research article study of three-component fbg vibration sensor...

Research ArticleStudy of Three-Component FBG VibrationSensor for Simultaneous Measurement of VibrationTemperature and Verticality

Jiang Shan-chao Wang Jing Sui Qing-mei Ye Qing-lin and Wang Li-jun

School of Control Science and Engineering Shandong University Jinan 250061 China

Correspondence should be addressed to Wang Jing wangjingkzsdueducn

Received 5 October 2014 Revised 21 December 2014 Accepted 21 December 2014

Academic Editor Fei Dai

Copyright copy 2015 Jiang Shan-chao et alThis is an open access article distributed under theCreative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

To achieve simultaneous measurement of measurand vibration temperature and verticality a three-component fiber Brag grating(TVFBG) vibration sensor is proposed in this paper Polymer and metal diaphragm sensitization methods are utilized to improvethis sensor measurement sensitivity Project matrix theory is adopted to analyze this sensor Theoretically 9 times 9 nonsingularmeasuring coefficient matrix of this TVFBG sensor made up by three 3 times 3 measurand coefficient matrixes is established Inorder to effectively extract measurand Hilbert-Huang transform (HHT) is accepted to process this sensorrsquos center wavelengthsignals Calibration experiments are carried out to verify the performance of this TVFBG sensor Experiment data confirm thatthis sensor has excellent frequency response and show good linearity at temperature and verticality measurement Wrist rotationangle measurement experiment is also implemented to further identify this sensor practical value Through analyzing by HHTexperiment results show that the angle measurement sensitivities of three fiber Brag gratings which are included in this sensor areseparately 252 pm∘ 382 pm∘ and 383 pm∘

1 Introduction

Simultaneous multiparameter measurement has providedone way which reduces the number of measuring sensors andcuts down detection cost to monitor the health status of engi-neering structure Based on the characteristics of fiber Bragggrating (FBG) such as high accuracy small size immunity toelectromagnetic interference andmultiplexing capacity FBGsensors have been widely used in aerospace energy industrytransportation and geotechnical and civil engineering [1ndash8] During the latest decades there are many works aboutisochronous multiparameter measurement by FBG sensorshave been down Rao et al [9] performed the simultaneousmeasurement of static strain temperature and vibrationusing amultiplexed in-FBGfibre-F-P sensor Zhang et al [10]demonstrated an integrated inlinemicrofiber sensor based onfiber Bragg gratings to simultaneously measure vibration andtemperature information for state estimation of cable-stayedbridges

Based on available research results a three-componentFBG vibration (TVFBG) sensor for synchronous measure-ment of vibration temperature and verticality is proposed inthis paper Due to the fact that axial strain sensitive coefficientof bare FBG is only 0003 nmMPa [11] many methods havebeen reported to improve its coefficient such as polymersensitization [12 13] metal diaphragm sensitization [14 15]and some other mechanical structures [1 16] Polymer andmetal diaphragm sensitization methods are both used toimprove measurement sensitivity of this TVFBG sensor

According to project matrix theory 9 times 9 nonsingularmeasuring coefficient matrix made up by three 3 times 3measur-and coefficientmatrixes is established All these 3times3matrixesare deduced from this sensor theoretical model Three fiberBragg gratings (TFBGs) are included in this TVFBG sensor asthe sensitive elements All center wavelengths of TFBGs con-tain the information of vibration temperature and vertical-ity So as to effectively extract the measurand vibration tem-perature and verticality Hilbert-Huang transform (HHT) is

Hindawi Publishing CorporationJournal of SensorsVolume 2015 Article ID 382865 9 pageshttpdxdoiorg1011552015382865

2 Journal of Sensors

(a) Schematic diagram of metal transfer structure (b) Prototype of this TVFBG sensor

(c) Sensing element component parts (d) Components of link rob

Figure 1 Basic block diagram and prototype of this TVFBG sensor

used to analyze the dynamic wavelength signals Calibrationexperiment is carried out to test this sensor performance andwrist rotation angle measurement experiment further provesits practical value

