The Leak Detection of Heating Pipe Based on Multi-Scale Correlation Algorithm of Wavelet

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1 Sensors & Transducers Vo. 5 Speca Issue December 03 pp Sensors & Transducers 03 by IFSA The Lea Detecton of Heatng Ppe Based on ut-scae Correaton Agorthm of Waeet Xufang Wang Yngwe Guo Runnng Gao Xn Wang Northeast Petroeum Unersty Schoo of Eectrca Engneerng & Informaton 6338 Chna 80 W. Bg Sprngs rd. apt. 3 Rersde Caforna 9507 USA Te.: E-ma: wfdqp@63.com; guoyngwe.good@63.com Receed: 6 September 03 /Accepted: 5 October 03 /Pubshed: 3 December 03 Abstract: Tmey detecton and hgh postonng accurate of eaage sgnas are the guarantee to the safe transport of heatng ppene whch can reduce economc osses and mproe heatng quaty. In order to detect eas tmey and accuratey ths paper presents a method that mut-scae correaton agorthm of waeet to anayze the snguar aues by montorng nfrasonc sgna. Combnng the mproed hgh-frequency coeffcent doman agorthm of waeet wth mut-scae cross-correaton agorthm the method deas wth sgnas by cross-correaton anayss ayer by ayer based on the mut-scae of waeet. By weghtng n the frequency doman and whtenng the sgnas the sgna to nose rato can be mproed and snguar aues may be detected accuratey. Epermenta resuts show that the agorthm has a better effect of postonng and mproe the postonng accuracy of ea detecton of ppene. Copyrght 03 IFSA. Keywords: Waeet decomposton ut-scae cross-correaton Infrasound sgna Ppene ea Postonng accuracy.. Introducton Due to the deeopment of the networ dstrbuton of heatng ppe and the ncreasng of enronmenta corroson factors nsde and outsde of the ppe eaage accdent occurred frequenty and resut from whch we may suffer economc osses and enronmenta damage and aso a ow quaty of fe. So accurate postonng and deang wth faut n tme are the guarantee to heatng safey. The methods of ea detecton can be dded nto detecton nsde of ppe [] and detecton outsde of the ppe []. Usng utrasonc magnetc fu deo and other technooges by pacng the detecton equpment nto the ppe the detecton nsde of ppe can ony detect ntermttenty because of whch t s easy to happen that congeston and outage and the cost s hgh. Wth the rapd deeopment of nformaton and modern contro theory outsde of the ppe detecton has become a hot research. Usuay the method ncudes baance method [3] rea-tme mode method [4] and transent fow detecton method [5] etc. Generay most of ndrect detecton methods often detect when the ea has happened so we can not fnd eas prompty and accuratey that s to say ony when a arge ea occurs can we found t. Among most methods of detectng eas n ppene nfrasound sensors and optca sensors may be the trend n the future. Because the sgnas receed from them hae a hgh accuracy and a strong ant-nterference abty. Combned wth ntegent detecton agorthm they can achee detecton and ocaton of ppene ea. Caed as athematca mcroscope waeet anayss becomes a good too of tme-frequency 80 Artce number P_SI_459

2 Sensors & Transducers Vo. 5 Speca Issue December 03 pp anayss [6] whch can fter nose detect snguar aue and etract feature. By dentfyng mutatons of eaage sgna and fterng sgna detecton accuracy of ppene can be mproed. ut-scae transform of waeet [7] can hghght oca mamum of waeet coeffcents and hep to etract snguarty characterstc of the ea sgna n ppe. The prncpe of cross-correaton anayss [8] s anayzng the nfrasound sgnas that receed from sensors on the both ends of ppe. When the aues of crosscorreaton functon hae sgnfcanty changed there s a ea occurs. Accordng to the poston formua we can now the ea pont. The method does not need to