Estimation of reflection location by the correlation coefficient function

Transcription

1 Acoustics 8 Paris Estimatio of reflectio locatio by the correlatio coefficiet fuctio H. Shibayama a, T. Araya b, Y. Maabe b ad E. Oarura b a Shibaura Istitute of Techology, 3-7-5, Toyosu, Koto-u, Toyo, Japa b Hitachi Iformatio & Commuicatio Egieerig, Ltd, 393 Totsuamati Totsua-u, Yoohama Kaagawa, Japa sibayama@sic.shibaura-it.ac.jp 467

2 Acoustics 8 Paris It is desirable to avoid excavatio durig the maiteace of gas pipes. As a o excavatio method, the measuremet of pipe legth o the basis of reflected acoustic waves travelig i a pipe is cosidered. This method has the advatage i that a ispectio device ca be costructed i a relatively simple maer by combiig a loudspeaer, a microphoe, ad a operatig uit, but it also has the disadvatage that the types of pipe that ca be examied are limited owig to the large decay of travelig acoustic waves. I this study, the decay of acoustic waves travelig i a carbo-steel pipe that complies with the Japaese Idustrial Stadard (JIS) ad methods of correctig measuremet errors are described. Itroductio It is ecessary to carry out regular maiteace of gas pipes to esure the safe supply of gas to cosumers []. Whe gas pipes are buried udergroud, miimum excavatio is a prerequisite to achievig quic ad low-cost maiteace. I particular, owers are required to pay for the cost of gas pipe maiteace o their property. Therefore, a icrease i maiteace cost may affect the cotiuous, stable ad safe supply of gas. Amog the various tass that should be carried out i the maiteace of gas pipes, we examie the prior measuremet of the legth of buried pipes, which is ecessary for repairig the iteral surface of gas pipes without excavatio. Although the use of a i-pipe camera is oe method of realizig such measuremet, it is better to use acoustic waves to rapidly obtai measuremet results. However, because of the large decay of acoustic waves travelig i a pipe, the amplitude of the acoustic waves observed as reflected waves is very low. I this study, the decay is quatitatively evaluated ad the methods of correctig it are described. Yuus et al. proposed a visually uderstadable method of measurig impulse respose by removig icidet sigals from observed sigals. However, i their method, it is ecessary to coect sigle pipes for measuremet, which ievitably causes a decrease i operatio efficiecy durig the measuremet []. We propose three methods of correctig the decay of acoustic waves without decreasig operatio efficiecy. I the first method, the decay is corrected o the basis of the correlatio betwee the impulse respose ad the waveform extracted from the respose. I the secod method, stadig waves are geerated i a pipe ad pipe legth is measured from their frequecy. I the third method, a correlatio fuctio for cotiuous sigals geerated i a pipe is used. I this study, measuremet experimets are carried out usig a carbo-steel pipe that complies with the Japaese Idustrial Stadard (JIS), ad the validities of the above three methods are cofirmed ad compared. Prior to the descriptio regardig those methods, the decay of acoustic waves travelig i a carbo-steel pipe is examied. Decay Characteristics of Acoustic Wave i Carbo-Steel Pipe. Measuremet of decay characteristics The measuremet system show i Fig. is used i the experimets. The pipes used i this study are carbo-steel pipes (legth:,mm; diameter: 7.6mm) that comply with JIS-G345. For the measuremet of pipe legth, the use of pulse waves whose icidet waves ad reflected waves are ot superimposed is effective. The impulse respose based o such properties was measured by the time-stretched pulse (TSP) method [3]. A sigal pr() is a reverse sequece sigal for the drivig TSP sigal p(), =,,,, N-. The impulse respose h() betwee the sigal q() ad the observed sigal q() i the pipe is calculated by N = h ( ) = q( ) pr( ) () Here, a drivig sigal p(), which was obtaied via D/A coverter of a sigal (N=3, 768) at a samplig frequecy = Hz, was used.. Measured amout of decay The ormalized impulse respose calculated by the TSP method is show i Fig.. The separated may waves are observed visually i the impulse respose. The first wave is the respose wave for the drivig sigal, ad the secod wave is the reflected wave geerated at the pipe eds. The others are the reflected waves geerated at the drivig ed ad at the pipe ed. To represet the soud decay of the travelig waves quatitatively, we pay attetio to the cumulative chage i power calculated by squarig the impulse respose show i Fig.. The cumulative chage for power as a fuctio of the travelig distace sigificatly atteuates from the results show i Fig. 3(a). From the amout of the acoustic decay of each power obtaied at the travelig distace, the curve of soud decay for the travelig soud wave i the pipe is calculated. The symbol o has show i Fig. 3(a) represets the cumulative acoustic power as a fuctio of the travelig distace of the observed reflected waves. The ormalized amplitude for distace from m to m is show by the symbol o i Fig. 3. I figure, a straight lie is calculated from the obtaied cumulative acoustic power by the least-squares method. The eergy decay per propagatio distace ca be estimated. From the gradiet of the lie, the acoustic decay is up to -.5dB/m. 467