Generally speaking in this sensor polymer and metaldiaphragm sensitization methods are used to improve itsmeasuring sensitivityTheoretical calculationmodel based onproject matrix theory is set up and HHT is utilized to extractand reconstruct the measurand It realizes three-parametermeasurement at the same time Due to calibration andwrist rotation measurement experiment results this TVFBGsensor possesses great potential in engineering application

2 Structure of the TVFBG Sensor

Basic metal transfer structure and prototype of this TVFBGsensor are shown in Figure 1 This TVFBG sensor is com-posed of three sensing elements and one metal transferstructure All these three sensing elements are equidistantdistributed around the axial direction and the angle interval is120∘ in the circumferential distribution The sensing elementwhich is shown in Figure 1(c) includes two connectionterminals one spring as the elastic element and one fiberBragg grating as sensitive element

Metal transfer structure shown in Figure 1(a) is made upby three link rods upper fixed and lower free rings Link rodexhibited in Figure 1(d) is composed of two omnidirectionalwheels distributed at both ends and the middle elasticelement Basic geometric parameters of this metal transferstructure are presented in Table 1

3 Signal Analysis andMeasurand Identification

Due to the advantages unlimited by fixed wavelet andadaptive signal processing HHT [13 17] is widely adoptedas a powerful tool to deal with nonlinear and nonstationarysignals HHT is utilized to pick out three different signals

Table 1 Basic geometric parameters of metal transfer structure(unit mm)

Length Height Outer radius Inner radiusThe ring 7 110 70Link rod 155 4Omnidirectionalwheel 5

Elastomer in themiddle of link rod 25 5 4

Δ120582119894119881 Δ120582119894119879 and Δ120582

119894119875(119894 = 1 2 3) from the original center

wavelengths 120582FBG119894 (119894 = 1 2 3) Δ120582119894119881 Δ120582119894119879 and Δ120582

119894119875are

wavelength changes caused by external vibration tempera-ture and verticality angle Through analyzing by HHT theoriginal signals could be expressed as

120582FBG1 = 12058210+

119899

sum

119894=1

1198881119894

120582FBG2 = 12058220+

119899

sum

119894=1

1198882119894

120582FBG3 = 12058230+

119899

sum

119894=1

1198883119894

(1)

where 1205821198940(119894 = 1 2 3) and 119888

119898119894(119898 = 1 2 3) stand for residual

signals and intrinsic mode functions of the original signals

31 Vibration Identification Because of middle elastic ele-ment the external vibration signal induces axial dynamicstrain on these TFBGs and further leads to the centerwavelength changes Relationship between axial strain 120576 andcenter wavelength shift Δ120582 could be expressed as

Δ120582

120582= (1 minus 119901

119890) 120576 (2)

Journal of Sensors 3

(a) (b)

Figure 2 (a) The fixed ring parallels the ground plane (b) Verticality angle 120572 between the fixed ring and the ground plane

where 119901119890is the elastic-optic coefficient of optical fiber and

its theoretical value equals 022 So the efficiency of dynamicstress 119865 worked on the optical fiber could be expressed as

119865 = 119864120576 = 119896119890sdot 119881 (119905) (3)

where 119864 is elasticity modulus of optical fiber 119896119890is the elastic

coefficient of elastomer in the link rob and 119881(119905) representsthe exterior dynamic signal

Through (2) and (3) we could get that

Δ1205821119881

=(1 minus 119901

119890)

119864sdot 12058210sdot 1198961198901sdot 1198811(119905)

Δ1205822119881

=(1 minus 119901

119890)

119864sdot 12058220sdot 1198961198902sdot 1198812(119905)

Δ1205823119881

=(1 minus 119901

119890)

119864sdot 12058230sdot 1198961198903sdot 1198813(119905) or

[[

[

Δ1205821119881

Δ1205822119881

Δ1205823119881

]]

]

= V sdot[[

[

1198811(119905)

1198812(119905)

1198813(119905)

]]

]

(4)

where1198811(119905)1198812(119905) and119881

3(119905) are exterior vibration signals and

V represents the vibration coefficient matrix

32 Temperature Identification Temperature changes can beobtained by

Δ1205821119879

= 12058210sdot (120572 + 120585) sdot 119879

1(119905)

