research article blind source separation model of earth ...research article blind source separation...

Research ArticleBlind Source Separation Model of Earth-Rock Junctionsin Dike Engineering Based on Distributed Optical FiberSensing Technology

Huaizhi Su12 Meng Yang12 Kunpeng Zhao3 and Zhiping Wen4

1State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering Hohai University Nanjing 210098 China2College of Water Conservancy and Hydropower Engineering Hohai University Nanjing 210098 China3National Engineering Research Center of Water Resources Efficient Utilization and Engineering Safety Nanjing 210098 China4Department of Computer Engineering Nanjing Institute of Technology Nanjing 211167 China

Correspondence should be addressed to Huaizhi Su su huaizhihhueducn

Received 17 October 2014 Accepted 2 March 2015

Academic Editor Zhenhua Zhu

Copyright copy 2015 Huaizhi Su et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Distributed temperature sensing (DTS) provides an important technology support for the earth-rock junctions of dike projects(ERJD) which are binding sites between culvert gates and pipes and dike body and dike foundation In this study a blind sourceseparation model is used for the identification of leakages based on the temperature data of DTS in leakage monitoring of ERJDFirst a denoising method is established based on the temperature monitoring data of distributed optical fiber in ERJD by a waveletpacket signal decomposition technique The temperature monitoring messages of fibers are combined response for leakages andother factors Its character of unclear responding mechanism is very obvious Thus a blind source separation technology is finallyselected Then the rule of temperature measurement data for optical fiber is analyzed and its temporal and spatial change processis also discussed The realization method of the blind source separation model is explored by combining independent componentanalysis (ICA) with principal component analysis (PCA) The practical test result in an example shows that the method couldefficiently locate and identify the leakage location of ERJD This paper is expected to be useful for further scientific research andefficient applications of distributed optical fiber sensing technology

1 Introduction

China is a country affected bymonsoons significantly Floodsand other natural disasters are often caused for rainy seasonA large number of dikes are built in order to reduce the losscaused by flooding and invasion of storm tide However theintegrity and safety of dike projects are objectively under-mined by crossing culverts and other hydraulic structuresespecially earth-rock junctions [1] The operating experienceof hydraulic structures of dikes indicated that strengthen-ing real-time location and identification of leakage hazardsfor the earth-rock junctions of dike projects (ERJD) hadspecial significances to ensure the safety of entire culvertsand dike projects [2] Research and analysis of high-techleakage monitoring in ERJD have gotten more and moreattention in engineering and academia during improvement

and optimization of traditional monitoring techniques andmethods [3] The temperature tracing technology is a geo-physical technique based on geophysics and it has broadapplication prospects in seepage monitoring [4] Comparedto the traditional leakage monitoring technology such aspiezometer tubes and osmometers the early temperaturetracing technology was more sensitive and effective and hadlower unit acquisition cost However the early temperaturetracing method was still a point-monitoring technology Thesingular area of internal temperature in buildings would notbe detected inevitably because of a large layout spacing ofthermistor thermometers and other reasons [5]

DTS as a new approach was produced by combination ofoptical fiber sensing technology and leakage risk monitoringtechnique [6 7] The new leakage monitoring method DTSprovides a possible way to the distributed long-distance and

Hindawi Publishing CorporationJournal of SensorsVolume 2015 Article ID 281538 6 pageshttpdxdoiorg1011552015281538

2 Journal of Sensors

large-scalemonitoring [8 9] In general the use of distributedfiber sensing technology in leakagemonitoring of buildings isstill in its infancy stage for theoretical research experimentalsimulation and engineering application research especiallyfor monitoring the combination between two mediums inERJD The consequent analysis of temperature monitoringdata and processing aspects still needmore studiesThereforean experimental model of ERJD was established and the dis-tributed fiber leakage monitoring technology was developedaccording to the working features of ERJD In-depth studiesof models and methods for leakage identification of ERJDhave important science and engineering applications basedon features of monitoring data

2 Denoising Research of DTS MonitoringData with Wavelet Packet

Wavelet transform method was proposed by Morlet in theearly 1980s and then it changed rapidly to be a very powerfultool for digital signal processing image processing datacompression data denoising and so forth

Wavelet is a breakthrough to Fourier transform analysisIt is a time-frequency analysismethodwith fixedwindow sizeand changeable shape time window and frequency windowLocal features signal can be well characterized in both timedomain and the frequency domain

Its main advantage is the ability to do local refinementand analysis for signal which overcomes the difficulties of notprocessing the nonstationary signals for Fourier transformtechnique and short-time Fourier transform method

During practical applications wavelet transform will dis-perse the stretching factor 119886 and translation factor 120591 in orderto adapt to the computer calculation 119886 takes 1198860

