Research Article A PCA and ELM Based Adaptive …downloads.hindawi.com/journals/mpe/2014/124968.pdfResearch Article A PCA and ELM Based Adaptive Method for Channel Equalization in

Research ArticleA PCA and ELM Based Adaptive Method forChannel Equalization in MFL Inspection

Zhenning Wu1 Huaguang Zhang1 Jinhai Liu1 Zongjie Qiu2 and Mo Zhao1

1 School of Information Science and Engineering Northeastern University Shenyang Liaoning 110004 China2 CNOOC (China) Co Ltd Beijing 100010 China

Correspondence should be addressed to Zhenning Wu wuzn2003hotmailcom

Received 28 April 2014 Revised 30 June 2014 Accepted 14 July 2014 Published 12 August 2014

Academic Editor Ruqiang Yan

Copyright copy 2014 Zhenning Wu 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

Magnetic flux leakage (MFL) as an efficient method for pipeline flaw detection plays important role in pipeline safety Thisnondestructive test technique assesses the health of the buried pipeline The signal is gathered by an array of hall-effect sensorsdisposed at the magnetic neutral plane of a pair of permanent magnet in the pipeline inspection gauge (PIG) clinging to the innersurface of the pipe wallThemagnetic fluxmeasured by the sensors reflects the health condition of the pipeThe signal is influencedby not only the condition of the pipe but also by the lift-off value of the sensors and various properties of electronic componentThe consistency of the position of the sensors is almost never satisfied and each sensor measures differently In this paper a newscheme of channel equalization is proposed for MFL signal in order to correct sensor misalignments which eventually improvesaccuracy of defect characterization The algorithm proposed in this paper is adaptive to the effects of error on the disposition ofthe sensor due to manufacturing imperfections and movements of the sensors The algorithm is tested by data acquired from anexperimental pipeline The results show the effectiveness of the proposed algorithm

1 Introduction

MFL is a widely used nondestructive testing (NDT) methodsfor pipeline inspection The inspection machine is usuallycalled PIG A PIG using MFL consists of several pairs ofstrong permanent magnets which magnetize the pipe alongthe axial direction of the pipe Each pair of the strongpermanent along with the yoke iron and the hall sensors andalso brush is called a carrierThe carrier with the pipe consistsof a magnetic circuit Details of the PIG can be found at somefamous inspection companies website ROSEN PII and soforth A lot of research work has been done to analyze thesignal of MFL Carvalho et al [1] Christen and Bergamini[2] and Xiang and Tso [3] purposed neural network basedmethods to detect flaws Mukhopadhyay and Srivastava [4]proposed wavelet based technique to denoise the signal oftheMFL inspectionMukherjee et al proposed wavelet basedinverse mapping system [5] Kathirmani et al [6] using PCA[7] and wavelet [8ndash11] technique to compress data of theMFLsignal

But there is still one problem that needs to be studiedThe sensing arrangement that is each sensor its mechan-ical support and the underlying electronics for acquiringthe magnetic leakage flux data commonly referred to asa channel suffers mismatch among each other A lot offactors can cause channel-to-channel mismatch includingthe lift-off value between the pipeline and position of halland coil sensors and the various properties of electroniccomponent Other factors influence the factors mentionedabove can also impact the output of the signal such as thedifference of the sensors location caused by assembly theshake when the detector running in the pipeline and soforth All these factors make the output of the signal differenteven under same testing condition and testing object Thiswill lower the capacity of the detector especially during thepost processing of the signal Such kind of mismatch mayalso exist in other multisensor data processing Commonly itcan be equalized by using adaptive techniques An adaptivechannel equalization algorithm to deal with the problemof channel-to-channel mismatch of MFL signals is given in

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 124968 8 pageshttpdxdoiorg1011552014124968

2 Mathematical Problems in Engineering

[12] In [12] they assume that at least one sensor out of thesensor array is ideal and can be used as a reference Forimplementation this assumption imposes serious limitationson the performance of post processing algorithm as toleranceandmisalignment of an individual sensor is not deterministicand needs to be accounted for in a stochastic frameworkfor choice of a clear cut candidate qualifying as a referencechannel To solve the problem Mukherjee et al [13] gives anadaptive method which does not need to choose a referencechannel In [13] the reference channel required for channelequalization is replaced with the baseline estimation Thebaseline estimation reflects the background leakage fluxBut the baseline estimation is not available under a defector feature It is estimated by first order forward or backprediction of the neighboring MFL data

In this paper a new adaptive channel equalization algo-rithm tominimize channel-to-channelmismatch is proposedfor MFL signals In contrast to [12] our algorithm does notneed to choose any reference channel Because the idealreference channel is not easy to get and the character of eachchannel may have little difference equalizing the channelsadaptively with no reference channel is reasonableThe signalof all channel is learned by a neural network The trainingdata set is selected as a clean pipe (almost no flaw) whichreflects the character of the pipe And distinguished from[13] we mainly focus on the signal around and including theflaw In [13] the signal around the flaw is only estimated byfirst order forward or backward prediction of the neighboringMFL data which may cause distortion of the flaw signal Asflaw evaluation needs the exact shape of the signal aroundand including the flaw our algorithm has more advantageA PCA based flaw detection algorithm is given in this paperto find the location of the flaw signal A median correctedalgorithm is also given from the engineering point of viewThe simulation results show that the algorithm proposed inthis paper is efficient