Δ1205822119879

= 12058220sdot (120572 + 120585) sdot 119879

2(119905)

Δ1205823119879

= 12058230sdot (120572 + 120585) sdot 119879

3(119905) or

[[

[

Δ1205821119879

Δ1205822119879

Δ1205823119879

]]

]

= T sdot[[

[

1198791(119905)

1198792(119905)

1198793(119905)

]]

]

(5)

where 120572 is thermal expansion coefficient 120585 is thermoopticcoefficient of FBG 119879

1(119905) 1198792(119905) and 119879

3(119905) are the measured

temperature and T is the coefficient matrix of temperature

33 Verticality Identification While connecting line betweenupper and lower ring center points is not parallel withgeodetic vertical line the free ring could ceaselessly wiggleuntil the connecting line parallels the geodetic vertical linebased on the function of omnidirectional wheel The anglebetween geodetic vertical line and axis of this sensor metaltransfer structure is selected as vertical evaluation standardand named as verticality angle 120572 When this sensor positionchanges from Figures 2(a) to 2(b) verticality angle 120572 isgenerated by gravity

Adding the Cartesian coordinate system to this sensorand assuming that the link rod with FBG1 is vertical orthog-onal with 119909-axis verticality calculation model is shown inFigure 3

So the length changes Δ119871119894(119894 = 1 2 3) of three link robs

are expressed as

Δ1198711= 119903 (1 + cos 120579) sdot sin120572

Δ1198712= 119903 [1 minus cos(120587

3+ 120579)] sdot sin120572

Δ1198713= 119903 [1 minus cos(120587

3minus 120579)] sdot sin120572

(6)

where 119903 is radius of the upper fixed ring and 120579 is thedirectional angle between radius lineA and 119909 axis in the119883119884plane

Based on the above analysis verticality calculation for-mula is expressed as

Δ1205821V = 120582

10sdot (1 minus 119901

119890) sdot 119903 (1 + cos 120579) sdot sin120572

ℎ

Δ1205822V = 120582


119890) sdot 119903 [1 minus cos(120587

3+ 120579)] sdot

sin120572ℎ

Δ1205823V = 120582


119890) sdot 119903 [1 minus cos(120587

3minus 120579)] sdot

sin120572ℎ

or

[[

[

Δ1205821V

Δ1205822V

Δ1205823V

]]

]

= V sdot[[

[

1198751(119905)

1198752(119905)

1198753(119905)

]]

]

(7)


x

Y

FBG1

FBG3FBG2

120579

1

120∘ 120

∘

120∘

(a) Cross section of these three fiber Bragg grat-ings

X

Y

Z

r

h

1

120572

120572

(b) Geometry of verticality reconstruction based on the centerwavelength changes

Figure 3 Verticality calculation model of this sensor

where ℎ is height of this sensor andV is the verticality coeffi-cient matrix Through (7) verticality angle 120572 and directionalangle 120579 are obtained

The measurand identification could be concluded in foursteps

(1) Use HHT to extract different signals Δ120582119894119881 Δ120582119894119879 and

Δ120582119894119875(119894 = 1 2 3) from the center wavelengths 120582FBG119894

(119894 = 1 2 3)

(2) External dynamic signals 1198811(119905) 1198812(119905) and 119881

3(119905) are

obtained by bringing Δ120582119894119881(119894 = 1 2 3) to (4)

(3) Environment temperatures 1198791(119905) 1198792(119905) and 119879

3(119905) are

picked out by bringing Δ120582119894119879(119894 = 1 2 3) to (5)

(4) Verticality angle 120572 and directional angle 120579 are calcu-lated by bringing Δ120582

119894119875(119894 = 1 2 3) to (7)

Therefore the relationship between center wavelengthchanges and measurand could be expressed as

[[

[

Δ120582FBG1

Δ120582FBG2

Δ120582FBG3

]]

]

HHT997888rarr

[[[[[[[[[[[[[[[[[[[

[

Δ1205821119881

Δ1205822119881

Δ1205823119881

Δ1205821119879

Δ1205822119879

Δ1205823119879

Δ1205821119875

Δ1205822119875

Δ1205823119875

]]]]]]]]]]]]]]]]]]]