estabsh ppene mathematca mode and easy to cacuate. In ths paper we detect eaage sgna of heatng ppene by mut-scae correaton agorthm of waeet. where d f φ (4) ( t) c ( t) V ( t) d ( t) W ψ (5) and f ( t) s the ow-frequency porton whch comes from decomposton of f d ( t) s the hghfrequency components n the mut-scae resouton and s the data from to. Low-frequency sgna can be seen as the whoe sgna and hghfrequency sgna represents the specfc detas of sgna.. Waeet Reconstructon Agorthm Based on Improed Hgh Frequency Coeffcents of Waeet.. Waeet Decomposton Agorthm Waeet decomposton [9] of nfrasonc sgna s carred out based on some certan condtons and the condton need to contan the nformaton of sgna [0]. Generay assumng that decomposton can be acheed when the sgna meet the condton that f s smar to f and f s contaned nv where V s determned by the sampng frequency and mutscae characterstcs. And ntegra can be done to the functon space used n ths method ( L ( R) ) n the range of rea numbers. Therefore when the functon meets the condton that f(t) s contaned n L ( R) we can get that: f () t < f > ψ () t Z ψ Especay for any subspace V V V V V n ( R) ( > ) L : () () So any functon f n V can be shown wth mut-scae resouton as foows: f f f f d (3).. The Waeet Reconstructon Agorthm that Improes Waeet Coeffcents Usng waeet transform a set of hgh-frequency coeffcents (that s { d d d d }) can be obtaned []. Because the dfference between neghborng waeet coeffcents s sma t has been erfed that the detecton effect of snguar aue s not dea. So we present an mproed method n ths paper. In the method eponentaton that based on e can be operated to waeet coeffcents one by one []. And then a new set of frequency coeffcents can be obtaned whch s shown as the formua (6): {d - { d - e...d... e d d d d e } (6) e d Then orgna sgna can be restored by waeet reconstructon agorthm shown as formua (7): {d - { d - e...d... e d d d d e } e d } (7) After anayzng db6 waeet s chosen to be the optma waeet to anayze the sgna n mut-scae. Shown as Fg. that a6 stand for ow frequency coeffcents and d to d6 are hgh-frequency coeffcents and a of whch are obtaned by waeet decomposton. Accordng to hgh-frequency coeffcents of waeet decomposton smuaton resut of mut-scae anayss to the sgna s shown n Fg.. Db6 waeet s chosen to mae mut-scae anayss of sgnas. In genera the more decomposton ee the more conduce to separate sgna from nose. But for reconstructon more decomposton ee can brng bgger reconstructon error and greater dstorton. In ths paper db6 waeet s chosen to mae s ayers waeet } 8

3 Sensors & Transducers Vo. 5 Speca Issue December 03 pp decomposton to orgna sgna. The sgna that from the frst ayer to the sth ayer s deta sgna and aso hgh-frequency sequence and the sth ayer appromaton sgna s ow-frequency sequence. Seen from Fg. when the sgna s not anayzed by waeet coeffcent doman transform the snguar aue of nfrasound sgna at dfferent scaes s not obous. Thus we can not determne the tme doman poston that correspondng to mutatons. Shown as Fg. deang wth sgna by waeet coeffcent doman transform hgh-frequency coeffcents n the d ayer hae an obous pea and sampng ponts that corresponded s the th pont. And then we can not determne whether the eas occur. By usng the mproed method the range of pea s more focused and the postonng of the pont of mutatons s more precsey. Accordng to sampng frequency tme doman poston can be cacuated. 3. Waeet ut-scae Cross-correaton Anayss Agorthm Usuay t s dffcut to detect the true poston and the type of snguar aues n snge scae [3]. Ony when there are etreme ponts n a mut-scae the ocaton of mutatons can be determned accuratey. So the method that cross-correaton anayss based on mut-scae s proposed to detect snguar aue and by whch we can reduce errors and mproe accuracy of eaage detecton. 