0 1198861

0 1198862

0 119886

119895

0

The sampling interval of displacement amount 120591 isΔ120591 = 11988611989501205910

Thus wavelet function is

120601119886120591(119905) = 119886

minus1198952

0120601 (119886minus119895

0(119905 minus 119896119886

119895

01205910)) (1)

where 119895 and 119896 are positive integersTaking 119886

0= 2 and 120591

0= 1 in practical operation wavelet

basis function 120601119886120591(119905) can be expressed as follows

120601119895119896 (119905) = 2

minus1198952120601 (2minus119895119905 minus 119896) (2)

Corresponding discrete wavelet transform is

WT119909(119895 119896) = ⟨119909 (119905) 120601

119895119896(119905)⟩ = int

119877

119909 (119905) 120601119895119896(119905)119889119905 (3)

The signal can be decomposed into a high frequencyportion named 119863 and a low frequency part marked 119860by wavelet transformation Compared to the wavelet trans-form wavelet packet decomposition analysis is a moresophisticated approach which well disassembles the highand low frequency parts of each layer simultaneously Itgreatly improves the resolution of signal and overcomes theinsufficient of wavelet decomposition in ldquolow-resolution ofhigh-frequencyrdquoThewavelet packet decomposition hasmorebroad application prospects and the 3-layer wavelet packetdecomposition process was expressed in Figure 1

S

A1 D1

AA2 AD2 DA2 DD2

AAA3 AAD3 ADA3 ADD3 DAA3 DAD3 DDA3 DDD3

Figure 1 Transform decomposition process of wavelet packet

As shown in Figure 1 the decomposition relationship of3-layer wavelet packet is as follows

119878 = 1198601198601198603+ 119860119860119863

3+ 119860119863119860

3+ 119860119863119863

3

+ 1198631198601198603+ 119863119860119863

3+ 119863119863119860

3+ 119863119863119863

3

(4)

The denoising procedure of wavelet packet for DTSleakage measurement data is summarized as below

(1) Wavelet packet decomposition Select wavelets anddetermine the decomposition level 119873 then decom-pose 119873-layer wavelet packet for original signal 119878During data processing the wavelet packet decompo-sition level is determined by the wavelet packet noisereduction effect

(2) Thresholds quantization Select the appropriatethreshold quantization method to quantify treatmentfor each wavelet packet coefficients decomposed

(3) Reconstruction of wavelet packet Reconstruct thelow-frequency coefficients of wavelet packet 119873-layerand its corresponding high-frequency coefficients

Among the previous steps the keys are selection of thewavelet packet decomposition level and approach to thethreshold quantization Wavelet packet decomposition levelis generally notmore than 5-layerThe threshold quantizationcan be processed by denoising with the soft threshold andhard threshold method

Coefficient of wavelet packet of hard threshold estimatedis

119908119895119896=

119908119895119896

10038161003816100381610038161003816119908119895119896

10038161003816100381610038161003816ge 120582

0

10038161003816100381610038161003816119908119895119896

10038161003816100381610038161003816lt 120582

(5)

Coefficient of wavelet packet built for soft threshold isgiven

119908119895119896=

sign (119908119895119896) (

10038161003816100381610038161003816119908119895119896

10038161003816100381610038161003816minus 120582)

10038161003816100381610038161003816119908119895119896

10038161003816100381610038161003816ge 120582

0

10038161003816100381610038161003816119908119895119896

10038161003816100381610038161003816lt 120582

(6)

For (5) and (6) 119908119895119896

represents wavelet packet coefficientand 120582 is preset threshold or threshold value which iscalculated in the form

120582 =

120590radic2 lg119873lg (119895 + 1)

(7)

Journal of Sensors 3

where 120590 is noise variance 119895 is decomposed scale and119873 is sig-nal length

Signal to noise ratio (SNR) and root mean square error(RMSE) are usually selected as a signal denoising perfor-mance evaluation which are calculated by following equa-tions

SNR = 10 lg(sum119873

119899=11199042(119899)

sum119873

119899=1[119904 (119899) minus 119904 (119899)]

2)

RMSE = radic 1119873

[119904(119899) minus 119904(119899)]2

(8)

where 119904(119899) is original signal 119904(119899) represents signal afterdenoising by wavelet packet and119873 is signal length

3 Blind Source Separation Modelsand Methods of DTS TemperatureMonitoring Data

Seepage will lead to a change in the stability temperature fieldin themedia and a partial volatile region can be generated [1011] However the temperature field distribution of structurebody is affected not only by leakage field but also soil char-acteristics natural phenomena optical fiber laying elevationcross artificial cavities and other factors Further the mea-sured value of the optical fiber temperature sensing system isaffected Therefore the temperature field of structure body isa result caused bymultiple-factor under the combined effectsThe positioning of leakage points inside ERJD under nationalcondition can be attributed to the blind source separationproblem for the influence of multiple-factor [12]