]

=[[

[

VT

P

]]

]

[[[[[[[[[[[[[[[[[[

[

1198811(119905)

1198812(119905)

1198813(119905)

1198791(119905)

1198792(119905)

1198793(119905)

1198751(119905)

1198752(119905)

1198753(119905)

]]]]]]]]]]]]]]]]]]

]

(8)

4 Calibration Experiment

For testing the performance of this TVFBG sensor frequencyresponse temperature sensitivity and verticality measuringexperiment are all carried outThe basic instruments in theseexperiments are ASE broadband flattened light source opti-cal fiber circulator and sense 2020 Sense 2020 is producedby Bay Spec Inc and acts as fiber dynamic demodulationinstrument Some other auxiliary equipment such as INV1601vibration platform produced by Beijing Dongfang Vibrationand Noise Technology Research Institute thermostatic watertank and protractor are also used in these experiments Theinitial center wavelengths of FBG1 FBG2 and FBG3 are15405533 nm 15344096 nm and 15307497 nm

41 Frequency Response Experiment Figure 4 shows diagramand basic instruments of frequency response experimentwhich is set up to simulate the exterior vibration envi-ronment This sensor is adhered together with vibrationplatform through epoxy resin Its status is kept vertical Inorder to improve coupling coefficient a thin layer ethyl 120572-cyanoacrylate is coated at the surface of simply supported


LightCirculator

Sense 2020

Data acquisition card

Vibrationplatform

FBG vibration sensor Coupler

JZ-1

YJ9A

(a) Basic diagram of frequency response experiment

FBG Vibration Sensor

The demodulation software interface

Fiber dynamic demodulation instrument

Vibration source controller

YJ9A acceleratorSimply supported beam

(b) Instruments in frequency response experiment

Figure 4 Frequency response experiment platform

beamDetection frequency ranges of sense 2020 are 0ndash5KHzand its frequency demodulation precision is 1Hz JZ-1 typevibration source included in the INV1601 vibration platformgenerates a series frequency from 100Hz to 1 KHz in steps of100Hz with precision 01Hz The output amplitude is kept at13ms2 in the whole experiment Comparative analysis databetween detected data by this TVFBG sensor and generateddata by JZ-1 are utilized as reference indicator to evaluate thissensor frequency response

42 Temperature Sensitivity Experiment Thermostatic watertank is utilized to change this sensor environment tem-perature Diagram of temperature sensitivity experiment isshown in Figure 5 So as to avoid that the center wavelengthsof TFBGs are influenced by exterior strain this TVFBGsensor is statically placed at the bottom of the tank SM125(demodulation ranges 1510ndash1590 nm demodulation preci-sion 1 pm) is chosen as fiber interrogator In this wholeprocess temperature variation ranges are 20∘Cndash60∘C and itsstep interval is 5∘C Water temperature is also measured bythermal resistance which is selected as contrastive data withthis TVFBG sensor Water temperature is remaining stablefor almost one minute at each step The heating and coolingprocesses are repeated twice

43 Verticality Measuring Experiment Protractor which isused in teaching acts as measure verticality angle measuringinstrument and its precision is 1∘ Instruments used in thisexperiment are shown in Figure 6 Achieving the purposethat data processing is more convenient the axis of FBG1is kept vertical orthogonal with zero depicting line at thebeginning of this experiment The manually controlled FBG1axis rotates counterclockwise to change the verticality angle120572 Due to metal transfer structure center wavelength ofFBG2 is increased and these other two wavelengths are bothdecreased Limited by the theoretical maximum strain valueof FBG which is 7860 120583120576 small ranges verticality measuringexperiment is carried outThemanually controlled verticalityangle 120572 increases from 0∘ to 5∘ with step interval 1∘

5 Data Analysis and Results

Analyzing the experiment data acquired in previous cali-bration experiment the basic characteristics of the TVFBGsensor are identified in this section