3.. ut-scae Decomposton System Assumng that the state equatons and measurement equatons n scae are obtaned and system mode [4] of ppene s shown as foow: ( ) F ( ) ( ) w ( ) (8) z w ( ) N( 0 Q ( ) ) (9) ( ) H ( ) ( ) ( ) (0) ( ) N( 0 R ( ) ) () Fg.. Resut of waeet anayss. Formua (8) s decomposed by waeet transform wth the scae from to - and the resuts are shown as foow: ( ) F ( ) ( ) w ( ) w ( ) N 0 Q ( ) ( ) () (3) where the resuts are obtaned by decomposton n the scae : F ( ) F ( ) F ( ) (4) Q T ( ) F ( ) h ( ) Q ( ) F ( ) h () Q ( ) (5) Formua (0) s decomposed by waeet transform from scae to - and the resuts are shown as foow: Fg.. The anayss n hgh-frequency coeffcent doman wth waeet decomposton. z ( ) H ( ) ( ) ( ) ( ) N 0 R ( ) ( ) (6) (7) 8

4 Sensors & Transducers Vo. 5 Speca Issue December 03 pp where R C ( ) C ( ) (8) ( ) h ( ) R ( ) (9) 3.. ut-scae Cross-correaton Anayss The step of ut-scae cross-correaton anayss agorthm s as foows: A. In ths paper () t and () t are two group of data that coected n a certan tme n the fed. In order to descrbe the dynamc system of mut-scae decomposton agorthm assumng that state equaton and measurement equaton anayss can be done n the scae. Due to the nfuence of sampng frequency the coected data s seen as eaage sgna n the fnest scae here the fnest scae tae N 5 ; B. Dong waeet decomposton n 5 dfferent dynamc equatons can be obtaned and we can get smoothed sgna. C. The deta sgna n the 5th scae s the dfference between the sgna to be detected and the smoothed sgna. If the deta sgna does not ncude eaage nformaton t s seen as Gaussan nose whch can be ftered. If t does not meet dstrbuton of Gaussan then the eaage sgna s contaned and we shoud detect and ocate on the scae otherwse t w cause postonng errors. D. If the detas of the sgna can be ftered out then the obsered data shoud be contnue to do waeet decomposton unt the resut meet wth the stop condton n the thrd step or. E. The deta sgnas that come from waeet decomposton are used to do cross-correaton anayss to determne and ocate the ea. F. The measured data s transferred to the host computer and the data w be ftered and correaton cacuaton w be done n snge-scae and mutscae ATLAB smuaton resuts are shown n Fg. 3 Fg. 4 and Fg. 5. The nfrasound sgna shown n Fg. 3 s coected by sensors whch are set on both ends of ppe at the scene. Smuaton resut of snge-scae correaton anayss to the sgnas that hae been ftered s shown n Fg. 4. The deta of the cures n the fgure s not obous and man pea of reated s submerged n the bacground nose because of whch we can not see reated man pea. So the effect of nfrasound detecton s not good. Smuaton resuts of mutscae cross-correaton anayss s shown n Fg. 5 n whch deta of ths method s more promnent and there s a cear reated pea and sgna to nose rato s mproed. The resuts of compare of snge-scae crosscorreaton anayss and mut-scae cross-correaton anayss are shown n Tabe and the compare of waeet decomposton agorthm and mut-scae cross-correaton anayss agorthm are shown n Tabe. The resuts show that the postonng error of mut-scae cross-correaton anayss s sgnfcanty ower than the snge-scae cross-correaton anayss and the detecton precson of mut-scae crosscorreaton anayss s hgher than snge-scae crosscorreaton anayss and the sgna nose rato (SNR) of mut-scae cross-correaton anayss s superor to the waeet decomposton agorthm and the mean square error s hgher than waeet decomposton agorthm. Fg. 3. Infrasound sgna. Fg. 4. Snge scae cross-correaton anayss. Fg. 5. ut-scae cross-correaton anayses. Tabe. Resuts of compare of snge scae wth mutscae cross-correaton anayss. Postonng error of ea pont (%) Deay(s) Snge-scae crosscorreaton anayss ut-scae crosscorreaton anayss