Leakages soil characteristics or other factors causingchanges in temperature monitoring data unit have a cor-responding source component which is a function of thedistance between the sampling point and the starting pointSoil characteristics natural phenomena and other factorsshould be possibly separated out of the temperature dataexcept for the leakage factorThe separated data can be a resultof temperature field change only affected by the leakage factoras much as possible And the leakage factor is just the finalconcern

The effects of leakage factor soil characteristics or otherfactors on the measured temperature data can also be con-sidered to be independent units The temperature data inmost regions along fiber are not affected by leakages guttersand other factors which are small probability events on timeand space Based on non-Gaussian distribution and statisticalindependent of the source signal ICA is selected in blindsource separation technique In addition PCA is determinedas a pretreatment method for ICA technique in order toreduce the computational complexity and effective multiple-variable correlation

The key of PCA is the certain degree of relevance andredundancy of information between the variables At thesame time adjacent sampling points have similar work envi-ronment and strong correlation which provide a possibilityto the use of PCA The mathematical model of PCA can beobtained by the following process First a 119901 dimensional

random vector is consisted by 119901 scalars and it is expressed as119883 = (119883

1 119883

119901)1015840 119901 is defined as an arbitrary number 119883 is

used for orthogonal transformation ordering 119884 = 1198791015840119883 and119879 is orthogonal matrix Each component of 119884 is not relevantand the variance of the first variable of 119884 is the largest thesecond variable coming afterThis process can be representedby the following matrix

1198841= 119905111198831+ 119905121198832+ sdot sdot sdot + 119905

1119901119883119901= 1198791015840

1119883

1198842= 119905211198831+ 119905221198832+ sdot sdot sdot + 119905

2119901119883119901= 1198791015840

2119883

119884119901= 11990511990111198831+ 11990511990121198832+ sdot sdot sdot + 119905

119901119901119883119901= 1198791015840

119901119883

(9)

The definition of singular value decomposition (SVD) ofPCA can be described 119872 represents a matrix with 119898 rowsand 119899 columns whose elements belong to the field of realnumbers or complex field There is the following decom-position

119872 = 119880119878119881119879 (10)

where 119880 represents a unitary matrix with 119898 times 119898 order andis called left singular matrix of119872 119881 is a unitary matrix with119899 times 119899 order and is named right singular matrix of119872 119881119879 istranspose ofmatrix119881 the same bellow 119878 represents a positivesemidefinite diagonal matrix with119898 times 119899 order and elementson the diagonal matrix are singular values of 119872 which areequal to the square root of eigenvalues of 119872119879 lowast 119872 It isorthogonal matrix as the elements of unitary matrix are realnumbers Relationship between the main component of 119884and monitoring data matrix119883 can be obtained by

119884 = 119883119879 (11)

Thus

119883 = 1198841198791015840 (12)

where matrix of 119879 is constituted by eigenvectors of diagonalmatrix and119883119879119883 is orthogonal matrix

From the theory of SVD it can be obtained that

119883 = 1198801198781198811015840 (13)

Comparing formula (12) with (13) it can be known that119879 = 119881 then 119884 = 119880119878 = 119883119881

Therefore the main component of matrix is the productof left singular matrix and its corresponding singular valuesand is also equal to the product of monitoring data matrixand the right singular matrix The number of principalcomponents can be determined through the cumulativevariance contribution rate Variance contribution rate andcumulative variance contribution rate are described follows

120593119896=

120582119896

sum119901

119896=1120582119896

120595119898=

sum119898

119896=1120582119896

sum119901

119896=1120582119896

(14)


where 120582119896represents the eigenvalues of covariancematrix and

120593119896and 120595

119898are respectively called variance contribution rate

and cumulative variance contribution rateIn order to avoid inconsistencies between dimensions and

units of data the data is typically normalized

119883lowast

119894=

119883119894minus 119864 (119883

119894)

radic119863 (119883119894)

(15)

The mathematical model of ICA can be expressed by

1199091= 119886111199041+ 119886121199042+ sdot sdot sdot + 119886

1119899119904119899

1199092= 119886211199041+ 119886221199042+ sdot sdot sdot + 119886

2119899119904119899

119909119899= 11988611989911199041+ 11988611989921199042+ sdot sdot sdot + 119886

119899119899119904119899

(16)

where 1199091 1199092 119909

119899represent 119899 random variables named

mixed signals 1199041 1199042 119904

119899are 119899 independent components

called source signals 119886119894119895(119894 119895 = 1 2 119899) is mixing coeffi-

cientParallel algorithm calculation steps of several indepen-

dent components are described as follows

(1) standardize the data so that the mean and variance ofeach column are respectively 0 and 1

