Research Article Defect Automatic Identification of Eddy

Research ArticleDefect Automatic Identification of Eddy CurrentPulsed Thermography

Kai Chen Libing Bai Yifan Chen Yuhua Cheng Shulin Tian and Peipei Zhu

School of Automation Engineering University of Electronic Science and Technology of China 2006 Xiyuan AvenueChengdu Sichuan 611731 China

Correspondence should be addressed to Libing Bai libingbaiuestceducn

Received 18 July 2014 Revised 31 October 2014 Accepted 31 October 2014 Published 31 December 2014

Academic Editor Ignacio R Matias

Copyright copy 2014 Kai Chen et alThis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Eddy current pulsed thermography (ECPT) is an effective nondestructive testing and evaluation (NDTampE) technique and has beenapplied for a wide range of conductive materials Manual selected frames have been used for defects detection and quantificationDefects are indicated by highlow temperature in the frames However the variation of surface emissivity sometimes introducesillusory temperature inhomogeneity and results in false alarm To improve the probability of detection this paper proposes a two-heat balance states-based method which can restrain the influence of the emissivity In addition the independent componentanalysis (ICA) is also applied to automatically identify defect patterns and quantify the defects An experiment was carried outto validate the proposed methods

1 Introduction

A review of current literature shows that thermography isapplicable to a wide range of materials [1ndash6] Eddy currentpulsed thermography (ECPT) has been attempted in pre-vious studies The temperature distribution around a crackwith different penetration depths in metallic materials wasinvestigated in [7] The potential for small defects detectionin components of complex geometry such as compressorblades and low pressure turbine vanes was discussed in[8] The probability of detection (POD) of fatigue cracks insteel titanium and nickel-based superalloy was estimatedin [9] Multiple cracks from rolling contact fatigue in railtrack in a single measurement were detected in [10] In allof these works defects were detected and quantified usingmanually selected frames Defects were indicated by highlowtemperature spot in the frames In the in situ application theunits under test always have oil or the oxidation layer on thesurface which changes the thermal emissivity significantlyThe variation of surface emissivity sometimes introduces illu-sory temperature inhomogeneity and results in false alarm

To remove the influence of surface emissivity variationseveral methods have been attempted in previous studiesNoethen et al put a very thin water film on sample surface

to homogenize the emissivity of the oxidized surface [11]Avdelidis and Almond sprayed black paint on aluminiumsample to eliminate high reflectance and raise emissivity [12]These methods can improve the homogeneity of the surfaceemissivity And to a certain extent the signal-to-noise ratio ofthe image is improvedHowever water or black paint not onlypollutes the sample but also increases the cost and complexityof the test procedure

Shepard proposed thermographic signal reconstruction(TSR) based flash thermography to reduce the influence ofthe thermal emissivity [13]Maldague et al inhibited the ther-mal emissivity variation influence by the pulse phase infraredthermography method [14 15] Chatterjee and Tuli removedinfluence of nonuniform heating and surface emissivity vari-ation using a Fourier transformation based image reconstruc-tion algorithm [16] Fourier transformation attracts a wideapplication in flash stimulation thermal imaging [17] lock-in thermography [16] However the defect information isseparated into several frequency components which concealsthe defect quantification information conceived in transientresponse [18ndash20]

To solve the problem mentioned above this paper com-bines the authorsrsquo two previous proposed methods two-heatbalance states [21] and blind source separation [22] which

Hindawi Publishing CorporationJournal of SensorsVolume 2014 Article ID 326316 7 pageshttpdxdoiorg1011552014326316

2 Journal of Sensors

promises defect automatic identification in the in situ appli-cationThe rest of the paper is organized as follows Section 2discusses the implementation of emissivity inhibition andautomatic detection Section 3 introduces the experimentalsetup Sections 4 and 5 present the experiment results and theconclusions

2 Theoretical Considerations

21 TheTheory of the Two-Heat Balance States-Based MethodThe equation of the theory of the two-heat balance states-based method can be described as

119895119894119895 (119905) =

119895lowast119894119895(119905)