5 Sensors & Transducers Vo. 5 Speca Issue December 03 pp Tabe. Comparng resut of mut-scae waeet decomposton agorthm and ut-scae cross-correaton anayss agorthms. Performance nde ut-scae waeet decomposton agorthm ut-scae crosscorreaton anayss SNR SE The Cross-correaton Tme Deay Estmaton 4.. Smuaton and Anayss ethod of Cross-correaton Tme Deay Estmaton When deang wth nfrasonc sgna wth the method of tme deay assumng that the receed sgnas from both ends are seen as (n) and the number and number of sgnas are shown as foows: ( n) a s( n ) w ( n) τ (0) ( n) a s( n ) w ( n) τ () where s ( n) s the nfrasound sgna w ( n) and w ( n) are Gaussan whte nose but no reated wth each other s( n) and w ( n) are uncorreated random sgnas τ and and ( n) a and τ are the propagaton tme of ( n) a are attenuaton factor. The cross-correaton functons of ( n) ( n) s R ( τ ): ( τ ) E( ( n) ( n τ )) and R () Anayzng the correaton of sgna we can get that: R ( τ ) aa E( s( n τ ) s( n τ τ )) a a R ( τ ( τ τ )) The aue of R ( τ ) equa to sτ. τ τ s (3) s mamum when τ s and τ represents the tme deay that 4.. Spectrum Densty of Cross-correaton When spectra densty of cross-correaton wth dfferent weghtng wndow do mutpy n the frequency doman error estmaton of crosscorreaton functon can be obtaned by IFFT and by whch we can reduce the effect of nose. Deang wth two sgnas by FFT functon of cross-correaton spectra densty s shown as foow: πfd ( f ) R ( f ) e S ( f ) S s mn (4) where s( t) are the usefu sgna n() t and m( t) are the nose sgna and D s the tme dfference between eaage sgnas from sensor on both end of ppe. ( f ) R ( f ) R ( f ) 0 Snn n m (5) Tme dfference of arra s cacuated by crosscorreaton functon and the cross-spectra densty functon n frequency doman we can further reduce the mpact of nose to usefu sgna. Cross-spectra densty s weghted and the aue s that: A (6) IFFT s done to weghted cross-spectra densty. The cross-correaton spectra densty s shown as foow: G S y ( τ ) AS ( f ) S S ( f ) ( f ) e πfτ e πfτ df df (7) Tme dfference between sgna spread to the both end of sensors can be cacuated by fndng the mamum of eaage nfrasonc sgna Frequency-doman Weghtng Anayss Accordng to cross-correaton agorthm of crosspower spectrum weghtng n the frequency doman can be reazed. By whtenng the sgna and nose SNR of the sgna can be mproed. The drect crosscorreaton functon of two sgnas can be got accordng to the nerse transformaton of tme doman by FFT. R g () t AG ( τ ) e πτ t dτ (8) 84

6 Sensors & Transducers Vo. 5 Speca Issue December 03 pp where A s weghted functon of cross-correaton and dependng on the specfc nformaton of sgna and nose the pea obtaned by generazed correaton functon of cross-power spectrum can be sharpened accordng to the dfferent weghts of dfferent noses. T faut N c ζ T Nc ζ ( N ) (3) c 4.4. Appcaton of ut-scae Anayss of Waeet n Ppene Lea Detecton ) Process of mpementaton. The sgna s decomposed nto mutpe scaes and deang wth two parae sgnas by crosscorreaton anayss on the snge scae then we can recee the tme dfference that s t and the dfference become a set of ectors that are T t t... t where s the ee of the scae of the waeet decomposton. The accuracy of ea pont can be mproed by weghtng aerage to the deay estmaton on mut-scae. A. Frsty we shoud seect the approprate waeet db6 s chosen to anayze and the ee