The paper is organized as follows In Section 2 an ELMbased method is given to dynamically compensate eachchannel and also with a PCA based statistic method toseparate normal and flaw signal and extract signal charactersThe details of our algorithm proposed in this paper are statedtoo A median corrected algorithm is given and simulationresults are shown in Section 3 Section 4 concludes the paperindicating major achievements and future scope of this work

2 PCA and ELM Based Channel Equalization

21 Channel Equalization Using ELM Neural Networks Neu-ral networks are very efficient and popular tool to doregression and classification The advantages of the neuralnetworks are mainly two points one is that the modelof the data does not need to be known the other is itshigh capability to deal with nonlinear problems There existmany types of neural networks however feedforward neuralnetworks may be one of the most popular neural networksThe feedforward neural network usually consists of one inputlayer receiving the stimulin from external environments oneor multihidden layers and one output layer sending the

Input layer Output layerHidden layer

Channel 1 Channel 1

Channel nChannel ncompensation

compensation

Figure 1 Neural network model for channel equalization

network output to external environments Widely used neu-ral networks include backpropagation (BP) neural network[14] radial basis function (RBF) neural network [15] andsupport vector machine (SVM) [16] Three main approachesare usually used to train feedforward networks includinggradient-descent based method (eg BP neural networks)least-square based method (eg RBF network learning) andstandard optimization method based method (eg SVM)Different from traditional learning algorithms ELM [17]tends to reach not only the smallest training error but alsothe smallest norm of output weights According to the neuralnetwork theory for feedforward neural networks smallertraining error results in smaller norm of weights and bettergeneralization performance Since the hidden layer needs notbe tuned in ELM and the hidden layer parameters can befixed the output weights can then be resolved using the least-square method The model of channel equalization usingELM is given as Figure 1

The output function of single-hidden layer feedforwardnetworks (SLFNs) with 119871 hidden nodes can be representedby

119891 (119909) = Σ119897

119894=1120573119894119892119894 (119909) (1)

where 119892119894(119909) denotes the output function of the 119894th hiddennode

For 119873 arbitrary distinct samples (119909119894 119905119894) SLFNs with 119871

hidden nodes are mathematically modeled as

Σ119897

119894=1120573119894119892119894 (119909119895) = 119910119895 119895 = 1 119873 (2)

That SLFNs can approximate these119873 samples with zero errormeans that

Σ119897

119895=1

10038171003817100381710038171003817119910119895 minus 119905119895

10038171003817100381710038171003817= 0 (3)

The parameters in 119892119894(119909) can be trained according to (2)This can be written as

119866120573 = 119879 (4)

Mathematical Problems in Engineering 3

where

119866 =[[

[

119866 (1199091)

119866 (119909119873)

]]

]

=[[

[

119892 (1199081 1198871 1199091) 119892 (119908119897 119887119897 1199091)

d

119892 (1199081 1198871 119909119873) 119892 (119908119897 119887119897 119909119873)

]]

]

120573 =[[

[

120573119879

1

120573119879

119897

]]

]119897times119898

119879 =[[

[

119879119879

1

119879119879

119897

]]

]119873times119898

(5)

It is proved in [17] that given any small positive value 119890 gt

0 activation function 119892 119877 rarr 119877 which is infinitelydifferentiable in any interval and119873 arbitrary distinct samples(119909119894 119905119894) there exists 119897 le 119873 such that for any 119908119894 119887119894

119897

119894=1

(parameters need to be trained in 119892119894(119909)) randomly generatedfrom any intervals of 119877119889 times 119877 according to any continuousprobability distribution with probability one 119867119873times119897120573119897times119898 minus119879119873times119898 lt 119890 And from the interpolation point of view themaximum number of hidden nodes required is not largerthan the number of training samples In fact if 119871 = 119873 thetraining errors can be zero

Though the ELM has good regression ability there is stillone obverse problem that the results of the ELM rely on thetraining data set But the flaw difference is from not onlylength and width but also depth which may cause the MFLsignal variance It is impossible to include all flaw signal in thetraining data set A better way is to use a small training dataset to train the ELM which can generate good compensationresults One solution is given in this paper in Section 22

22 PCA Based Flaw Exclusion To train the ELM and solvethe problem mentioned in Section 21 one solution is given

Because the property of pipe is learned using ELM wecan use the channel with no flaw to predict the channel withflaw when flaw is detected By using the predicted result tosubstitute the channels which detect flaw the compensationresult can be obtained using ELM And then using the ELMresult the compensation is given to each channelThis avoidstraining ELM with every type of flaw To exclude the flaw aPCAbased algorithm is stated as follows which detectswhichchannels and which sampling points detest flaw signal

PCA [18] as an efficient statistical learning algorithm isuseful to deal with multivariable problems The PIG has 119899sensors surrounding the vessel Consider one sampling of allsensors as 119909 = (1199091 1199092 119909119899)

119879 The linear transform of thesensors result can be written as

1199101 = 119886111199091 + 119886121199092 + sdot sdot sdot + 1198861119899119909119899 = 119886119879

1119909

1199102 = 119886111199091 + 119886221199092 + sdot sdot sdot + 1198862119899119909119899 = 119886119879

