement Positions 1 and 2 with the leak located between these positions Two measurements are carried out. First, the actuator at Position 2 is excited, generating a wave which propages along the pipe to Position 1. The vibration of the pipe is measured using two sensors, one mounted next to the actuator at Position 2 and the other mounted at Position 1. If there is coherence between the two measured signals, the cross-correlation function can be calculated [14], and give information about the wavespeed and attenuation factor. The actuator at Position 1 is then excited, and the measurement procedure is repeated. The wave then propagates in the opposite direction. The procedure to calculate the wave attenuation in dB/m for the section of the pipe involves some manipulation of the cross-correlation functions, including the determination of their envelopes using the Hilbert transform [15]. Moreover, an estimation of the maximum distance that the leak noise would travel at each frequency can be calculated. In the presence of a leak two types of excitation act simultaneously on the pipe. One is the controlled excitation from an actuator, and the other is from the leak. The frequency response function (FRF) between the pressure at the leak position and the acceleration on the pipe at a distance x from the leak is given by [10]: (1) where Ha (m, x ) = -m H (m, x), H (co, x) = eml3xeimxlc, in which p and c are the attenuation factor and the phase velocity of the propagating wave, respectively. The frequency response function between the two accelerometer signals is given by H(m, d1+d2). In Eq. (2) -mp is the imaginary part of the wavenumber Im{&}, which has units of 1/m, and the attenuation factor in the pipe is given by 20 Im{k}/ln{10}. If the actuator at Position 2 is driven at the same time as there is a leak, the cross-spectral density function S21(m) between the measurement Positions 2 and 1, is given by: (m) = CO4 H * (m, dj ) H (m, d2)Sn (m) -+H (m, dj + d2)See (m), (3) (2) where Sn(a>) and See(m) are the auto-spectral density functions of the leak and the acceleration at the actuator position, respectively, and the superscript (2) indicates that the actuator at Position 2 is being excited. The corresponding cross-correlation function R2f (t) , can be determined from the inverse Fourier transform F-1 of Eq. (3) to give R^T) = F-1 {f (t)} ,which can be written as: R%(t) = Rn (T) ® h(z) ®S(z-To) + +Ree (T) ®¥(T) ®S(T- Tact), (4) where ® denotes convolution, Rll (t) = F-1 {Su(m)} is the auto-correlation of the leak signal, Ree (t) = F-1 {See(m)} is the auto-correlation function of the acceleration signal at the actuator excitation position, ¥(T) = F{(d1+d2)} , h(T) = F} , T0 = (dj - d2) / c is the time delay due to the leak, Tact = (d1 + d2) / c is the time delay due to the actuator excitation and S( ) is the Dirac delta function. Eq. (4) shows that the delta function S(t - T0) is smeared by the leak spectrum Sll(m) and the behaviour of di+d2), and the delta function S(v - Tact) is smeared by the external excitation spectrum See(m) and the frequency characteristics of ¥(«>) = e'mSi{dx+dl). For simplicity, in the model the spectral characteristics of the leak and the excitation are considered to be white noise. The auto-spectral density function of the leak is thus assumed to be given by Sn(m) = S0 and the external excitation by See(m) = nS0, where n is the ratio of the spectral density of the leak noise to the spectral density of the external excitation. If the signals from the sensors are passed through ideal band-pass filters with frequency response G(m), in which G(m) = 1 for mlow < m < mupp and zero otherwise, the cross-correlation function becomes: Measurement of Wave Attenuation in Buried Plastic Water Distribution Pipes 299 Strojniski vestnik - Journal of Mechanical Engineering 60(2014)5, 298-306 R%(z) = S0[h(z) ® g (t) ®S(j- To) + +V(r) ® g(T) ®5(r-Tact)], (5) where g(T) is given by g(z) = F-j {G(m)}, which can be written as: a® sin(a®r/2) g M =--7-rf^ COS^e^X (6) ^ afflr/2 in which Am = mupp - mlow is the bandwidth of the filter and mcen = (mlow + mupp) / 2 is the central frequency. The band-pass filter introduces a ripple with frequency mcen into the cross-correlation function. Eq. (5) shows that the delta function is further smeared by the introduction of the band-pass filter. According to Eq. (5) there are two possible peaks present in the cross-correlation function; one is due to the leak and another is due to the external excitation. In this particular case, where the external excitation source is at Position 2, the peak in the cross