of waeet decomposton s determned. B. In ths part d s waeet coeffcent of ayers of sgna that get from waeet decomposton. Where s the data from to N namey ectors of two waeet coeffcents are shown as foow: d () t d () t d () t d ()] t [ d () t () t d () t d ()] t d [ (9) (30) C. N-ayer waeet coeffcents are seected from the two sgnas to mae cross-correaton the resut s shown as foow: N c s T (33) where T s the aerage of the tme of mutaton and we now that ζ : ζ : ζ ( T T ) ( T T ) ( T T ) : Nc : : Nc (34) G. In ths part T s changed to tme deay namey D t ma ( τ ma τma) and where f s the sampng frequency. f (35) ) Anayss of the epermenta resuts. Smuaton s done to mut-scae crosscorreaton of waeet and t s operated to hgh frequency nformaton of ayers by addng weght. A. In the 6th ayer the hgh frequency nformaton of sgnas on the both end are shown n Fg. 6 and Fg. 7. The resut of cross-correaton anayss for the sgnas n ths scae s shown n Fg. 8. We can see the tme deay from the resuts and t 0.67s. R ( τ ) E d ( t) d ( t τ ) ] (3) [ N N τ A set of ectors of can be obtaned whch s named τ τ τ τ ]. [ N D. In a scaes mamum of R ( τ ) s seected and the tme deay that correspondng to the mamum s seen asτ namey τ s equa to ma τ ma where s data from to τ E. ma s the sampng tme that correspondng to the tme when K-ayer waeet coeffcents change suddeny and the tme named ast. F. Weghtng to T and the resut s shown as foow: Fg. 6. Hgh frequency nformaton of Db6 on the start sde Fg. 7. Hgh frequency nformaton of Db6 on the end sde 85

7 Sensors & Transducers Vo. 5 Speca Issue December 03 pp Fg. 8. Cross-correaton functon of Db6 Fg. 3. Hgh frequency nformaton of Db4 on the end sde. B. In the 5th ayer the hgh frequency nformaton of sgnas on the both end are shown n Fg. 9 and Fg. 0. The resut of cross-correaton anayss for the sgnas n ths scae s shown n Fg.. We can see the tme deay from the resuts and t 0.3s. Fg. 4. Cross-correaton functon of Db4. Fg. 9. Hgh frequency nformaton of Db5 on the start sde. D. In the 3rd ayer the hgh frequency nformaton of sgnas on the both end are shown n Fg. 5 and Fg. 6. The resut of cross-correaton anayss for the sgnas n ths scae s shown n Fg. 7. We can see tme deay from the resuts and t 0.8s. Fg. 0. Hgh frequency nformaton of Db5 on the end sde. Fg. 5. Hgh frequency nformaton of Db3 on the start sde. Fg. 6. Hgh frequency nformaton of Db3 on the end sde. Fg.. Cross-correaton functon of Db5. C. In the 4th ayer the hgh frequency nformaton of sgnas on the both end are shown n Fg. and Fg. 3. The resut of cross-correaton anayss for the sgnas n ths scae s shown n Fg. 4. We can see tme deay from the resuts and t 0.3s. Fg. 7. Cross-correaton functon of Db3. Fg.. Hgh frequency nformaton of Db4 on the start sde. E. In the nd ayer the hgh frequency nformaton of sgnas on the both end are shown n Fg. 8 and Fg. 9. The resut of cross-correaton anayss for the sgnas n ths scae s shown n Fg. 0. We can see the tme deay from the resuts and t 0.0s. 86

8 Sensors & Transducers Vo. 5 Speca Issue December 03 pp Fg. 8. Hgh frequency nformaton of Db on the start sde. Fg. 9. Hgh frequency nformaton of Db on the end sde. Cross-correaton anayss s done to the hghfrequency coeffcents whch come from waeet decomposton n d to d6 scae and weghtng anayss of the resuts shoud be done and the fuson resut s shown n Tabe 3. Scae Number Tabe 3. Resuts of fuson agorthm. Tme Dfference t (s) Sampng Number d d 0.0 d d d d Weght Computaton Accordng to the mproed mut-scae crosscorreaton anayss of waeet decomposton dstance between eaage pont and the start sde sensor s : Fg. 0. Cross-correaton functon of Db. F. In