2119909

119910119899 = 11988611989911199091 + 11988611989921199092 + sdot sdot sdot + 119886119899119899119909119899 = 119886119879

119899119909

(6)

1199101 is called the 119894th principle component The computationsteps is as follows

First 119898 samples from each sensor are collected andwritten as a matrix 119883 isin 119877

119898times119899 The matrix is scaled to zeromean and in addition to unit variance

The second step is to compute the singular values Thecovariance matrix is computed as

Σ cong1

119898 minus 1119883119879119883 (7)

An SVD (singular value decomposition) is used to com-pute the principal components and the associated singularvectors as

1

119898 minus 1119883119879119883 = 119879Λ119879

119879

Λ = [Λ pc 0

0 Λ res]

(8)

where

Λ pc = diag (12059021 120590

2

119897) isin 119877119897times119897 1205901 ge sdot sdot sdot 120590119897 ge sdot sdot sdot 120590119899

Λ res = diag (1205902119897+1 120590

2

119899) isin 119877(119899minus119897)times(119899minus119897)

119879 = [119879pc 119879res] isin 119877(119899times119899)

119879pc isin 119877119899times119897 119879res isin 119877

119899times(119899minus119897)

119879119879119879= 119879pc119879

119879

pc + 119879res119879119879

res = 119868119899times119899

119879pc119879119879

pc [119879119879

pc119879119879

res] [119879pc 119879res]

(9)

119897 is the number satisfying

Σ119897

119894=11205902

119894

Σ119899

119894=11205902

119894

ge 120572 0 le 120572 le 1 (10)

1205902

119894Σ119899

119894=11205902

119894ge 120572 is called the significance level And (10) is

called the cumulated significance level which shows howmuch the first 119897 principle components can reflect data119883 TheHotelling 1198792 statistic is used to detect fault

1198792

119894= Σ119897

119895=1

1199102

119894119895

120582119895

(11)

With a set threshold flaw signal can be separated fromnormal signal Suppose there are only two sensors Take500 sampling The result is shown in Figure 2 The lineartransformof119910 is also shown in this figureUsing theHotelling1198792 statistic which is shown as formula (11) the flaw data can

be detected

23 Details of PCA and ELM Based Algorithm for ChannelEqualization Thedata gathered using a PIG can be describedas 119883 isin 119877

119898times119899 where 119898 is the sampling number and 119899 isthe number of sensors The algorithm proposed in this papertreats data with two points of view one is from the samplingview and the other is from the sensor view


265265

27

2726

275

275

285

285

28

28 29

Figure 2 PCA analysis of 500 sampling using 2 sensors

From the sampling view the PCA algorithm is used todetect flaw which determines at which sampling points theflaw locates For example take 119898 sampling using PCA flawlocates at [119896 119896 + Δ] where 1 le 119896 le 119898 and 1 le 119896 + Δ le 119898

can be detected with a preset 1198792 statistic The normal partis tested using a trained ELM neutral network to removechannelmismatches which is called ELM 1 And the flaw partis treated from the sensor point of view The normal part isadded to the training set dynamically in order to learn morecharacter of this part of pipe

From the sensor view the flaw data is also treated usingPCA to determine which sensors detect flaw For exampleonly sensors 119904 to 119904 + Δ119904 detect flaw where 1 le 119904 le 119904 + Δ119904 le 119899The normal channel is used as input data using ELM trainedwith channels of normal from training data set the flaw partof signal can be forecasted as normal partThis step is to revertthe flaw part to its normal condition in order to determinehow much each channel needs to be compensated with ELM1 And using ELM 1 the channelmismatch of the flawpart canbe removed It is clear that each flaw needs an ELM neuralnetwork to compute the compensation which is called theELM p in Figure 3

The flow chart of the algorithm is shown in Figure 3 withsteps and details stated as follows

Step 1 An ELM is trained using training data set to learnthe character of the normal condition of the pipe for channelequalization The target is each channels compensation TheELM trained is marked as ELM 1

Step 2 Using PCA with 119909 = (1199091 1199092 119909119899)119879 represents

sensors to detect flaw which is stated in Section 22 with athreshold The 1198792 statistic up over the threshold denotes theflaw signalThe signal will be separated into normal parts andflaw parts in Step 3

Step 3 The signal of flaw detected from Step 2 is tested usingPCAwith119909 = (1199091 1199092 119909119898)

119879 represents sampling points Athreshold is also set automaticallyThe1198792 statistic up over thethreshold denotes the channels which detects flaw It makes

the flaw signal detected from Step 2 separated into two partsthe signal of normal channels and the signal channel of flaw

Step 4 Signal of normal parts acquired from Step 2 is testedusing ELM 1 trained in Step 1

Step 5 For the flaw signal detected in Steps 2 and 3 anotherELM is trained with training data set The normal channelsare used as inputs of the ELM and the flaw channels are usedas output of the ELM For example the flaw is detected atsampling point from 119905 to 119905+Δ119905 and channels from 119904 to 119904+Δ119904The training data set from channel 1 to 119904 minus 1 and 119904 + Δ119904 + 1 to119899 is used to train this neural network The target of the ELMis set as the training data set with channels from 119904 to 119904 + Δ119904Each flaw has an ELM The ELM is marked as ELMp with 119901representing the number of flaw