correlation function related to the external excitation occurs at t = (d1+d2) / c. However, when the external excitation is at Position 1, the peak occurs in R^iz) at t = -(dj+d2) / c. The peak in the cross-correlation function due to the leak occurs at t = (dj-d2) / c irrespective of the position of the external source. If the band-pass filter is broad enough [10] such that ¥(m) << 1, the envelope of the cross correlation function Ri^t) or R^i'C7) normalised by its peak value when t = Tact, is given by [10]: Env (( (t)} = Env (((t)} = Pd )2 + (T — rac,)2 (7) The product of the normalised envelopes can be shifted so that its peak occurs at 0 rather than Tact, i.e., Env(( (t + taa)) x Env(( (t + taa)) = 1 1 + (T/fid )2 . (8) It can be seen that the envelope given by Eq. (8) is a function of the attenuation factor, which is the unknown quantity to be determined, d which is known and t which can be obtained from the measurements. Two ways of estimating the attenuation factor are proposed here. The first is based on setting Eq. (8) to be equal to 1/2, which is a measurable quantity. In this case the attenuation factor is given by: P = '1/2 (9) where |t1/2| is the absolute value of t when Eq. (8) is equal to 1/2. The second method is based on the area A of the envelope given in Eq. (8). If it is assumed that the envelope is symmetric then: 7 1 A = 21-- dz, (10) 01 + (z/pd )2 where Tj is the upper limit of the integral. Evaluating the integral in Eq. (10) results in: P = A 2d arctan (z/ fid) (11) Note that if tj ^ ® then arctan (T/ftd) ^ n/ 2, so that p = A / dn. In practice, the area A is calculated numerically from measured results and in Eq. (11) tj is set to a finite value to avoid noise in the data. 2 SIMULATIONS To illustrate the methodology described in the previous section, some simulations are carried out prior to presenting some experimental results in the following section. The system in Fig. 1 is considered with the parameters given in Table 1, which corresponds to one of the measurements made in the Blithfield test rig, which is described in Section 3. Table 1. Parameters used to illustrate the method to determine the wave attenuation factor dJ 30 m d2 20 m P 2.9x10-4 s/m c 390 m/s flow = mlow' 2ti 20 Hz fupp 2ti 35 Hz, 200 Hz n 2x1010 Note that it is assumed arbitrarily that the amplitude of the peak due to the leak is less than half of the amplitude of the peak due to the actuator. This assumption is based on the experience that the actuator excitation has always dominated the signal at one of the sensors in the experiments carried out by the authors. Two cases are considered. In the first case, a large bandwidth is set with lower and upper limits set to 20 and 200 Hz, respectively. This represents a case where the vibration due to the actuators is effectively transmitted along the pipe, leading to good coherence over a wide frequency range. Second, a much smaller d 300 Almeida, F.C.L. - Brennan, M.J. - Joseph, P.F. - Dray, S. - Whitfield, S. - Tabone, A.P. Strojniski vestnik - Journal of Mechanical Engineering 60(2014)5, 298-306 bandwidth is set with lower and upper limits set to 20 and 35 Hz, respectively. This represents a case when the distance and or damping in the pipe is large enough to significantly attenuate high frequency vibration at the sensor positions. Figs. 2a(i) and (ii) show, R^T) and R^CO normalized by their maximum values together with their envelopes calculated using the Hilbert transform, for the two different bandwidths. The largest peaks in each of the cross-correlation functions correspond to the time delays due to wave propagation from Positions 2 to 1, and from Positions 1 to 2. Note that one of these occurs when t is negative, and one occurs when t is positive. The small peak in Fig. 2a(i) is due to the leak. The effect of a much reduced bandwidth on the appearance of the peak due to the leak can be seen in Fig. 2a(ii). The peak cannot be seen as it is masked by side-lobes of the peaks from the actuator excitation. This effect can be understood using Eqs. (5) and (6). When the filter bandwidth decreases, the side-lobes around the main peaks in the envelopes increase, and move away from these peaks as shown in Fig. 2a(ii). A rule of thumb as to whether or not the peak due to the leak is masked, can be determined using an approximation for the envelopes, which is given by the modulus of the sinc function in Eq. (6). It is found that the peak due to the leak will be masked and not be present in the envelopes if T0 < Tact - 6n/Am. To simplify the presentation of the data from the two measurements discussed above, they