Portablecomputer

Gauze wire

Demodulationinstrument

Transmission fiber

VibrationsensorSLDC-2030

CouplerCL

Constant temperaturewater basin

Figure 5 Diagram of temperature sensitivity experiment platform

Figure 6 Instruments in the verticality response experiment

51 Frequency Characteristic Analysis Limited by length ofthis paper Figure 7 just displays parts of sectional graphsof the demodulation software interface and the controllersignals generated by JZ-1 These sectional graphs just displaythe frequency signals detected by FBG1

Fast Fourier transform (FFT) is selected to extract fre-quency information of this TVFBG sensor in the frequencyresponse experimentThe detected frequency data are shownin Table 2

Formula of relative measuring error is expressed as

120575119865=(119865FBG119894 minus 119865119881119878)

119865119881119878

sdot 100 (9)


Amplitude frequency diagram Frequency (Hz) 10040282200180014001000600

200

minus200

Am

plitu

de

50 60 70 80 90 100 110 120 130 140 150

Frequency (Hz)

(a) 100Hz

Frequency (Hz) 5020142Amplitude frequency diagram2000180016001400120010008006004002000

Am

plitu

de

Frequency (Hz)455 465 475 485 495 505 515 525 535 545

(b) 500Hz

Frequency (Hz) 1004028312000110001000090008000700060005000400020001000

0minus1000

960 970 980 990 1000 1010 1020 1030 1040 1050

Amplitude frequency diagram

Am

plitu

de

Frequency (Hz)

(c) 1000Hz

Figure 7 Left front panel of vibration source controller Right demodulation software interface sectional graphs

Table 2 Detected frequency data by this TVFBG sensor

GeneratedfrequencyHz

Detected frequencyHzFBG1 FBG2 FBG3

100 1004028 1004028 1004028200 2008057 2008057 2008057300 3012085 3012085 3012085400 4013062 4016113 4013062500 5020142 5020142 5020142600 602417 602417 602417700 7028198 7028198 7028198800 8032227 8032227 8032227900 9036255 9036255 90362551000 10040283 10040283 10040283

where 119865FBG119894 (119894 = 1 2 3) and 119865119881119878

represent detected frequencyand the generated frequency respectively

Calculating the measuring error between generated anddetected frequency through (9) its ranges are from 0327 to0403 Such data effectively prove that this TVFBG sensorhas excellent frequency response

52 Temperature Sensitivity Analysis Data in the first heatingprocess are displayed in Table 3 and Figure 8 shows changesof center wavelengths following the temperature variations inthe whole temperature sensitivity experiment

Figure 8 exhibits the fact that the relationship betweentemperature and center wavelengths has excellent linearityand reproducibility Temperature sensitivities of FBG1 ana-lyzed by least squaresmethod are 00114 pm∘C 00113 pm∘C00113 pm∘C and 00113 pm∘C in the twice heating andcooling processes Average value of these four sensitivities isselected as temperature sensitivity of FBG1 and its value is113 pm∘C Similarly temperature sensitivities of FBG2 andFBG3 are 134 pm∘C and 112 pm∘C Temperature sensitivi-ties of TFBGs are all approximated to the bare FBG There-fore this sensor realizes precise temperature measurement


15405

15406

15407

15408

15409

1541

20 25 30 35 40 45 50 55 60

Cen

ter w

avele

ngth

(nm

)FBG1

First heatingFirst cooling

Second heatingSecond cooling

Temperature (∘C)

(a)

15343

15344

15345

15346

15347

15348

15349

20 25 30 35 40 45 50 55 60

FBG2

Cen

ter w

avele

ngth

(nm

)



Temperature (∘C)

(b)

15307

15308

15309

1531

15311

15312

20 25 30 35 40 45 50 55 60

Cen

ter w

avele

ngth

(nm

)



Temperature (

FBG3

∘C)

(c)

Figure 8 Fitting curves between center wavelengths and temperature

Table 3 Experiment data in first heating procedure

Temperature∘C Center wavelength of FBGnmFBG1 FBG2 FBG3

20 1540400517 1534314647 153070388125 1540553308 153440965 153074972430 1540609982 1534470089 153080400235 1540666616 1534529987 153086077640 1540724015 1534593595 153091899245 1540780719 1534657476 153097915250 1540838631 153472566 153103974255 1540897591 1534797819 153110008660 1540952174 1534864976 1531129372