(2) data whitened of 119911 is gotten from the data obtainedfrom Step (1)

(3) 119898 is selected as the number of independent compo-nent to be estimated

(4) the mixing coefficient of 119908119894is initialized 119894 = 1

2 119898 and every119908119894is changed to be a unit 2-norm

then matrix 119882 is orthogonalised by the method ofStep (6)

(5) update each 119908119894 119908119894larr 119864119911119892(119908

119879

119894119911) minus 119864119892

1015840(119908119879

119894119911)119908119894

the function of 119892 can be selected from formula (17) toformula (19)

(6) matrix 119882 = (1199081 119908

119898)1015840 is orthogonalised 119882 larr

(1198821198821015840)minus12119882

(7) return to Step (5) if the result is not converged

The function of119892 can be selected from the following func-tions

1198921(119910) = tanh (119886

1119910) (17)

1198922(119910) = 119910 exp(minus

1199102

2

) (18)

1198923(119910) = 119910

3 (19)

Leakage location

Figure 2 Model experiment of ERJD

DTS system

Heating system

Figure 3 DTS monitoring and heating system

The corresponding derivative functions are described asfollows

1198921015840

1(119910) = 119886

1(1 minus tanh2 (119886

1119910))

1198921015840

2(119910) = (1 minus 119910

2) exp(minus

1199102

2

)

1198921015840

3(119910) = 3119910

2

(20)

where 1198861is a constant valuing in [1 2] and the value is usually

taken as 1 tanh(119909) represents hyperbolic tangent function

4 Application Case Analyses

A model experiment platform was formed and shown inFigure 2 to simulate the existence of leakages for ERJD TheDTS monitoring system of Sentinel DTS-LR produced bySensornet was applied The DTS monitoring and heatingsystem was shown in Figure 3 A schematic diagram of themodel was given in Figure 4 Multimode four core armoredcable of 50125 um was used as the monitoring optical cablewith a type of ZTT-GYXTW-4A1a

TheZTT-GYXTW-4A1a was a special optical cable whichcould be used to be heated And its structure section wasdrawn in Figure 5


Monitoringopticalcable

Modelexperiment

pool of ERJD

Figure 4 Schematic diagram of the model

Water-blockingmaterial

Polyethylenejacket

Heatingwire

Fiberpaste

Opticalfibre

Loosetube

Steel-plasticcompound

Figure 5 Structure section of ZTT-GYXTW-4A1a

The leakage location was washed by a water pipe and thevelocity of seepage was controlled The monitoring data wasnoted as the stable velocity was formed

For simplicity just one leakage point was introduced inthe model and the sampling distance was 1 m and the sam-pling interval was 2 hours for 5 days Thus each measuringpoint obtained 60 groups of data First the original tempera-ture data should be denoised and a typical point was selectedas an example analyzed After calculation the decompositionlevels of the wavelet packet were 3-layer Figure 6 was shownto compare the raw signal with the wavelet denoising signal

The first principal component was calculated and listed inFigure 7

The corresponding variance contribution rate of the firstprincipal component 120590

1sum120590 was 8721 and it could be

concluded that the contribution of the first principal compo-nent to informationwas largerThe difference of the principalcomponent value between the leakage point presented and

Raw signal

Time (h)0 20 40 60 80 100 120

4

2

0

minus2

minus4

Tem

pera

ture

(∘C)

Wavelet denoising signal

Time (h)0 20 40 60 80 100 120

4

2

0

minus2

minus4

Tem

pera

ture

(∘C)

Figure 6 Comparative diagram between raw signal and the waveletdenoising signal

minus02

minus04

minus06

06

04

02

0

5 10 15 20 25 30 35

Distance (m)

Valu

e

Figure 7 Result diagram after PCA method

other points was much larger than the one of the first prin-cipal component Therefore the second and third principalcomponents were selected to the next ICA which meant119894 = 2 One of the two principal components was used toconstruct a separate component of the signal space and theother one was made to build a separate part of the salvagespace The difference of the separate component 1 in theleakage point was more evident than the one of other pointswhose distribution was more stable Thereby the separatecomponent 1 was considered to establish a salvage spaceThe separate component 2 constructed a separate componentsignal space The corresponding grey-scale map of residualspace was shown in Figure 8

From the result of data processing it can be known thatthe problem of the optical fiber temperature monitoring datacould be analyzed by the blind source separation and ICAwas used to process data In Figure 8 the leakage area of14m was larger than the area of 32m And the test distanceof the model was less than 32m Therefore the area of 32m


minus05

0

05

1

minus1

minus15

Dist

ance

(m)