are combined as follows. First, R® (t) is calculated instead of R^Cr), which has a peak for positive t instead of negative t. If the wave speed estimate is the same in each direction then this coincides with the peak for Rffiy). The product of the envelopes of these cross-correlation functions is then calculated. This has a large peak corresponding to the time it takes for a wave to propagate from the actuator to the sensor, and the peak corresponding to the leak is much diminished. This can be seen in Figs. 2b(i) and (ii), which are normalised plots of the product of the envelopes of R® (t) and R^iT), for two different bandwidths. It can be seen that the effect of multiplying the two envelopes together is to accentuate the peak due to the actuators and diminish Peak due to the leak a(i) R 21 a(ii) R 21 1 0.5 0 -0.5 -1 -0.5 \ 1 1 1 \ 1 \ 1 1 1 1 1 t 1 1 \ I 1 vW I 0 T [S] 0.5 b(i) Env( R(t + Tact)) x Env( Rf>(r + T^)) This can be determined from a measurement by 05 0 0.05 0.1 0.5 b) 0.01 it ii fi\ \\ Vv_ -0.1 -0.05 0 0.05 0.1 T + Tact ---Theoretical results calculated using Eq. (9) ----Theoretical results calculated using Eq. (11) -Experimental data Fig. 8. The normalised product of the envelopes: a) no leak; b) with leak [10]: Attenuation = -20ln\H (to, dl + d2 (dl + d2 )ln (10) (13) Thus, if the frequency response function is calculated from the two accelerometer measurements, then Eq. (13) can be used to verify the attenuation factor determined from the methodology described in Section 1. Eq. (13) is plotted in Figs 9a(i) and b(i) using experimental data from the Blithfield test rig, when the pipe was excited at Positions 1 and 2 respectively when there was no leak. Figs. 9a(ii) and b(ii) show the corresponding results when a leak was induced. Also plotted is the attenuation calculated using the two methods discussed above, which are given by Eq. (9) and Eq. (11), using data filtered within the frequency regions shown on the graphs. The frequency bandwidth over which the analysis was conducted, was calculated using the method described in [13]. It can be seen that the area method gives a better attenuation estimate when the excitation is set at Position 1, but the half amplitude method gives a slight better attenuation estimate when the actuator is set at Position 2. Although both methods give different 300 Almeida, F.C.L. - Brennan, M.J. - Joseph, P.F. - Dray, S. - Whitfield, S. - Tabone, A.P. Strojniski vestnik - Journal of Mechanical Engineering 60(2014)5, 298-306 ■ Wave attenuation estimate -----Wave attenuation estimate given by Eq. (9) given by Eq. (11) Fig. 9. Wave attenuation in dB/m; a(i) Actuator set at Position 1 with no leak; b(i) Actuator at Position 2 with no leak; a(ii) Actuator at Position 1 with a leak present; b(ii) Actuator set at Position 2 with a leak present attenuation estimates, in general they give a reasonable attenuation estimate for the cases presented. It can also be seen that the presence of a leak does not interfere dramatically with the estimation of the attenuation factor. 4 CONCLUSIONS In this paper, a method to automatically estimate the wave attenuation factor in buried water pipes, has been proposed. This method involves two measurements made by attaching an actuator to two different positions with co-located accelerometers. The technique is based on the envelope of the cross-correlation function of the two measurements. An analytical model has been used to describe and to investigate some of the features and limitations of the method. The technique can also be used in the presence of a leak. Experimental results from a bespoke test rig have also been presented to demonstrate the efficacy of the method. 5 REFERENCES [1] Royal, A.C.D., Atkins, P.R., Brennan, M.J., Chapman, D.N., Chen, H., Cohn, A.G., Foo, K.Y., Goddard, K.F., Hayes, R., Hao, T., Lewin, P.L., Metje, N., Muggleton, J.M., Naji, A., Orlando, G., Pennock, S.R., Redfern, M.A., Saul, A.J., Swingler, S.G., Wang, P., Rogers, C.D.F. (2011). Site assessment of multiple-sensor approaches for buried utility detection. International Journal of Geophysics, Article ID 496123, DOI:10.1155/2011/496123. [2] Cheong, L.C. (1991). Unaccounted-for Water and the Economics of Leak Detection. Water Supply, vol. 9, p. IR 1-1 to 1-6. 53 Measurement of Wave Attenuation in Buried Plastic Water Distribution Pipes Strojniski vestnik - Journal of Mechanical Engineering 60(2014)5, 298-54 [3] AWWA (1987). Leaks in Water Distribution Systems - A Technical/Economic Overview, American Water Works Association, Denver. 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