Step 6 The flaw signal from 119905 to 119905 + Δ119905 and channels from 119904

to 119904+Δ119904 is replaced temporarily by the test result with ELMp

Step 7 Thesignal segment in Step 6 is tested using ELM 1Theoutput is compensated to the original signal from 119905 to 119905 + Δ119905and channels from 119904 to 119904 + Δ119904

Step 8 Update the training data set with normal dataacquired in Step 2

3 Experiment Results

The PIG used to collect data in this paper consists of 15carriers with 5 axial sensors on each carrier An 8-inchseamless steel pipewith length of about 14meters is used to dothis experiment 9 exterior flaws were made on this pipe Thepipeline in our experiment is connected with two flanges andone weld The sampling is controlled by an odometer wheelwith the sampling frequency of 1 sampling per 2mm Severalexperiments were done with different load angel of the PIG

In order to train our algorithm some signal of MFLof normal condition pipeline with no flaw is needed Thetraining data is obtained in two way (i) The first way isto obtain from the original training data One test data isselected as original training data with flaw signal excludedmanually (ii) The second way of getting the training data isgenerated from each test using algorithms stated in Sections21 and 22The algorithm used in this paper treats data batchby batch One batch of data treated using the algorithm canseparate this batch of data into normal data and flaw dataThe normal part of data is added to the training data set inorder to reinforce the training result By adding new trainingdata the training set is updated New character of the normalcondition is studiedThismeans as the process goes the resultof the algorithm proposed in this paper gets better To avoidthe training data set getting too large the length of the data setis set to a certain length When length of the training data setgrows up to its limits the earlier training data will be erasedand new training data will be added to replace the vacancy

And in order to show the efficiency of our algorithm thelength of the original training data is reduced to only lessthan 15 of one test though theoretically a bigger training


Training data set Data

data

Normal data

Training data setupdate

Normal channel Flaw channel data

Flaw channelcomfirmation

Flaw data

Flaw detectionELM 1 train

ELM 1 regression

Result

ELM p train

ELM p regression

Figure 3 Flow chart of algorithm proposed

data set will get better result Also restricted to the experimentenvironment it is not possible to build a pipelinewith enoughlength of hundreds of meters or even miles The resultswith less original training data also show that the algorithmproposed in this paper generates satisfying results

And algorithm of median corrector is also adopted tocompare with our results Amongmany factors that influencechannel-to-channel mismatch the lift-off value and thedifference of the baseline play the main role The influencecaused by difference of the lift-off value among sensors can bereduced by improving the assembly skills And the influenceof the baseline (zero output) of sensors can be reduced bycalculating the average of sensors as baseline The channelequalization can be computed as three steps Assume 119883 asdata gathered by sensing a clean pipe (almost no flaw) Firstcalculate each channels average119909119894 Second calculate119909mean theaverage of 119909119894 Third compensate 119909mean minus 119909119894 to each channelBut as the MFL data is processed automatically this methodneeds to be operated manually And it is not that easy to findsuch steady state signal To overcome these we use mediancorrector to do rough channel equalization in engineeringInstead of calculating the average of each channel in the firststep 119909119894 is each channelrsquos median value Other steps are sameas the average method

All data of one test is treated using the algorithm pro-posed in this paper Figure 4 shows the PCA result of Step 2 inSection 23 The threshold is automatically generated with 119865distribution parameter of 95 All the components and flawsare described in Figure 4 Details of raw signal of 3 flaws areshown to illustrate the following steps in Figure 5The dashedline shows the flaw sampling point intervals detected usingPCA as shown in Figure 5 By applying the sensor view ofPCA stated as Step 3 in Section 23 the flaw signal channelsare marked within the solid line in Figure 5 The sensorview PCA result is shown in Figure 6 with 119865 distribution

0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000

500

1000

1500

2000

2500

3000

3500

4000

4500

Sampling points

Flaw 1

Weld

FlangeFlaw 2 Flaw 3

Flaw 5 Flaw 4 Flaw 6Flaw 7

Flaw 8

FlangeFixing iron beltT2

stat

istic

scor

e

Figure 4 PCA flaw exclusion result of sampling view

2000 2100 2200 2300 2400 2500 2600

5

4

55

45

35

253

665

775

Sampling points

Flaw 3Flaw 4Flaw 2 ELM 4

ELM 3

ELM 2

Test inputs

Test inputsTest inputs

Figure 5 Detail of flaw signal


0 10 20 30 40 50 60 70 800

10

20

30

40

50

60

70

Number of sensor

T2

stat

istic

scor

e

Figure 6 PCA flaw exclusion result of sensor view

020

4060

80

0

20

40

60

29

28

27

26

25

Channel index

Sampling number

Sens

or o

utpu

t (V

)

Figure 7 Raw data of flaw 1

020

4060

80

020

4060

265

275

28

27

26

Channel indexSampling number

Sens

or o

utpu

t (V

)

Figure 8 Median treated data of flaw 1

parameter of 95 The normal channels is used as input ofELM p and test result is shown from Figures 7ndash12

To show the result the standard deviation (SD) and peaksignal to noise ratio (PSNR) are adopted The results areshown in Tables 1 and 2 Lower standard deviation reflectsthat the signal is cleaner with less channel mismatch Toillustrate the result two segments of flaw signal are plotted

020

4060

80

020

4060

265

26

275

28

27


Sens

or o

utpu

t (V

)