Time

Leakage point

0

5

10

15

20

25

30

6050403020100

Figure 8 Grey-scale map of residual space

was not considered Finally the leakage location could be wellimplemented

5 Conclusions

In this paper ERJD was the studied object and its leakageidentificationwas for the research emphasis Based on leakagecharacteristics of monitoring ERJD by DTS the affectingfactors of optical fiber temperaturemonitoring datawere ana-lyzed The wavelet packet denoising method and thresholddetermining method were also studied A blind source sepa-rationmodel of optical fiber temperature datawas finally builtand the corresponding temperature change process of theleakage source was extracted The implementation methodof blind source separation technique was discussed In-depth research on characteristics of optical fiber temperaturedata was carried out and optimal applicable conditions forrealization method of the blind source separation techniqueswere also analyzed The blind source separation techniqueimplementation combining ICA with PCA was finally pro-posed With leakage fiber-optic model experiment of ERJDthe reliability of optical fiber temperature measuring databased on the blind source separation method is validated

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research has been partially supported by Jiangsu NaturalScience Foundation (SN BK2012036) the National Natu-ral Science Foundation of China (SN 51179066 5113900141323001 and 51409167) the Specialized Research Fund forthe Doctoral Program of Higher Education of China (SN20130094110010) the Nonprofit Industry Financial Program

of MWR (SN 201301061 and 201201038) the Open Founda-tion of State Key Laboratory of Hydrology-Water Resourcesand Hydraulic Engineering (SN 20145027612) the ResearchProgram on Natural Science for Colleges and Universities inJiangsu Province (SN 14KJB520016) the Priority AcademicProgram Development of Jiangsu Higher Education Institu-tions (SN YS11001) and the Scientific Innovation ResearchScheme for Jiangsu University Graduate (SN 2013B25514)

References

[1] H-H Zhu A N L Ho J-H Yin H W Sun H-F Pei andC-Y Hong ldquoAn optical fibre monitoring system for evaluatingthe performance of a soil nailed sloperdquo Smart Structures andSystems vol 9 no 5 pp 393ndash410 2012

[2] B Shi C-S Tang L Gao C Liu and B-J Wang ldquoObservationand analysis of the urban heat island effect on soil in NanjingChinardquo Environmental Earth Sciences vol 67 no 1 pp 215ndash2292012

[3] J F Yan B Shi D F Cao H H Zhu and G Q Wei ldquoExper-iment study on carbon coated heating optical fiber for sandleakage monitoring based on distributed temperature systemrdquoin Proceedings of the 6th International Conference on StructuralHealth Monitoring of Intelligent Infrastructure Paper no MS03-06 Hong Kong 2013

[4] S Johansson ldquoLocalization and quantification of water leakagein ageing embankment dams by regular temperature measure-mentsrdquo inProceedings of the 17th International Congress on LargeDams (ICOLD rsquo91) pp 991ndash1005 Vienna Austria 1991

[5] O Kappelmeyer ldquoThe use of near surface temperature mea-surements for discovering anomalies due to causes at depthsrdquoGeophysical Prospecting vol 5 no 3 pp 239ndash258 1957

[6] A H Hartog ldquoDistributed fiber-optic temperature sensorsprinciples and applicationsrdquo inOptical Fiber Sensor TechnologyK T Grattan and B T Meggitt Eds pp 241ndash301 KluwerAcademic Publishers New York NY USA 2000

[7] H Z Su J Y Li J Hu and Z Wen ldquoAnalysis and back-analysisfor temperature field of concrete arch dam during constructionperiod based on temperature data measured by DTSrdquo IEEESensors Journal vol 13 no 5 pp 1403ndash1412 2013

[8] S Yin ldquoDistributed fiber optic sensorsrdquo in Fiber Optic SensorsF T Yu and S Yin Eds pp 201ndash229 Marcel Dekker New YorkNY USA 2000

[9] A D Kersey ldquoOptical fiber sensors for downwell monitoringapplications in the oil and gas industryrdquo in Proceedings of the13th International Conference on Optical Fiber Sensors (Ofs-13rsquo99) pp 326ndash331 1999

[10] S Grosswig A Graupner and E Hurtig ldquoDistributed fiberoptical temperature sensing techniquemdasha variable tool formonitoring tasksrdquo in Proceedings of the 8th International Sym-posium on Temperature and Thermal Measurements in Industryand Science pp 9ndash17 2001

[11] S A Wade K T V Grattan B McKinley L F Boswell andC DrsquoMello ldquo Incorporation of fiber optic sensors in concretespecimens testing and evaluationrdquo IEEE Sensors Journal vol 4no 1 pp 127ndash134 2004