3 Loudspeaer Carbo steel pipe (Legth:4,mm, Caliber:7.6mm) 3 Correctio Method for Decayed Acoustic Wave Acoustics 8 Paris p() Microphoe Fig. The measurig bloc diagrams. (a) A/D F S =Hz q() p(-)*q() Impulse respose (c) (closed) Time (s) Fig. The TSP sigal, the measured reflected waves ad the impulse respose. (a) TSP sigal p(). The reflected wave q() of the measured TSP sigal. (c) The impulse respose obtaied by the TSP method. Magitude (db) Normalized soud pressrue - - (a) Distace (m) Distace (m) Fig. 3 Cumulative power curve ad the decay curve. (a) The cumulative chage i power for impulse respose. The symbol o represets the travelig distace of the observed reflected waves. The cumulative power curve as a fuctio of the travelig distace. The solid lie is calculated by the least-squares method. 3. [Method I] Measuremet based o impulse respose waveform Because the amplitude of the measured acoustic waves decreases by the decay, a detectig method that is idepedet of amplitude for the reflected waves is ecessary. I this study, the amplitude of reflected waves is estimated by the followig procedure. First, a referece wave is selected from the observed acoustic waves. Next, reflected waves with the same elemets that costructed the referece wave are selected at the every samplig rate. The correlatio coefficiet betwee the both selected sigals is calculated. I procedure, the referece wave is fixed ad selected reflected waves chage i every samplig rate. Fially, the correlatio coefficiet sequece is obtaied. We show the results calculated by the metioed above method. Here, the referece wave that is icluded the 5th reflected wave is selected. Ad the other referece sigal is selected i the reflected waves at every samplig rate startig from s. By chagig the selected time, the correlatio coefficiet as a fuctio of the time is calculated. The correlatio coefficiet depeds o the ier product betwee the waves, ad the amplitude of the wave is idepedet. Fig. 4(a) shows the calculated the correlatio coefficiet fuctio. Each symbol o i the figure idicates the propagated distace of the travellig waves. The local peas correspod to the distace at which acoustic waves are reflected; the distaces at which waves are actually reflected are compared with the theoretical distaces i Fig. 4. The results idicate that the estimatio of the distace with a accuracy of mm or better is possible for propagatio distaces of up to 5m ad this estimatio method ca be comfortably applied to actually buried pipes. However, it is difficult to select the appropriate referece wave by this method because its required specificatios have ot bee established. Estimated reflective locatio (m) Correlatio coefficiet Distace (m) 5 5 Distace (m) Fig. 4 Results estimated usig correlatio coefficiet. Upper: calculated correlatio coefficiet fuctio. The symbol o expresses the estimated returs distace. Bottom: Compariso betwee the calculated ad estimated distace. The solid lie is calculated by the least-squares method. 4673