Figure 9 PCA and ELM based algorithm treated data of flaw 1

020

4060

80

020

4060

80

29

28

27

2625

3


Sens

or o

utpu

t (V

)


020

4060

80

020

4060

80

275

285

29

28

27


Sens

or o

utpu

t (V

)


The baseline estimation algorithm proposed in [13] is alsocompared in Tables 1 and 2 From Table 1 it can be seen thatthe flaw in show is typical small size flawThe PSNR results inTable 2 also indicate that our algorithm minimizes channel-to-channel mismatches

From Figures 7 and 10 it is clear that the signal has greatchannel mismatches which makes it impossible to evaluatethe flaw size Using median algorithm corrected data shownas Figures 8 and 11 the flaw signal is prominent and the signalof normal channel is smooth but still some ripple exists


Table 1 SD of raw data and corrected data

Index of flaw SD of raw data SD of mediancorrected data

SD of baselineestimation equalized

data

SD of adaptive channelequalized data

flaw size (length lowast width lowastdepth unit mm)

1 00544 00129 00121 00093 40 times 20 times 12 00548 00138 00136 00108 1206016 perforation3 00565 00175 00169 00158 1206018 perforation4 00617 00324 00318 00288 20 times 40 times 45 00564 00182 00179 00160 40 times 20 times 46 00560 00143 00143 00142 20 times 20 times 27 00544 00115 00104 00089 40 times 20 times 28 00573 00174 00163 00141 20 times 40 times 2

Table 2 PSNR of raw data and corrected data

Index of flaw PSNR of raw data PSNR of mediancorrected data

PSNR of baselineestimation equalized

data

PSNR of adaptivechannel equalized data



020

4060

80

020

4060

80

28285

265

275

26

27

29


Sens

or o

utpu

t (V

)


Figures 9 and 12 show the results of algorithm proposed inthis paper the flaw signal is more prominent and the normalpart is smoother which results easy to evaluate the flaw TheSD shown in Table 1 also indicates that data treated by ouralgorithm has less channel mismatches and noise

4 Conclusion

In this paper a new adaptive channel equalization is proposedfor processing of MFL signal prior to flaw characterization

The scheme performs channel equalization by using singlelayer neural networks and the fast learning algorithmof ELMis used to give excellent processing speed Focusing on thesignal of flaw a PCA based flaw detect algorithm is given tolocate the flaw signal The algorithm proposed in this paperminimizes the channel-to-channelmismatch and reduces thedistortion of the signal of the flaw Both theory analysis andsimulation results show the efficiency of our algorithm Forthe flaw signal the algorithm proposed in this paper needsto locate the flaw first For shallow and small flaw how tolocate it andmake less false detection is still a problem in boththeory and engineering

Conflict of Interests

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

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (61034005 61104021) the NationalHigh Technology Research and Development Program ofChina (2012AA040104) the Fundamental Research Fundsfor the Central Universities of China (N120404022) andthe Natural Science Foundation of Liaoning province China(2013020043)


References

[1] A A Carvalho J M A Rebello L V S Sagrilo C S Cameriniand I V J Miranda ldquoMFL signals and artificial neural networksapplied to detection and classification of pipe weld defectsrdquoNDT amp E International vol 39 no 8 pp 661ndash667 2006

[2] R Christen and A Bergamini ldquoAutomatic flaw detection inNDE signals using a panel of neural networksrdquo NDT and EInternational vol 39 no 7 pp 547ndash553 2006

[3] Y Xiang and S K Tso ldquoDetection and classification of flaws inconcrete structure using bispectra and neural networksrdquo NDTand E International vol 35 no 1 pp 19ndash27 2002

[4] S Mukhopadhyay and G P Srivastava ldquoCharacterization ofmetal loss defects from magnetic flux leakage signals withdiscrete wavelet transformrdquo NDT and E International vol 33no 1 pp 57ndash65 2000

[5] DMukherjee S Saha and SMukhopadhyay ldquoInversemappingof magnetic flux leakage signal for defect characterizationrdquoNDT amp E International vol 54 pp 198ndash208 2013

[6] S Kathirmani A K Tangirala S Saha and S MukhopadhyayldquoOnline data compression of MFL signals for pipeline inspec-tionrdquo NDT and E International vol 50 pp 1ndash9 2012

[7] Q He R Yan F Kong and R Du ldquoMachine condition moni-toring using principal component representationsrdquoMechanicalSystems and Signal Processing vol 23 no 2 pp 446ndash466 2009

[8] R Yan R X Gao and X Chen ldquoWavelets for fault diagnosis ofrotary machines a review with applicationsrdquo Signal Processingvol 96 pp 1ndash15 2014

[9] B Li and X Chen ldquoWavelet-based numerical analysis a reviewand classificationrdquo Finite Elements in Analysis and Design vol81 pp 14ndash31 2014

[10] Z K Zhu R Yan L Luo Z H Feng and F R Kong ldquoDetectionof signal transients based on wavelet and statistics for machinefault diagnosisrdquo Mechanical Systems and Signal Processing vol23 no 4 pp 1076ndash1097 2009

[11] R Yan and R X Gao ldquoAn efficient approach to machinehealth diagnosis based on harmonic wavelet packet transformrdquoRobotics and Computer-IntegratedManufacturing vol 21 no 4-5 pp 291ndash301 2005