[12] H-H Zhu L-C Liu H-F Pei and B Shi ldquoSettlement analysisof viscoelastic foundation under vertical line load using afractional Kelvin-Voigt modelrdquo Geomechanics and Engineeringvol 4 no 1 pp 67ndash78 2012

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large-scalemonitoring [8 9] In general the use of distributedfiber sensing technology in leakagemonitoring of buildings isstill in its infancy stage for theoretical research experimentalsimulation and engineering application research especiallyfor monitoring the combination between two mediums inERJD The consequent analysis of temperature monitoringdata and processing aspects still needmore studiesThereforean experimental model of ERJD was established and the dis-tributed fiber leakage monitoring technology was developedaccording to the working features of ERJD In-depth studiesof models and methods for leakage identification of ERJDhave important science and engineering applications basedon features of monitoring data

2 Denoising Research of DTS MonitoringData with Wavelet Packet

Wavelet transform method was proposed by Morlet in theearly 1980s and then it changed rapidly to be a very powerfultool for digital signal processing image processing datacompression data denoising and so forth

Wavelet is a breakthrough to Fourier transform analysisIt is a time-frequency analysismethodwith fixedwindow sizeand changeable shape time window and frequency windowLocal features signal can be well characterized in both timedomain and the frequency domain

Its main advantage is the ability to do local refinementand analysis for signal which overcomes the difficulties of notprocessing the nonstationary signals for Fourier transformtechnique and short-time Fourier transform method

During practical applications wavelet transform will dis-perse the stretching factor 119886 and translation factor 120591 in orderto adapt to the computer calculation 119886 takes 1198860

0 1198861

0 1198862

0 119886

119895

0

The sampling interval of displacement amount 120591 isΔ120591 = 11988611989501205910

Thus wavelet function is

120601119886120591(119905) = 119886

minus1198952

0120601 (119886minus119895

0(119905 minus 119896119886

119895

01205910)) (1)

where 119895 and 119896 are positive integersTaking 119886

0= 2 and 120591

0= 1 in practical operation wavelet

basis function 120601119886120591(119905) can be expressed as follows

120601119895119896 (119905) = 2

minus1198952120601 (2minus119895119905 minus 119896) (2)

Corresponding discrete wavelet transform is

WT119909(119895 119896) = ⟨119909 (119905) 120601

119895119896(119905)⟩ = int

119877

119909 (119905) 120601119895119896(119905)119889119905 (3)

The signal can be decomposed into a high frequencyportion named 119863 and a low frequency part marked 119860by wavelet transformation Compared to the wavelet trans-form wavelet packet decomposition analysis is a moresophisticated approach which well disassembles the highand low frequency parts of each layer simultaneously Itgreatly improves the resolution of signal and overcomes theinsufficient of wavelet decomposition in ldquolow-resolution ofhigh-frequencyrdquoThewavelet packet decomposition hasmorebroad application prospects and the 3-layer wavelet packetdecomposition process was expressed in Figure 1

S

A1 D1

AA2 AD2 DA2 DD2

AAA3 AAD3 ADA3 ADD3 DAA3 DAD3 DDA3 DDD3

Figure 1 Transform decomposition process of wavelet packet

As shown in Figure 1 the decomposition relationship of3-layer wavelet packet is as follows

119878 = 1198601198601198603+ 119860119860119863

3+ 119860119863119860

3+ 119860119863119863

3

+ 1198631198601198603+ 119863119860119863

3+ 119863119863119860

3+ 119863119863119863

3

(4)

The denoising procedure of wavelet packet for DTSleakage measurement data is summarized as below

(1) Wavelet packet decomposition Select wavelets anddetermine the decomposition level 119873 then decom-pose 119873-layer wavelet packet for original signal 119878During data processing the wavelet packet decompo-sition level is determined by the wavelet packet noisereduction effect

(2) Thresholds quantization Select the appropriatethreshold quantization method to quantify treatmentfor each wavelet packet coefficients decomposed

(3) Reconstruction of wavelet packet Reconstruct thelow-frequency coefficients of wavelet packet 119873-layerand its corresponding high-frequency coefficients

Among the previous steps the keys are selection of thewavelet packet decomposition level and approach to thethreshold quantization Wavelet packet decomposition levelis generally notmore than 5-layerThe threshold quantizationcan be processed by denoising with the soft threshold andhard threshold method

Coefficient of wavelet packet of hard threshold estimatedis

119908119895119896=

119908119895119896

10038161003816100381610038161003816119908119895119896

10038161003816100381610038161003816ge 120582

0

10038161003816100381610038161003816119908119895119896

10038161003816100381610038161003816lt 120582

(5)