the st ayer the hgh frequency nformaton of sgnas on the both end are shown n Fg. and Fg.. The resut of cross-correaton anayss for the sgnas n ths scae s shown n Fg. 3. We can see the tme deay from the resuts and t 0.474s. L * t * m And postonng error s: % 0.6% 50 (36) (37) Fg.. Hgh frequency nformaton of Db on the start sde. Fg.. Hgh frequency nformaton of Db on the end sde. Fg. 3. Cross-correaton functon of Db. The postonng error of mut-scae correaton anayss of waeet s greaty reduced. It says that mproed mut-scae correaton anayss agorthm has certan mproement n the detecton and ocaton of eaage sgna and the postonng s more precse. ore nformaton about the ea can be got accordng to mut-scae correaton anayss of waeet. As seen from the data n Tabe 4 compared wth waeet decomposton agorthm and mut-scae cross-correaton anayss mut-scae crosscorreaton anayss that based on waeet decomposton mproes the SNR of reconstructed sgna and a smaer mean square error can be gotten. Tabe 4. Resuts of comparng SNR and SE of three agorthms. Performance nde SNR SE Waeet decomposton agorthm ut-scae crosscorreaton anayss reated fuson of Waeet mut-scae

9 Sensors & Transducers Vo. 5 Speca Issue December 03 pp Concusons Accordng to the mproement for waeet decomposton agorthm and the anayss for mutscae correaton agorthm we can do crosscorreaton anayss to the sgna of ppene eaage on mut-scae. The correspondng sampe pont of ea mutaton can be got accordng to cacuaton of weght for snguar aue pont. The epermenta resuts show that ut-scae correaton anayss agorthm of waeet decomposton has seera adantages as foows: the accuracy of postonng s hgh; the SNR of sgna s hgh; the SE of sgna s ow. So the am to mproe the accuracy of nfrasonc sgna for ea detecton has been fnshed. References []. Henngar G. W. Adances n gas ea detecton Ppe and Gas Journa 985 pp []. Hamced A. ahotra V. N. Detecton of ea from process ppes Ppes and Ppenes Internatona 999 pp [3]. Rangaswamy Shanta Shobha G. Autonomc Onne Indeng for Databases Usng Query Woroads. Journa of Computatona Integence and Eectronc Systems Vo. Issue 0 pp [4]. Zhang X. J. Statstca ea detecton n gas and qud Ppenes Ppes Ppenes nternatona 993 pp [5]. Wade W. R. Rchford Detectng eas n ppenes usng SCADA nformaton Ppe Lne Industry 988 pp [6]. Quadr S. A. Sde Othman Roe of Agorthm Engneerng n Data Fuson Agorthms Journa of Computatona Integence and Eectronc Systems Vo. Issue June 03 pp [7]. Bec S. B.. Curran. D. Sms N. D. Sternway. R. Ppene networ features and ea detecton by cross-correaton anayss of refected waes Journa of Hydrauc Engneerng 005 pp [8]. Ye Hao Wang Guzeng Fang Chongzh Appcaton of Waeet Transform to Lea Detecton and Locaton n Transport Ppenes Engneerng Smuaton Vo pp [9]. Habb d. Ahasan Zabn ahe Uddn Ja An Approach to Waeet Based Image Denosng Journa of Computatona Integence and Eectronc Systems Vo. Issue 03 pp [0]. Abdu Hammed V N ahotra Detecton of Leas from process ppes Ppes&Ppenes Internatona 999 Vo. 5 pp []. Zhou Xaoyong Ye Ynzhong The detecton of faut base on waeet Contro Engneerng 003 Vo. 4 pp []. Omoogo. Sazer P. Acoustc Eent Locazaton Usng a rosspower-spectrum Phase Based Technque Proc. ICASSP Adeade 994 pp [3]. Chen J. D Beaste J. Huang. Y. T. Performance of GCC and A-DF-based tme deay estmaton n practca reerberant enronments EURASIP Journa on Apped Sgna Processng 005 Vo. pp [4]. atthew K. Kande Robert Bobby Grsso Thomas E. Der Afred L. Wcs J. echatron ontor System to Detect Heat Stress and Poston of Youth Lawn Care Worers Journa of echatroncs Vo. Issue 0 pp Copyrght Internatona Frequency Sensor Assocaton (IFSA). A rghts resered. ( 88