4 Acoustics 8 Paris 3. [Method II] Detectio of reflectio distace usig frequecy data of stadig waves The distace measuremet method by use of stadig wave proposed by Uebo et al. has a advatage that eables i acoustic ear-field measuremet [4]. The miimum detectio distace ca theoretically be as short as m, if two detectors ad a differetial amplifier are itroduced. Moreover, because the direct-curret term icluded i the sigal is ot cosidered i the distace measuremet system used for the estimatio, sigals with high SNR ca be obtaied usig stadig-wave radar, compared with that i the case of usig covetioal radar. Naasao et al. measured the distace by the acoustic stadig-wave method i which radio waves were replaced with acoustic waves. They placed a reflector at distaces of. ad.3m from the loudspeaer i a ordiary room without ay acoustic material, such as acoustic absorptio, ad estimated the distace withi errors of -3mm, demostratig the feasibility of acoustic radar [5]. Cosiderig that the reflectio distace ca be detected at a high accuracy whe the stadig-wave method is used, as show by the measuremet results obtaied by Naasao et al., we report the result of our experimetal measuremet of pipe legth. First, the distace measuremet method based o the stadig-wave radar proposed by Uebo is described.(4) Assumig that stadig waves are geerated by the iterferece of a travellig wave, V T, with waves reflected from each reflectio poit V R, V R,, V R ad that each reflectio distace is d (=,,,), d is obtaied usig stadig waves. The amplitude of the drivig sigal source, frequecy, ad acoustic velocity are deoted as A, f, ad c, respectively. Let us examie the case i which a plae-wave acoustic source moves alog the x-axis. The travellig wave at a arbitrary poit x o the propagatio path is expressed as VT πf x c ( f, x) = Ae () Deotig the distace from the th reflectio poit as d, ad the reflectio coefficiet ad phase as γ ad φ respectively, the wave reflected from the reflectio poit is expressed by V R ( f, x) f π ( d-x ) jφ c = Ar e e (3) The output power of the microphoe placed at a distace x=x s is expressed by P( f, xs) V ( f, x) + V ( f, x) T = (4) = Whe γ pp is satisfied, the output power of the microphoe is approximated as P ( f, x s ) + r = A + r = R 4πf(d x) cos + φ c (5) The first, secod ad third terms represet the power of the drivig acoustic wave, that of the reflected wave, ad that geerated by stadig waves, respectively. Therefore, Equatio 5 is separated ito the direct-curret term ad power term of the reflected wave P( f, xs) m P DC 4πf f )cos θ ( f ) x c + ( s, (6) where the direct-curret term is PDC = A + = r. (7) The power term of the reflected wave is m ( f ) + b Ad, the phase term is = A a. (8) ( f ) = ta b a θ, (9) where, a ad b i Eq. (9) are expressed as follows: a = r = b = r = 4πf cos c d 4πf si c d + φ + φ () () The secod term of the reflected wave icludes the followig parameters: the reflectio coefficiet γ, the drivig frequecy f, the geeratio poit of the reflected wave d the observatio poit x s, ad the phase φ.therefore, d should be determied to obtai the pipe legth. Figure 5 shows the measured respose sigal ad the spectrum for a -m-log straight ope pipe. It is foud that the sesitivity of the reproducig frequecy of the loudspeaer i the bad from.38 Hz to 5 Hz is high. Because the stadig-wave method has the advatage that the reflectio distace ca be estimated eve withi a limited frequecy bad, o particular care i measurig the frequecy characteristics is ecessary. To estimate reflectio distace, the results that are estimated i the frequecy bad from. Hz to. Hz are show i Fig. 5. Figure 5(a) shows the power spectrum of the sigal measured at the observig poit. The power spectrum i Fig. 5 is Fourier trasform of the spectrum i Fig. 5(a). I characteristics, regular frequecy itervals are observed. To cofirm this pitch frequecy, Fourier trasform of the spectrum show i Fig. 5(a) carried out. Ad, it represets a id of autocorrelatio fuctio i the frequecy domai. The autocorrelatio fuctio of the power spectrum i a limited frequecy bad is show i Fig. 5. It is foud that the autocorrelatio fuctio has a pitch frequecy f p = 86 Hz. Because the room temperature is o C durig the measuremet, the acoustic velocity is 343.6m/s. Travellig distace of returs from the observig poit to the ed of the pipe is.m calculated by the equatio c / (f p ). 4674