[12] Y Zhang Z Ye and X Xu ldquoAn adaptive method for channelequalization in MFL inspectionrdquo NDT amp E International vol40 no 2 pp 127ndash139 2007

[13] D Mukherjee S Saha and S Mukhopadhyay ldquoAn adaptivechannel equalization algorithm for MFL signalrdquo NDT and EInternational vol 45 no 1 pp 111ndash119 2012

[14] D E Rumelhart G E Hinton and R J Williams ldquoLearningrepresentations by back-propagating errorsrdquo Nature vol 323pp 533ndash536 1986

[15] D Lowe ldquoAdaptive radial basis function nonlinearities andthe problem of generalisationrdquo in Proceeding of the 1st IEEInternational Conference on Artificial Neural Networks pp 171ndash175 London UK October 1989

[16] C Cortes and V Vapnik ldquoSupport-vector networksrdquo MachineLearning vol 20 no 3 pp 273ndash297 1995

[17] G Huang L Chen and C Siew ldquoUniversal approximationusing incremental constructive feedforward networks withrandom hidden nodesrdquo IEEE Transactions on Neural Networksvol 17 no 4 pp 879ndash892 2006

[18] G Li C F Alcala S J Qin and D Zhou ldquoGeneralizedreconstruction-based contributions for output-relevant faultdiagnosis with application to the Tennessee Eastman processrdquo

IEEE Transactions on Control Systems Technology vol 19 no 5pp 1114ndash1127 2011

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Stochastic AnalysisInternational Journal of


[12] In [12] they assume that at least one sensor out of thesensor array is ideal and can be used as a reference Forimplementation this assumption imposes serious limitationson the performance of post processing algorithm as toleranceandmisalignment of an individual sensor is not deterministicand needs to be accounted for in a stochastic frameworkfor choice of a clear cut candidate qualifying as a referencechannel To solve the problem Mukherjee et al [13] gives anadaptive method which does not need to choose a referencechannel In [13] the reference channel required for channelequalization is replaced with the baseline estimation Thebaseline estimation reflects the background leakage fluxBut the baseline estimation is not available under a defector feature It is estimated by first order forward or backprediction of the neighboring MFL data

In this paper a new adaptive channel equalization algo-rithm tominimize channel-to-channelmismatch is proposedfor MFL signals In contrast to [12] our algorithm does notneed to choose any reference channel Because the idealreference channel is not easy to get and the character of eachchannel may have little difference equalizing the channelsadaptively with no reference channel is reasonableThe signalof all channel is learned by a neural network The trainingdata set is selected as a clean pipe (almost no flaw) whichreflects the character of the pipe And distinguished from[13] we mainly focus on the signal around and including theflaw In [13] the signal around the flaw is only estimated byfirst order forward or backward prediction of the neighboringMFL data which may cause distortion of the flaw signal Asflaw evaluation needs the exact shape of the signal aroundand including the flaw our algorithm has more advantageA PCA based flaw detection algorithm is given in this paperto find the location of the flaw signal A median correctedalgorithm is also given from the engineering point of viewThe simulation results show that the algorithm proposed inthis paper is efficient

The paper is organized as follows In Section 2 an ELMbased method is given to dynamically compensate eachchannel and also with a PCA based statistic method toseparate normal and flaw signal and extract signal charactersThe details of our algorithm proposed in this paper are statedtoo A median corrected algorithm is given and simulationresults are shown in Section 3 Section 4 concludes the paperindicating major achievements and future scope of this work

2 PCA and ELM Based Channel Equalization

21 Channel Equalization Using ELM Neural Networks Neu-ral networks are very efficient and popular tool to doregression and classification The advantages of the neuralnetworks are mainly two points one is that the modelof the data does not need to be known the other is itshigh capability to deal with nonlinear problems There existmany types of neural networks however feedforward neuralnetworks may be one of the most popular neural networksThe feedforward neural network usually consists of one inputlayer receiving the stimulin from external environments oneor multihidden layers and one output layer sending the

Input layer Output layerHidden layer

Channel 1 Channel 1

Channel nChannel ncompensation

compensation

Figure 1 Neural network model for channel equalization

network output to external environments Widely used neu-ral networks include backpropagation (BP) neural network[14] radial basis function (RBF) neural network [15] andsupport vector machine (SVM) [16] Three main approachesare usually used to train feedforward networks includinggradient-descent based method (eg BP neural networks)least-square based method (eg RBF network learning) andstandard optimization method based method (eg SVM)Different from traditional learning algorithms ELM [17]tends to reach not only the smallest training error but alsothe smallest norm of output weights According to the neuralnetwork theory for feedforward neural networks smallertraining error results in smaller norm of weights and bettergeneralization performance Since the hidden layer needs notbe tuned in ELM and the hidden layer parameters can befixed the output weights can then be resolved using the least-square method The model of channel equalization usingELM is given as Figure 1

The output function of single-hidden layer feedforwardnetworks (SLFNs) with 119871 hidden nodes can be representedby

119891 (119909) = Σ119897

119894=1120573119894119892119894 (119909) (1)

where 119892119894(119909) denotes the output function of the 119894th hiddennode

For 119873 arbitrary distinct samples (119909119894 119905119894) SLFNs with 119871

hidden nodes are mathematically modeled as

Σ119897

119894=1120573119894119892119894 (119909119895) = 119910119895 119895 = 1 119873 (2)