Coefficient of wavelet packet built for soft threshold isgiven

119908119895119896=

sign (119908119895119896) (

10038161003816100381610038161003816119908119895119896

10038161003816100381610038161003816minus 120582)

10038161003816100381610038161003816119908119895119896

10038161003816100381610038161003816ge 120582

0

10038161003816100381610038161003816119908119895119896

10038161003816100381610038161003816lt 120582

(6)

For (5) and (6) 119908119895119896

represents wavelet packet coefficientand 120582 is preset threshold or threshold value which iscalculated in the form

120582 =

120590radic2 lg119873lg (119895 + 1)

(7)




SNR = 10 lg(sum119873

119899=11199042(119899)

sum119873

119899=1[119904 (119899) minus 119904 (119899)]

2)


[119904(119899) minus 119904(119899)]2

(8)








1 119883



1198841= 119905111198831+ 119905121198832+ sdot sdot sdot + 119905

1119901119883119901= 1198791015840

1119883

1198842= 119905211198831+ 119905221198832+ sdot sdot sdot + 119905

2119901119883119901= 1198791015840

2119883

119884119901= 11990511990111198831+ 11990511990121198832+ sdot sdot sdot + 119905

119901119901119883119901= 1198791015840

119901119883

(9)


119872 = 119880119878119881119879 (10)


119884 = 119883119879 (11)

Thus

119883 = 1198841198791015840 (12)



119883 = 1198801198781198811015840 (13)



120593119896=

120582119896

sum119901

119896=1120582119896

120595119898=

sum119898

119896=1120582119896

sum119901

119896=1120582119896

(14)



120593119896and 120595




119883lowast

119894=

119883119894minus 119864 (119883

119894)

radic119863 (119883119894)

(15)


1199091= 119886111199041+ 119886121199042+ sdot sdot sdot + 119886

1119899119904119899

1199092= 119886211199041+ 119886221199042+ sdot sdot sdot + 119886

2119899119904119899

119909119899= 11988611989911199041+ 11988611989921199042+ sdot sdot sdot + 119886

119899119899119904119899

(16)

where 1199091 1199092 119909


mixed signals 1199041 1199042 119904











(5) update each 119908119894 119908119894larr 119864119911119892(119908

119879

119894119911) minus 119864119892

1015840(119908119879

119894119911)119908119894


(6) matrix 119882 = (1199081 119908


(1198821198821015840)minus12119882



1198921(119910) = tanh (119886

1119910) (17)

1198922(119910) = 119910 exp(minus

1199102

2

) (18)

1198923(119910) = 119910

3 (19)

Leakage location


DTS system

Heating system



1198921015840

1(119910) = 119886

1(1 minus tanh2 (119886

1119910))

1198921015840

2(119910) = (1 minus 119910

2) exp(minus

1199102

2

)

1198921015840

3(119910) = 3119910

2

(20)








Modelexperiment

pool of ERJD



Polyethylenejacket

Heatingwire

Fiberpaste

Opticalfibre

Loosetube









Raw signal

Time (h)0 20 40 60 80 100 120

4

2

0

minus2

minus4

Tem

pera

ture

(∘C)


Time (h)0 20 40 60 80 100 120

4

2

0

minus2

minus4

Tem

pera

ture

(∘C)


minus02

minus04

minus06

06

04

02

0

5 10 15 20 25 30 35

Distance (m)

Valu

e





minus05

0

05

1

minus1

minus15

Dist

ance

(m)

Time

Leakage point

0

5

10

15

20

25

30

6050403020100



5 Conclusions




Acknowledgments



References















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












SNR = 10 lg(sum119873

119899=11199042(119899)

sum119873

119899=1[119904 (119899) minus 119904 (119899)]

2)


[119904(119899) minus 119904(119899)]2

(8)








1 119883



1198841= 119905111198831+ 119905121198832+ sdot sdot sdot + 119905

1119901119883119901= 1198791015840

1119883

1198842= 119905211198831+ 119905221198832+ sdot sdot sdot + 119905

2119901119883119901= 1198791015840

2119883

119884119901= 11990511990111198831+ 11990511990121198832+ sdot sdot sdot + 119905

119901119901119883119901= 1198791015840

119901119883

(9)


119872 = 119880119878119881119879 (10)


119884 = 119883119879 (11)

Thus

119883 = 1198841198791015840 (12)



119883 = 1198801198781198811015840 (13)



120593119896=

120582119896

sum119901

119896=1120582119896

120595119898=

sum119898

119896=1120582119896

sum119901

119896=1120582119896

(14)



120593119896and 120595




119883lowast

119894=

119883119894minus 119864 (119883

119894)

radic119863 (119883119894)

(15)