5 Acoustics 8 Paris Magitude (db) -5 (a) 3 4 Frequecy (Hz) Frequecy (Hz) Fig. 5 Power spectrum ad Autocorrelatio fuctio i frequecy domai. (a) Power spectrum at measurig poit. Auto correlatio fuctio i the frequecy domai i frequecy bad show i Fig. 5(a). The frequecy resolutio correspodig to the lag i the time domai is.33hz. Hece, the estimated distace is i the rage from.99 to.m, idicatig that the accuracy of the acoustic stadig-wave method is sufficietly high. 3.3 [Method III] Method usig correlatio fuctio Whe the acoustic wave is travellig i the pipe, soud pressure decay of icreases depedig o frequecy ad pipe diameter. I high frequecy rage, decay is a mared large. Therefore, whe the reflectio distace is log, a impulse respose wave maily composed of compoets i a low-frequecy arrow bad is obtaied. Therefore, a impulse respose with filtered smooth waveforms is used for the estimatio of reflectio distace, which is a disadvatage i this method. The stadig-wave method described i sectio 3. has the advatage of high accuracy i the ear-field measuremets [3, 4]. However, it has bee experimetally cofirmed that its accuracy decreases with icreasig pipe legth or pipe ier diameter. As a evaluatio parameter for determiig the correlatio betwee referece ad respose wave, the correlatio coefficiet is applied. The correlatio coefficiet, which is calculated from the ier product of the referece ad respose waves, has the advatage of beig idepedet of amplitude. The correlatio coefficiet betwee the basic ad referece sigals to which attetio is paid shifts every samplig rate. The reflectio positio is estimated o the basis of sequece of the calculated correlatio coefficiet. The sigals measured are divided ito N frames composed of time-series sigals with (cosecutive iteger) elemets. A referece sigal arbitrarily selected from such frames is deoted as x. Similarly, the referece sigal i the ith frame is deoted as y(i). Assumig x=(x, x, x 3,..., x ) ad y(i)=(y(i), y(i), y(i) 3,..., y(i) ), the correlatio coefficiet betwee x ad y(i), C xy(i), is give as Correlatio coefficiet Auto correlatio (a) Time (s) Lag (s) Fig.6 Correlatio coefficiet fuctio ad its autocorrelatio fuctio. (a) Correlatio coefficiet fuctio betwee basic ad referece sigal. Autocorrelatio fuctio of correlatio coefficiet fuctio show Fig. 6. C xy ( i) x y( i) x y( i) =, () where the symbol i the equatio idicates the ier product operator. Figure shows the soud-pressure waveform geerated by the TSP sigals with duratio = s. Duratio of the observed waveform is up to.5s. I sigals measured, a lot of reflected wave iclude. Figure 6(a) shows the correlatio coefficiet fuctio betwee the basic ad referece sigals calculated from equatio (). The time o the abscissa represets the startig umber of the selected frame. The widow legth of the frame is 5.6ms ad shifts every samplig rate 5 μ s. Figure 6 shows the autocorrelatio fuctio of the correlatio coefficiet fuctio. The reflectio distace calculated from the period of this autocorrelatio fuctio is,997mm, which is equivalet to the distace estimated from the impulse respose. This method has the advatage i that the basic sigal ca be arbitrarily chaged, therefore the observed sigals ca be effectively used. I additio, this method has a icreased reliability of the estimated distace by icludig a averagig operatio. 4 Validity of Proposed Methods ad Their Compariso I Sectio 3, we proposed three correctio methods. To tabulate the features of these methods, their advatages ad disadvatages are summarized i Table. Whe the applicatio of the methods to a actual device is cosidered, the device is operated outside; therefore, SNR is cosidered to sigificatly deteriorate i such a oisy eviromet. To solve this problem, we cosider that the followig two coditios are required for each method. 4675

6 Acoustics 8 Paris Table [Method I] Usig impulse respose wave [Method II] Usig stadig wave [Method III] Usig correlatio coefficiet Features of proposal methods. Merits Visually uderstad able. Estimatio with hig h accuracy is possib le. The frame used as t he referece of corr elatio ca be arbitr arily set. Demerits. The amout of de cay is large.. It is difficult to se lect the referec e wave eve wh e the correlatio is used for cor rectio. The accuracy decre ase for log pipes. Accuracy decrease s, uless the compo et i a idetical bad appears may times, because the d rivig sigals are ob served i a wide fre quecy bad. Refereces [] The Japa Gas Associatio, Boolet of subsidy for measures o agig buried ier pipes ver.5. [] U. Yuus, M. Tsuasai, Y. He, ad M. Komiami, Discotiuity Detectio of Steel Pipe with Soud Wave, IEEJ. Tras. EIS C, Vol. 6, No., pp (6). [3] Y. Suzui, F. Asao, G. Kim, ad T. Soe, Cosideratio o desig method of time-stretched pulse, Shigaugiho, Vol. EA9-86, pp. 7-4 (99). [4] T. Uebo, Stadig-Wave Radar Capable of Measurig Distace from m, IEEJ Tras. EIS, Vol. 5, No., pp (5). [5] N. Naasao, T. Uebo, A. Mori, ad N. Ohmata, Basic Examiatio of Distace Estimatio Usig Stadig Wave, J. Acoust. Soc. Am., pp (6). Coditio : The measuremet result must be preseted o site as soo as possible. Coditio : Buried pipes -3 m or loger should be covered. Amog the methods examied i this study, the correlatio coefficiet method usig the correlatio fuctio satisfies the metioed above measurig coditios. We must examie the drivig sigal suitable for this method i the future. 5 Coclusio For estimatio the legth of the carbo-steel pipe which city gas is maily supplied through, we proposed three methods out of cosideratio of the decay of the acoustic waves uder the coditio of usig acoustic waves. It is possible to correct such decay by ay of the three methods proposed. However, cosiderig the advatages, disadvatages, ad future applicatios, the method usig the correlatio fuctio (Method III) is the most advatageous amog the three. Gas pipes actually buried iclude ot oly straight pipes, such as those used i this experimet, but also pipes bet at right agles usig joits. I the future, we would lie to examie the decay i such pipes ad correctio methods for such decay. 4676