That SLFNs can approximate these119873 samples with zero errormeans that

Σ119897

119895=1

10038171003817100381710038171003817119910119895 minus 119905119895

10038171003817100381710038171003817= 0 (3)

The parameters in 119892119894(119909) can be trained according to (2)This can be written as

119866120573 = 119879 (4)


where

119866 =[[

[

119866 (1199091)

119866 (119909119873)

]]

]

=[[

[

119892 (1199081 1198871 1199091) 119892 (119908119897 119887119897 1199091)

d

119892 (1199081 1198871 119909119873) 119892 (119908119897 119887119897 119909119873)

]]

]

120573 =[[

[

120573119879

1

120573119879

119897

]]

]119897times119898

119879 =[[

[

119879119879

1

119879119879

119897

]]

]119873times119898

(5)



119897

119894=1







1199101 = 119886111199091 + 119886121199092 + sdot sdot sdot + 1198861119899119909119899 = 119886119879

1119909

1199102 = 119886111199091 + 119886221199092 + sdot sdot sdot + 1198862119899119909119899 = 119886119879

2119909

119910119899 = 11988611989911199091 + 11988611989921199092 + sdot sdot sdot + 119886119899119899119909119899 = 119886119879

119899119909

(6)





Σ cong1

119898 minus 1119883119879119883 (7)


1

119898 minus 1119883119879119883 = 119879Λ119879

119879

Λ = [Λ pc 0

0 Λ res]

(8)

where

Λ pc = diag (12059021 120590

2


Λ res = diag (1205902119897+1 120590

2


119879 = [119879pc 119879res] isin 119877(119899times119899)


119899times(119899minus119897)

119879119879119879= 119879pc119879

119879

pc + 119879res119879119879

res = 119868119899times119899

119879pc119879119879

pc [119879119879

pc119879119879

res] [119879pc 119879res]

(9)


Σ119897

119894=11205902

119894

Σ119899

119894=11205902

119894

ge 120572 0 le 120572 le 1 (10)

1205902

119894Σ119899

119894=11205902



1198792

119894= Σ119897

119895=1

1199102

119894119895

120582119895

(11)


be detected




265265

27

2726

275

275

285

285

28

28 29
























data

Normal data




Flaw data


ELM 1 regression

Result

ELM p train

ELM p regression





0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000

500

1000

1500

2000

2500

3000

3500

4000

4500

Sampling points

Flaw 1

Weld

FlangeFlaw 2 Flaw 3


Flaw 8


stat

istic

scor

e


2000 2100 2200 2300 2400 2500 2600

5

4

55

45

35

253

665

775

Sampling points


ELM 3

ELM 2

Test inputs




0 10 20 30 40 50 60 70 800

10

20

30

40

50

60

70

Number of sensor

T2

stat

istic

scor

e


020

4060

80

0

20

40

60

29

28

27

26

25

Channel index

Sampling number

Sens

or o

utpu

t (V

)


020

4060

80

020

4060

265

275

28

27

26


Sens

or o

utpu

t (V

)




020

4060

80

020

4060

265

26

275

28

27


Sens

or o

utpu

t (V

)


020

4060

80

020

4060

80

29

28

27

2625

3


Sens

or o

utpu

t (V

)


020

4060

80

020

4060

80

275

285

29

28

27


Sens

or o

utpu

t (V

)








data







data




020

4060

80

020

4060

80

28285

265

275

26

27

29


Sens

or o

utpu

t (V

)



4 Conclusion





Acknowledgments



References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










where

119866 =[[

[

119866 (1199091)

119866 (119909119873)

]]

]

=[[

[

119892 (1199081 1198871 1199091) 119892 (119908119897 119887119897 1199091)

d

119892 (1199081 1198871 119909119873) 119892 (119908119897 119887119897 119909119873)

]]

]

120573 =[[

[

120573119879

1

120573119879

119897

]]

]119897times119898

119879 =[[

[

119879119879

1

119879119879

119897

]]

]119873times119898

(5)



119897

119894=1







1199101 = 119886111199091 + 119886121199092 + sdot sdot sdot + 1198861119899119909119899 = 119886119879

1119909

1199102 = 119886111199091 + 119886221199092 + sdot sdot sdot + 1198862119899119909119899 = 119886119879

2119909

119910119899 = 11988611989911199091 + 11988611989921199092 + sdot sdot sdot + 119886119899119899119909119899 = 119886119879

119899119909

(6)





Σ cong1

119898 minus 1119883119879119883 (7)


1

119898 minus 1119883119879119883 = 119879Λ119879

119879

Λ = [Λ pc 0

0 Λ res]

(8)

where

Λ pc = diag (12059021 120590

2


Λ res = diag (1205902119897+1 120590

2


119879 = [119879pc 119879res] isin 119877(119899times119899)


119899times(119899minus119897)

119879119879119879= 119879pc119879

119879

pc + 119879res119879119879

res = 119868119899times119899

119879pc119879119879

pc [119879119879

pc119879119879

res] [119879pc 119879res]

(9)


Σ119897

119894=11205902

119894

Σ119899

119894=11205902

119894

ge 120572 0 le 120572 le 1 (10)