53 Verticality Measuring Analysis Table 4 gives the centerwavelengths of this TVFBG sensor in the verticality measur-ing experiment

Fitting curves between wavelength 120582119861and verticality

angle 120572 are 120582FBG1 = minus00267120572 + 15403 (1198772 = 09969)

Table 4 Data of verticality measuring experiment

Angle 120572∘ Center wavelength of FBGnmFBG1 FBG2 FBG3

0 15400843 15352864 153047221 15400578 1535336 153043562 15400352 15353691 153039943 15400033 15354215 153036584 15399825 15354581 153032235 15399491 15354874 15302847

120582FBG2 = 00407120572 + 15353 (1198772 = 09935) and 120582FBG3 =

minus00375120572 + 15305 (1198772 = 09988) Due to the fact that theverticality angle 120572 is very small its sine value equals itselfRelationship between 120582

119861and 120572 presents excellent linearity

and the verticality measuring sensitivities are 267 pm∘407 pm∘ and 375 pm∘ severally All these verticality coef-ficients are available just under calibration experiment con-ditions So this TVFBG sensor realizes verticality measuring


404550

Orig

inal

signa

l (m

V)

0 01 02 03 04 05 06 07 08 09 1

Time (s)

(a)

05

0 01 02 03 04 05 06 07 08 09 1

Time (s)

minus5

IMF1

(mV

)

(b)

05

0 01 02 03 04 05 06 07 08 09 1

Time (s)

minus5

IMF2

(mV

)

(c)

01

0 01 02 03 04 05 06 07 08 09 1

Time (s)

minus1

IMF3

(mV

)

(d)

01

minus1IMF1

1(m

V)

0 01 02 03 04 05 06 07 08 09 1

Time (s)

(e)

404550

0 01 02 03 04 05 06 07 08 09 1

Time (s)

Tren

dsig

nal (

mV

)

(f)

Figure 9 Sample data analyzed by HHT

and shows excellent measuring linearity at small verticalityangle ranges

6 Wrist Rotation AngleMeasurement Experiment

So as to verify the practical value of this TVEBG sensor wristrotation angle measurement experiment is implementedWrist rotation angle changes from minus10∘ to 10∘ with stepinterval of 5∘ under the same condition in verticality mea-suring experiment Sense 2020 is chosen as the dynamicfiber interrogator Wavelength data of FBG1 correspondingto angle 0∘ are selected as sample data to explain signalprocessing The sample data processed by HHT is shown inFigure 9

After HHT analysis trend signals are chosen as thecorresponding verticality angle data Using the same signalprocessing methods the extracted data are shown in Table 5

Least squares method is used to acquire verticality mea-suring sensitivities and these values corresponding to TFBGsare 252 pm∘ 382 pm∘ and 383 pm∘ separately Hence thissensor can be used in practical measurement

7 Conclusion

A three-component FBGvibration sensorwhich could simul-taneously measure vibration temperature and verticality isrealized in this paper Project matrix theory is chosen asbasic theory to establish this sensor theatrical calculationmodel HHT is used to analyze this sensorrsquos wavelengthsignals and reconstruct measurand Calibration experimentsconsisting of frequency response temperature sensitivity andverticality measuring experiment are carried out Calibrationexperiments data confirm that this sensor could realizefrequency temperature and verticality measurements with

Table 5 Extracted center wavelength data analyzed by HHT

Wrist rotationangle 120572∘

Center wavelength of FBGnmFBG1 FBG2 FBG3

minus10 154031 1534899 1530858

minus5 15402125 15350854 15306487

0 15400843 15352864 15304722

5 15399491 15354874 15302847

10 15398126 1535653 1530082

high precision This TVFBG sensorrsquos frequency measuringerrors at ranges of 100ndash1000Hz are all less than 1 andits temperature and verticality measuring sensitivities are113 pm∘C 134 pm∘C 112 pm∘C 267 pm∘ 407 pm∘ and375 pm∘ In order to further verify this sensor practical valuewrist rotation angle experiment is also implemented Wristrotation experiment results show that this sensor realizeswrist angle measuring and its sensitivities are 252 pm∘382 pm∘ and 383 pm∘ All these experiment data prove thatthis sensor has certain practical value in engineering