119895lowast119894119895(1199051) minus 119895lowast119894119895(1199050)=1198794119894119895(119905)

11987941minus 11987940

(1)

where 119905 is time 119879119894119895(119905) denotes the temperature response of

the area corresponding to pixel (119894 119895) 1198790equals the ambient

temperature and 1198791equals the temperature of equilibrium

state 119895119894119895(119905) is independent of the emissivity and describes the

temperature changing process [21]

22 Quantifying Independence Using Kurtosis As there isonly one infrared camera in ECPT this refers to a typicalsingle channel source separation problemThe mathematicalmodel can be described as

Y (119905) =119873119904

sum119894=1

119898119894X119894 (119905) (2)

The ICA learning algorithmwhich is equivalent to search-ing for the linear transformation that makes the componentsas statistically independent as possible has been used toseparate the thermal response signal [23ndash25]The sources canbe estimated as

X1015840ICA (119905) = WICAU119879

119879times119873119904

(3)

where WICA is the linear transformation matrix [22] Themixing model can be shown in Figure 1

In the independent components the area without defectsis much bigger than the other area and contains amountof pixels which shows more centralized in statistics For aGaussian random variable the kurtosis is zero For most ofother cases kurtosis is nonzero for non-Gaussian randomvariables The bigger the kurtosis is the more abundant theinformation of defect isTherefore the kurtosis can be appliedto extract the defects automatically The kurtosis of thermalimages can be described as

kurt (119883119894 (119905)) =sum119872

119895=1sum119873

119896=1[119883119894119895119896 (119905) minus 119883119894 (119905)]

4

(119872119873 minus 1) 1205904minus 3 (4)

where 119883119894(119905) is the mean of the thermal image 119883

119894(119905) 120590 is the

standard deviation of 119883119894(119905) and 119872 and 119873 are the pixel of

thermographyThe process of automatic detection can be summarized as

shown in Figure 2

4

3

3

3

3

2

2

1

1

m4

m3

m1

m2

Y(t)

Figure 1 The mixing model of ICA

Start

Data acquisition

Filtration

Remove emissivity(two-heat balance states-

based method)

Image enhancement(ICA)

Calculate kurtosis

Automatic detection

End

Figure 2 Flow chart of automatic detection

3 Experiment Setup and Sample

The experimental setup is shown in Figure 3 The inductionheater used for coil excitation has a maximum excitationpower of 15 kW a maximum current of 700Arms and anexcitation frequency range of 30ndash100 kHz (150Arms and80 kHz are used in this study) The system has a quoted risetime (from the start of the heating period to full power) of250ms which was verified experimentally Water cooling ofcoil is implemented to counteract direct heating of the coil

The IR camera FLIR A655sc is an uncooled camera with480times 640 arrayThis camera has a sensitivity oflt50mKand amaximum full frame rate of 50Hz with the option to increase

Journal of Sensors 3

Induction heater

Functions generator

IR camera

PC

Coil

Sample

Figure 3 Experiment setup

(a) (b)

Figure 4 (a) Steel sample with slot (b) Directional excitation coil

frame rate with windowing of the image A rectangular coil isconstructed to apply directional excitation This coil is madeof inner diameter 7mm high conductivity hollow coppertube In the experiment only one edge of the rectangular coilis used to stimulate eddy current to the underneath sampleIn this study the frame rate is 100Hz with 240 times 640 arrayand 26 s videos are recorded in the experiments

A silicon steel sheet sample (033mmtimes 30mmtimes 160mm)with a slot of 8mm length and 2mm width is prepared(Figure 4(a)) There are equally spaced shinning and blackstripes on the sample surface The shinning strips are thepolished area and the black strips are the area sprayed blackpainting A 300msheating duration is selected for inspectionwhich is long enough to elicit an observable heat patternThe cooling time is 22 s which is long enough to ensurethe sample reaching a new thermal equilibrium state Theexcitation coil is placed at the back of the sample and parallelsthe sample as shown in Figure 4(b)