1199091= 119886111199041+ 119886121199042+ sdot sdot sdot + 119886

1119899119904119899

1199092= 119886211199041+ 119886221199042+ sdot sdot sdot + 119886

2119899119904119899

119909119899= 11988611989911199041+ 11988611989921199042+ sdot sdot sdot + 119886

119899119899119904119899

(16)

where 1199091 1199092 119909


mixed signals 1199041 1199042 119904











(5) update each 119908119894 119908119894larr 119864119911119892(119908

119879

119894119911) minus 119864119892

1015840(119908119879

119894119911)119908119894


(6) matrix 119882 = (1199081 119908


(1198821198821015840)minus12119882



1198921(119910) = tanh (119886

1119910) (17)

1198922(119910) = 119910 exp(minus

1199102

2

) (18)

1198923(119910) = 119910

3 (19)

Leakage location


DTS system

Heating system



1198921015840

1(119910) = 119886

1(1 minus tanh2 (119886

1119910))

1198921015840

2(119910) = (1 minus 119910

2) exp(minus

1199102

2

)

1198921015840

3(119910) = 3119910

2

(20)








Modelexperiment

pool of ERJD



Polyethylenejacket

Heatingwire

Fiberpaste

Opticalfibre

Loosetube









Raw signal

Time (h)0 20 40 60 80 100 120

4

2

0

minus2

minus4

Tem

pera

ture

(∘C)


Time (h)0 20 40 60 80 100 120

4

2

0

minus2

minus4

Tem

pera

ture

(∘C)


minus02

minus04

minus06

06

04

02

0

5 10 15 20 25 30 35

Distance (m)

Valu

e





minus05

0

05

1

minus1

minus15

Dist

ance

(m)

Time

Leakage point

0

5

10

15

20

25

30

6050403020100



5 Conclusions




Acknowledgments



References















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











120593119896and 120595




119883lowast

119894=

119883119894minus 119864 (119883

119894)

radic119863 (119883119894)

(15)


1199091= 119886111199041+ 119886121199042+ sdot sdot sdot + 119886

1119899119904119899

1199092= 119886211199041+ 119886221199042+ sdot sdot sdot + 119886

2119899119904119899

119909119899= 11988611989911199041+ 11988611989921199042+ sdot sdot sdot + 119886

119899119899119904119899

(16)

where 1199091 1199092 119909


mixed signals 1199041 1199042 119904











(5) update each 119908119894 119908119894larr 119864119911119892(119908

119879

119894119911) minus 119864119892

1015840(119908119879

119894119911)119908119894


(6) matrix 119882 = (1199081 119908


(1198821198821015840)minus12119882



1198921(119910) = tanh (119886

1119910) (17)

1198922(119910) = 119910 exp(minus

1199102

2

) (18)

1198923(119910) = 119910

3 (19)

Leakage location


DTS system

Heating system



1198921015840

1(119910) = 119886

1(1 minus tanh2 (119886

1119910))

1198921015840

2(119910) = (1 minus 119910

2) exp(minus

1199102

2

)

1198921015840

3(119910) = 3119910

2

(20)








Modelexperiment

pool of ERJD



Polyethylenejacket

Heatingwire

Fiberpaste

Opticalfibre

Loosetube









Raw signal

Time (h)0 20 40 60 80 100 120

4

2

0

minus2

minus4

Tem

pera

ture

(∘C)


Time (h)0 20 40 60 80 100 120

4

2

0

minus2

minus4

Tem

pera

ture

(∘C)


minus02

minus04

minus06

06

04

02

0

5 10 15 20 25 30 35

Distance (m)

Valu

e





minus05

0

05

1

minus1

minus15

Dist

ance

(m)

Time

Leakage point

0

5

10

15

20

25

30

6050403020100



5 Conclusions




Acknowledgments



References















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Modelexperiment

pool of ERJD



Polyethylenejacket

Heatingwire

Fiberpaste

Opticalfibre

Loosetube









Raw signal

Time (h)0 20 40 60 80 100 120

4

2

0

minus2

minus4

Tem

pera

ture

(∘C)


Time (h)0 20 40 60 80 100 120

4

2

0

minus2

minus4

Tem

pera

ture

(∘C)


minus02

minus04

minus06

06

04

02

0

5 10 15 20 25 30 35

Distance (m)

Valu

e





minus05

0

05

1

minus1

minus15

Dist

ance

(m)

Time

Leakage point

0

5

10

15

20

25

30

6050403020100



5 Conclusions




Acknowledgments



References















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










minus05

0

05

1

minus1

minus15

Dist

ance

(m)

Time

Leakage point

0

5

10

15

20

25

30

6050403020100



5 Conclusions




Acknowledgments



References















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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