1205902

119894Σ119899

119894=11205902



1198792

119894= Σ119897

119895=1

1199102

119894119895

120582119895

(11)


be detected




265265

27

2726

275

275

285

285

28

28 29
























data

Normal data




Flaw data


ELM 1 regression

Result

ELM p train

ELM p regression





0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000

500

1000

1500

2000

2500

3000

3500

4000

4500

Sampling points

Flaw 1

Weld

FlangeFlaw 2 Flaw 3


Flaw 8


stat

istic

scor

e


2000 2100 2200 2300 2400 2500 2600

5

4

55

45

35

253

665

775

Sampling points


ELM 3

ELM 2

Test inputs




0 10 20 30 40 50 60 70 800

10

20

30

40

50

60

70

Number of sensor

T2

stat

istic

scor

e


020

4060

80

0

20

40

60

29

28

27

26

25

Channel index

Sampling number

Sens

or o

utpu

t (V

)


020

4060

80

020

4060

265

275

28

27

26


Sens

or o

utpu

t (V

)




020

4060

80

020

4060

265

26

275

28

27


Sens

or o

utpu

t (V

)


020

4060

80

020

4060

80

29

28

27

2625

3


Sens

or o

utpu

t (V

)


020

4060

80

020

4060

80

275

285

29

28

27


Sens

or o

utpu

t (V

)








data







data




020

4060

80

020

4060

80

28285

265

275

26

27

29


Sens

or o

utpu

t (V

)



4 Conclusion





Acknowledgments



References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










265265

27

2726

275

275

285

285

28

28 29
























data

Normal data




Flaw data


ELM 1 regression

Result

ELM p train

ELM p regression





0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000

500

1000

1500

2000

2500

3000

3500

4000

4500

Sampling points

Flaw 1

Weld

FlangeFlaw 2 Flaw 3


Flaw 8


stat

istic

scor

e


2000 2100 2200 2300 2400 2500 2600

5

4

55

45

35

253

665

775

Sampling points


ELM 3

ELM 2

Test inputs




0 10 20 30 40 50 60 70 800

10

20

30

40

50

60

70

Number of sensor

T2

stat

istic

scor

e


020

4060

80

0

20

40

60

29

28

27

26

25

Channel index

Sampling number

Sens

or o

utpu

t (V

)


020

4060

80

020

4060

265

275

28

27

26


Sens

or o

utpu

t (V

)




020

4060

80

020

4060

265

26

275

28

27


Sens

or o

utpu

t (V

)


020

4060

80

020

4060

80

29

28

27

2625

3


Sens

or o

utpu

t (V

)


020

4060

80

020

4060

80

275

285

29

28

27


Sens

or o

utpu

t (V

)








data







data




020

4060

80

020

4060

80

28285

265

275

26

27

29


Sens

or o

utpu

t (V

)



4 Conclusion





Acknowledgments



References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











data

Normal data




Flaw data


ELM 1 regression

Result

ELM p train

ELM p regression





0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000

500

1000

1500

2000

2500

3000

3500

4000

4500

Sampling points

Flaw 1

Weld

FlangeFlaw 2 Flaw 3


Flaw 8


stat

istic

scor

e


2000 2100 2200 2300 2400 2500 2600

5

4

55

45

35

253

665

775

Sampling points


ELM 3

ELM 2

Test inputs




0 10 20 30 40 50 60 70 800

10

20

30

40

50

60

70

Number of sensor

T2

stat

istic

scor

e


020

4060

80

0

20

40

60

29

28

27

26

25

Channel index

Sampling number

Sens

or o

utpu

t (V

)


020

4060

80

020

4060

265

275

28

27

26


Sens

or o

utpu

t (V

)




020

4060

80

020

4060

265

26

275

28

27


Sens

or o

utpu

t (V

)


020

4060

80

020

4060

80

29

28

27

2625

3


Sens

or o

utpu

t (V

)


020

4060

80

020

4060

80

275

285

29

28

27


Sens

or o

utpu

t (V

)








data







data




020

4060

80

020

4060

80

28285

265

275

26

27

29


Sens

or o

utpu

t (V

)



4 Conclusion





Acknowledgments



References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 10 20 30 40 50 60 70 800

10

20

30

40

50

60

70

Number of sensor

T2

stat

istic

scor

e


020

4060

80

0

20

40

60

29

28

27

26

25

Channel index

Sampling number

Sens

or o

utpu

t (V

)


020

4060

80

020

4060

265

275

28

27

26


Sens

or o

utpu

t (V

)




020

4060

80

020

4060

265

26

275

28

27


Sens

or o

utpu

t (V

)


020

4060

80

020

4060

80

29

28

27

2625

3


Sens

or o

utpu

t (V

)


020

4060

80

020

4060

80

275

285

29

28

27


Sens

or o

utpu

t (V

)








data







data




020

4060

80

020

4060

80

28285

265

275

26

27

29


Sens

or o

utpu

t (V

)



4 Conclusion





Acknowledgments



References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra













data







data




020

4060

80

020

4060

80

28285

265

275

26

27

29


Sens

or o

utpu

t (V

)



4 Conclusion





Acknowledgments



References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Documents

Research Article A PCA and ELM Based Adaptive …downloads.hindawi.com/journals/mpe/2014/124968.pdfResearch Article A PCA and ELM Based Adaptive Method for Channel Equalization in