4 Results and Discussion

41 The Removement of the Emissivity By setting 1199051= 25 s

the transient response is corrected using (1) The results areshown in Figure 5 Figures 5(a) and 5(b) show the originaltemperature distribution and transient responses There is agreat difference between Pos1 and Pos2 Figure 5(c) showsthe corrected temperature distribution at the end of heating

(03 s) The black stripes are almost invisible Pos1 and Pos2show nearly similar temperature The transient responses ofthe 3 positions are shown in Figure 5(d) Pos3 has a highrising rate in the heating phase and high falling rate atthe cooling phase Pos1 has low rising rate in the heatingphase and low falling rate in the cooling phase Pos2 almostcoincided with Pos1 These are in line with the transientresponse acquired from homogeneity surface [22]

42 Automatic Defect Independent Component (IC) Identi-fication Using Kurtosis In order to realize the automaticdetection of the defect the images which have been processedby two-heat balance states-based method are processed byICA Table 1 shows the four ICs and the correspondingestimated mixing vectors It is noted that IC2 IC3 and IC4highlight different parts of the excitation coil and severalrelative areas due to reflection of the shining sample surfaceIn addition IC1 highlights the area including slot tips and itsestimatedmixing vector shows that the high rising and fallingrate in heating and cooling phase around the slot tip are in linewith the previous analysis [22]The kurtosis is also calculatedusing (4) The kurtosis of IC1 is the maxim value (257) overother ICs (IC2 18 IC3 56 IC4 38) that directly indicates thedefect area Hence the kurtosis can be calculated to detect thedefects automatically

To further verify the abovemethod one subsurface defectand three surface defects in stainless steel welds are employed


Table 1 Independent components and estimated mixing vectors

Component No IC patterns Estimated mixing vectors

IC1

50 100 150 200 250 300 350 400

20406080

100120140

Am

plitu

de

0 05 1 15 2 250

005

01

015

02

025

t (s)

IC2

50 100 150 200 250 300 350 400

20406080

100120140

Am

plitu

de

0 05 1 15 2 250

00501

01502

02503

03504

045

t (s)

IC3

50 100 150 200 250 300 350 400

20406080

100120140

Am

plitu

de

0 05 1 15 2 25

0002004006008

01012014

t (s)

minus002

IC4

50 100 150 200 250 300 350 400

20406080

100120140

Am

plitu

de

0 05 1 15 2 25

0002004006008

01012014

t (s)

minus002

minus004

minus006


Pos3

Pos1

Pos2

50 100 150 200 250 300 350 400

20

40

60

80

100

120

140

(a)

0 05 1 15 2 250

5

10

15

Pos1Pos2Pos3

T(D

L)

t (s)

(b)

Pos1

Pos2

Pos3

50 100 150 200 250 300 350 400

20

40

60

80

100

120

140

(c)

0 05 1 15 2 250

05

1

15

2

25

3

35

T(D

L)

t (s)

Pos1Pos2Pos3

(d)

Figure 5 (a) Original image (b) original transient responses (c) corrected infrared image at 03 s and (d) processed transient responses ofdifferent positions

for testing All testing was carried out from the top sideThe results are shown in Table 2 There is a slot of 5mmlength and 1mm width in sample (1) The IC1 highlights thearea including defect and its kurtosis is the maxim value(679) over other ICs (IC2 127 IC3 61 IC4 88) There isa subsurface defect of 5mm length 1mm width and 2mmdepth in sample (2) The IC1 highlights the area includingdefect and its kurtosis is the maxim value (400) over otherICs (IC2 114 IC3 113 IC4 36) There are two surface defectsof 1mm diameter 3mm and 5mm depth in sample (3)Similarly the IC1 highlights the area including defects andits kurtosis is the maxim value (628) over other ICs (IC2 161

IC3 62 IC4 33) It is clear that the proposed method candetect the defects effectively and automatically

5 Conclusion

In this paper two-heat balance states-based method andblind source separation are combined for defect automaticidentification A validated experiment is carried out Theconclusions can be drawn as follows

(1) The temperature and emissivity are separated by thetwo-heat balance states-based method