Conflict of Interests

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

Acknowledgments

This work is cosupported by the National Natural Sci-ence Foundation of China under Grant nos 61174018 and41202206 and Independent Innovation Foundation of Shan-dong University under Grant no yzc12081


References

[1] T-C Liang and Y-L Lin ldquoGround vibrations detection withfiber optic sensorrdquo Optics Communications vol 285 no 9 pp2363ndash2367 2012

[2] G Wild ldquoOptical fiber bragg grating sensors applied to gasturbine engine instrumentation andmonitoringrdquo inProceedingsof the 8th IEEE Sensors Applications Symposium (SASrsquo13) pp188ndash192 Galveston Tex USA February 2013

[3] R Chintakindi and S P S Rajesh ldquoVital role of FBG sensorsmdash2012 developments in electrical power systemsrdquo in Proceedingsof the International Conference Power Energy and Control(ICPEC rsquo13) pp 478ndash483 Sri RangalatchumDindigul February2013

[4] W Ecke and M W Schmitt ldquoFiber bragg gratings in industrialsensingrdquo in Proceedings of the Optical Fiber CommunicationConference and Exposition and the National Fiber Optic Engi-neers Conference (OFCNFOEC rsquo13) pp 1ndash67 March 2013

[5] H-H Zhu J-H Yin L Zhang W Jin and J-H DongldquoMonitoring internal displacements of a model dam using FBGsensing barsrdquo Advances in Structural Engineering vol 13 no 2pp 249ndash261 2010

[6] H-H Zhu J-H Yin A T Yeung and W Jin ldquoField pullouttesting and performance evaluation of GFRP soil nailsrdquo Journalof Geotechnical and Geoenvironmental Engineering vol 137 no7 pp 633ndash642 2011

[7] 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

[8] HH Zhu B Shi J F Yan J Zhang C C Zhang and B JWangldquoFiber Bragg grating-based performance monitoring of a slopemodel subjected to seepagerdquo Smart Materials and Structuresvol 23 no 9 Article ID 095027 2014

[9] Y J Rao P J Henderson D A Jackson L Zhang andI Bennion ldquoSimultaneous strain temperature and vibrationmeasurement using a multiplexed in-fibre-Bragg-gratingfibre-Fabry-Perot sensor systemrdquo Electronics Letters vol 33 no 24pp 2063ndash2064 1997

[10] Q Zhang T Zhu J D Zhang and K S Chiang ldquoMicro-fiber-based FBG sensor for simultaneous measurement of vibrationand temperaturerdquo IEEE Photonics Technology Letters vol 25 no18 pp 1751ndash1753 2013

[11] P-F Liu G-J Liu Q Zhao Y-J Wang and F Li ldquoA studyof the development and application of fiber Bragg gratingpressure sensorsrdquo in Proceedings of the Academic InternationalSymposium on Optoelectronics and Microelectronics Technology(AISOMT rsquo11) pp 232ndash235 October 2011

[12] Z XWei D C SongQM Zhao andH-L Cui ldquoHigh pressuresensor based on fiber bragg grating and carbon fiber laminatedcompositerdquo IEEE Sensors Journal vol 8 no 10 pp 1615ndash16192008

[13] K O Lee K S Chiang and Z Chen ldquoTemperature-insensitivefiber-Bragg-grating-based vibration sensorrdquo Optical Engineer-ing vol 40 no 11 pp 2582ndash2585 2001

[14] H Tsuda ldquoFiber Bragg grating vibration-sensing system insen-sitive to Bragg wavelength and employing fiber ring laserrdquoOptics Letters vol 35 no 14 pp 2349ndash2351 2010

[15] H-K Kang H-J Bang C-S Hong and C-G Kim ldquoSimul-taneous measurement of strain temperature and vibrationfrequency using a fibre optic sensorrdquoMeasurement Science andTechnology vol 13 no 8 pp 1191ndash1196 2002