Table 2 Samples and independent component

Sample IC patterns

(1) (top) (bottom)

IC1

100 200 300 400 500 600

50

100

150

200

(2) (top) (bottom)

IC1

100 200 300 400 500 600

50

100

150

200

(3) (top) (bottom)

IC1

100 200 300 400 500 600

50

100

150

200

(2) The IC highlighting the defect can also be identifiedusing kurtosis The singular pattern around cracktips has a high temperature in small area and hightemperature gradient around the edge This resultsin extremely super-Gaussian and maximum kurtosisvalue

Conflict of Interests

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

Acknowledgments

This paper is supported by ldquothe Fundamental Research Fundsfor the Central Universitiesrdquo (ZYGX2012YB029) and ldquotheNational Natural Science Foundation of Chinardquo (Grant nos61102141 and 51407024)

References

[1] N P Avdelidis B CHawtin andD P Almond ldquoTransient ther-mography in the assessment of defects of aircraft compositesrdquoNDT and E International vol 36 no 6 pp 433ndash439 2003


[2] Z Zeng N Tao L Feng and C Zhang ldquoSpecified value baseddefect depth prediction using pulsed thermographyrdquo Journal ofApplied Physics vol 112 no 2 Article ID 023112 2012

[3] C Meola ldquoNondestructive evaluation of materials with rearheating lock-in thermographyrdquo IEEE Sensors Journal vol 7 no10 pp 1388ndash1389 2007

[4] S Huth O Breitenstein A Huber and U Lambert ldquoLocal-ization of gate oxide integrity defects in silicon metal-oxide-semiconductor structures with lock-in IR thermographyrdquo Jour-nal of Applied Physics vol 88 no 7 pp 4000ndash4003 2000

[5] V S Ghali N Jonnalagadda and R Mulaveesala ldquoThree-dimensional pulse compression for infrared nondestructivetestingrdquo IEEE Sensors Journal vol 9 no 7 pp 832ndash833 2009

[6] N Biju N Ganesan C V Krishnamurthy and K Balasubra-maniam ldquoSimultaneous estimation of electrical and thermalproperties of isotropic material from the tone-burst eddycurrent thermography (TBET) timemdashtemperature datardquo IEEETransactions on Magnetics vol 47 no 9 pp 2213ndash2219 2011

[7] B Oswald-Tranta and G Wally ldquoThermo-inductive surfacecrack detection in metallic materialsrdquo in Proceedings of the 9thEuropean Conference on Non-Destructive Testing (ECNDT rsquo06)paper We383 Berlin Germany September 2006

[8] G Zenzinger J Bamberg W Satzger and V Carl ldquoThermo-graphic crack detection by eddy current excitationrdquo Nonde-structive Testing andEvaluation vol 22 no 2-3 pp 101ndash111 2007

[9] B Weekes D P Almond P Cawley and T Barden ldquoEddy-current induced thermographymdashprobability of detection studyof small fatigue cracks in steel titanium and nickel-basedsuperalloyrdquo NDT and E International vol 49 pp 47ndash56 2012

[10] J Wilson G Y Tian I Mukriz and D Almond ldquoPECthermography for imaging multiple cracks from rolling contactfatiguerdquoNDTampE International vol 44 no 6 pp 505ndash512 2011

[11] M Noethen K-J Wolter and N Meyendorf ldquoSurface crackdetection in ferritic and austenitic steel components usinginductive heated thermographyrdquo in Proceedings of the 33rdInternational Spring Seminar on Electronics Technology PolymerElectronics and Nanotechnologies Towards System Integration(ISSE rsquo10) pp 249ndash254 Warsaw Poland May 2010

[12] N P Avdelidis and D P Almond ldquoTransient thermographyas a through skin imaging technique for aircraft assemblymodelling and experimental resultsrdquo Infrared Physics and Tech-nology vol 45 no 2 pp 103ndash114 2004

[13] S M Shepard ldquoFlash thermography of aerospace compositesrdquoin Proceedings of the 4th Pan American Conference for NDTBuenos Aires Argentina October 2007

[14] X Maldague and S Marinetti ldquoPulse phase infrared thermog-raphyrdquo Journal of Applied Physics vol 79 no 5 pp 2694ndash26981996

[15] YHeG TianM Pan andDChen ldquoEddy current pulsed phasethermography and feature extractionrdquo Applied Physics Lettersvol 103 no 8 Article ID 084104 2013

[16] K Chatterjee and S Tuli ldquoImage enhancement in transientlock-in thermography through time series reconstruction andspatial slope correctionrdquo IEEE Transactions on Instrumentationand Measurement vol 61 no 4 pp 1079ndash1089 2012

[17] J-C Krapez L Spagnolo M Frieszlig H-P Maier and GU Neuer ldquoMeasurement of in-plane diffusivity in non-homogeneous slabs by applying flash thermographyrdquo Interna-tional Journal of Thermal Sciences vol 43 no 10 pp 967ndash9772004

[18] YHeM Pan andF Luo ldquoDefect characterisation based onheatdiffusion using induction thermography testingrdquoThe Review ofScientific Instruments vol 83 no 10 Article ID 104702 2012

[19] L Bai and G Y Tian ldquoStress measurement using pulsededdy current thermographyrdquo in Proceedings of the 51st AnnualConference of the British Institute of Non-Destructive Testing(BINDT 12) Daventry UK 2012

[20] L Cheng and G Y Tian ldquoSurface crack detection for carbonfiber reinforced plastic (CFRP) materials using pulsed eddycurrent thermographyrdquo IEEE Sensors Journal vol 11 no 12 pp3261ndash3268 2011

[21] L Bai S Tian Y Cheng G Y Tian Y Chen and K ChenldquoReducing the effect of surface emissivity variation in eddycurrent pulsed thermographyrdquo IEEE Sensors Journal vol 14 no4 pp 1137ndash1142 2014

[22] L Bai B Gao G Y TianW LWoo and Y Cheng ldquoSpatial andtime patterns extraction of eddy current pulsed thermographyusing blind source separationrdquo IEEE Sensors Journal vol 13 no6 pp 2094ndash2101 2013

[23] M Pan Y He G Tian D Chen and F Luo ldquoDefect character-isation using pulsed eddy current thermography under trans-missionmode andNDTapplicationsrdquoNDTandE Internationalvol 52 pp 28ndash36 2012

[24] L Cheng B Gao G Y Tian W L Woo and G BerthiauldquoImpact damage detection and identificationusing eddy currentpulsed thermography through integration of PCA and ICArdquoIEEE Sensors Journal vol 14 no 5 pp 1655ndash1663 2014

[25] Y He G Tian M Pan and D Chen ldquoImpact evaluation incarbon fiber reinforced plastic (CFRP) laminates using eddycurrent pulsed thermographyrdquo Composite Structures vol 109no 1 pp 1ndash7 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



promises defect automatic identification in the in situ appli-cationThe rest of the paper is organized as follows Section 2discusses the implementation of emissivity inhibition andautomatic detection Section 3 introduces the experimentalsetup Sections 4 and 5 present the experiment results and theconclusions

2 Theoretical Considerations

21 TheTheory of the Two-Heat Balance States-Based MethodThe equation of the theory of the two-heat balance states-based method can be described as

119895119894119895 (119905) =

119895lowast119894119895(119905)

119895lowast119894119895(1199051) minus 119895lowast119894119895(1199050)=1198794119894119895(119905)

11987941minus 11987940

(1)

where 119905 is time 119879119894119895(119905) denotes the temperature response of

the area corresponding to pixel (119894 119895) 1198790equals the ambient

temperature and 1198791equals the temperature of equilibrium

state 119895119894119895(119905) is independent of the emissivity and describes the

temperature changing process [21]

22 Quantifying Independence Using Kurtosis As there isonly one infrared camera in ECPT this refers to a typicalsingle channel source separation problemThe mathematicalmodel can be described as

Y (119905) =119873119904

sum119894=1

119898119894X119894 (119905) (2)

The ICA learning algorithmwhich is equivalent to search-ing for the linear transformation that makes the componentsas statistically independent as possible has been used toseparate the thermal response signal [23ndash25]The sources canbe estimated as

X1015840ICA (119905) = WICAU119879

119879times119873119904

(3)

where WICA is the linear transformation matrix [22] Themixing model can be shown in Figure 1

In the independent components the area without defectsis much bigger than the other area and contains amountof pixels which shows more centralized in statistics For aGaussian random variable the kurtosis is zero For most ofother cases kurtosis is nonzero for non-Gaussian randomvariables The bigger the kurtosis is the more abundant theinformation of defect isTherefore the kurtosis can be appliedto extract the defects automatically The kurtosis of thermalimages can be described as

kurt (119883119894 (119905)) =sum119872

119895=1sum119873

119896=1[119883119894119895119896 (119905) minus 119883119894 (119905)]

4

(119872119873 minus 1) 1205904minus 3 (4)

where 119883119894(119905) is the mean of the thermal image 119883

119894(119905) 120590 is the

standard deviation of 119883119894(119905) and 119872 and 119873 are the pixel of

thermographyThe process of automatic detection can be summarized as

shown in Figure 2

4

3

3

3

3

2

2

1

1

m4

m3

m1

m2

Y(t)

Figure 1 The mixing model of ICA

Start

Data acquisition

Filtration

Remove emissivity(two-heat balance states-

based method)

Image enhancement(ICA)

Calculate kurtosis

Automatic detection

End

Figure 2 Flow chart of automatic detection

3 Experiment Setup and Sample

The experimental setup is shown in Figure 3 The inductionheater used for coil excitation has a maximum excitationpower of 15 kW a maximum current of 700Arms and anexcitation frequency range of 30ndash100 kHz (150Arms and80 kHz are used in this study) The system has a quoted risetime (from the start of the heating period to full power) of250ms which was verified experimentally Water cooling ofcoil is implemented to counteract direct heating of the coil

The IR camera FLIR A655sc is an uncooled camera with480times 640 arrayThis camera has a sensitivity oflt50mKand amaximum full frame rate of 50Hz with the option to increase


Induction heater

Functions generator

IR camera

PC

Coil

Sample


(a) (b)













IC1

50 100 150 200 250 300 350 400

20406080

100120140

Am

plitu

de

0 05 1 15 2 250

005

01

015

02

025

t (s)

IC2

50 100 150 200 250 300 350 400

20406080

100120140

Am

plitu

de

0 05 1 15 2 250

00501

01502

02503

03504

045

t (s)

IC3

50 100 150 200 250 300 350 400

20406080

100120140

Am

plitu

de

0 05 1 15 2 25

0002004006008

01012014

t (s)

minus002

IC4

50 100 150 200 250 300 350 400

20406080

100120140

Am

plitu

de

0 05 1 15 2 25

0002004006008

01012014

t (s)

minus002

minus004

minus006


Pos3

Pos1

Pos2

50 100 150 200 250 300 350 400

20

40

60

80

100

120

140

(a)

0 05 1 15 2 250

5

10

15

Pos1Pos2Pos3

T(D

L)

t (s)

(b)

Pos1

Pos2

Pos3

50 100 150 200 250 300 350 400

20

40

60

80

100

120

140

(c)

0 05 1 15 2 250

05

1

15

2

25

3

35

T(D

L)

t (s)

Pos1Pos2Pos3

(d)




5 Conclusion





Sample IC patterns

(1) (top) (bottom)

IC1

100 200 300 400 500 600

50

100

150

200

(2) (top) (bottom)

IC1

100 200 300 400 500 600

50

100

150

200

(3) (top) (bottom)

IC1

100 200 300 400 500 600

50

100

150

200




Acknowledgments


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Induction heater

Functions generator

IR camera

PC

Coil

Sample


(a) (b)













IC1

50 100 150 200 250 300 350 400

20406080

100120140

Am

plitu

de

0 05 1 15 2 250

005

01

015

02

025

t (s)

IC2

50 100 150 200 250 300 350 400

20406080

100120140

Am

plitu

de

0 05 1 15 2 250

00501

01502

02503

03504

045

t (s)

IC3

50 100 150 200 250 300 350 400

20406080

100120140

Am

plitu

de

0 05 1 15 2 25

0002004006008

01012014

t (s)

minus002

IC4

50 100 150 200 250 300 350 400

20406080

100120140

Am

plitu

de

0 05 1 15 2 25

0002004006008

01012014

t (s)

minus002

minus004

minus006


Pos3

Pos1

Pos2

50 100 150 200 250 300 350 400

20

40

60

80

100

120

140

(a)

0 05 1 15 2 250

5

10

15

Pos1Pos2Pos3

T(D

L)

t (s)

(b)

Pos1

Pos2

Pos3

50 100 150 200 250 300 350 400

20

40

60

80

100

120

140

(c)

0 05 1 15 2 250

05

1

15

2

25

3

35

T(D

L)

t (s)

Pos1Pos2Pos3

(d)




5 Conclusion





Sample IC patterns

(1) (top) (bottom)

IC1

100 200 300 400 500 600

50

100

150

200

(2) (top) (bottom)

IC1

100 200 300 400 500 600

50

100

150

200

(3) (top) (bottom)

IC1

100 200 300 400 500 600

50

100

150

200




Acknowledgments


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












IC1

50 100 150 200 250 300 350 400

20406080

100120140

Am

plitu

de

0 05 1 15 2 250

005

01

015

02

025

t (s)

IC2

50 100 150 200 250 300 350 400

20406080

100120140

Am

plitu

de

0 05 1 15 2 250

00501

01502

02503

03504

045

t (s)

IC3

50 100 150 200 250 300 350 400

20406080

100120140

Am

plitu

de

0 05 1 15 2 25

0002004006008

01012014

t (s)

minus002

IC4

50 100 150 200 250 300 350 400

20406080

100120140

Am

plitu

de

0 05 1 15 2 25

0002004006008

01012014

t (s)

minus002

minus004

minus006


Pos3

Pos1

Pos2

50 100 150 200 250 300 350 400

20

40

60

80

100

120

140

(a)

0 05 1 15 2 250

5

10

15

Pos1Pos2Pos3

T(D

L)

t (s)

(b)

Pos1

Pos2

Pos3

50 100 150 200 250 300 350 400

20

40

60

80

100

120

140

(c)

0 05 1 15 2 250

05

1

15

2

25

3

35

T(D

L)

t (s)

Pos1Pos2Pos3

(d)




5 Conclusion





Sample IC patterns

(1) (top) (bottom)

IC1

100 200 300 400 500 600

50

100

150

200

(2) (top) (bottom)

IC1

100 200 300 400 500 600

50

100

150

200

(3) (top) (bottom)

IC1

100 200 300 400 500 600

50

100

150

200




Acknowledgments


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Pos3

Pos1

Pos2

50 100 150 200 250 300 350 400

20

40

60

80

100

120

140

(a)

0 05 1 15 2 250

5

10

15

Pos1Pos2Pos3

T(D

L)

t (s)

(b)

Pos1

Pos2

Pos3

50 100 150 200 250 300 350 400

20

40

60

80

100

120

140

(c)

0 05 1 15 2 250

05

1

15

2

25

3

35

T(D

L)

t (s)

Pos1Pos2Pos3

(d)




5 Conclusion





Sample IC patterns

(1) (top) (bottom)

IC1

100 200 300 400 500 600

50

100

150

200

(2) (top) (bottom)

IC1

100 200 300 400 500 600

50

100

150

200

(3) (top) (bottom)

IC1

100 200 300 400 500 600

50

100

150

200




Acknowledgments


References





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Sample IC patterns

(1) (top) (bottom)

IC1

100 200 300 400 500 600

50

100

150

200

(2) (top) (bottom)

IC1

100 200 300 400 500 600

50

100

150

200

(3) (top) (bottom)

IC1

100 200 300 400 500 600

50

100

150

200




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











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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