[16] H L Bao X Y Dong L-Y Shao C-L Zhao and S JinldquoTemperature-insensitive 2-D tilt sensor by incorporating fiberBragg gratings with a hybrid pendulumrdquo Optics Communica-tions vol 283 no 24 pp 5021ndash5024 2010

[17] C L Xu C Liang B Zhou and S Wang ldquoHHT analysisof electrostatic fluctuation signals in dense-phase pneumaticconveying of pulverized coal at high pressurerdquo Chemical Engi-neering Science vol 65 no 4 pp 1334ndash1344 2010

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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



(a) Schematic diagram of metal transfer structure (b) Prototype of this TVFBG sensor

(c) Sensing element component parts (d) Components of link rob

Figure 1 Basic block diagram and prototype of this TVFBG sensor

used to analyze the dynamic wavelength signals Calibrationexperiment is carried out to test this sensor performance andwrist rotation angle measurement experiment further provesits practical value

Generally speaking in this sensor polymer and metaldiaphragm sensitization methods are used to improve itsmeasuring sensitivityTheoretical calculationmodel based onproject matrix theory is set up and HHT is utilized to extractand reconstruct the measurand It realizes three-parametermeasurement at the same time Due to calibration andwrist rotation measurement experiment results this TVFBGsensor possesses great potential in engineering application

2 Structure of the TVFBG Sensor

Basic metal transfer structure and prototype of this TVFBGsensor are shown in Figure 1 This TVFBG sensor is com-posed of three sensing elements and one metal transferstructure All these three sensing elements are equidistantdistributed around the axial direction and the angle interval is120∘ in the circumferential distribution The sensing elementwhich is shown in Figure 1(c) includes two connectionterminals one spring as the elastic element and one fiberBragg grating as sensitive element

Metal transfer structure shown in Figure 1(a) is made upby three link rods upper fixed and lower free rings Link rodexhibited in Figure 1(d) is composed of two omnidirectionalwheels distributed at both ends and the middle elasticelement Basic geometric parameters of this metal transferstructure are presented in Table 1

3 Signal Analysis andMeasurand Identification

Due to the advantages unlimited by fixed wavelet andadaptive signal processing HHT [13 17] is widely adoptedas a powerful tool to deal with nonlinear and nonstationarysignals HHT is utilized to pick out three different signals

Table 1 Basic geometric parameters of metal transfer structure(unit mm)

Length Height Outer radius Inner radiusThe ring 7 110 70Link rod 155 4Omnidirectionalwheel 5

Elastomer in themiddle of link rod 25 5 4

Δ120582119894119881 Δ120582119894119879 and Δ120582

119894119875(119894 = 1 2 3) from the original center

wavelengths 120582FBG119894 (119894 = 1 2 3) Δ120582119894119881 Δ120582119894119879 and Δ120582

119894119875are

wavelength changes caused by external vibration tempera-ture and verticality angle Through analyzing by HHT theoriginal signals could be expressed as

120582FBG1 = 12058210+

119899

sum

119894=1

1198881119894

120582FBG2 = 12058220+

119899

sum

119894=1

1198882119894

120582FBG3 = 12058230+

119899

sum

119894=1

1198883119894

(1)

where 1205821198940(119894 = 1 2 3) and 119888

119898119894(119898 = 1 2 3) stand for residual

signals and intrinsic mode functions of the original signals

31 Vibration Identification Because of middle elastic ele-ment the external vibration signal induces axial dynamicstrain on these TFBGs and further leads to the centerwavelength changes Relationship between axial strain 120576 andcenter wavelength shift Δ120582 could be expressed as

Δ120582

120582= (1 minus 119901

119890) 120576 (2)


(a) (b)




119865 = 119864120576 = 119896119890sdot 119881 (119905) (3)




Δ1205821119881

=(1 minus 119901

119890)

119864sdot 12058210sdot 1198961198901sdot 1198811(119905)

Δ1205822119881

=(1 minus 119901

119890)

119864sdot 12058220sdot 1198961198902sdot 1198812(119905)

Δ1205823119881

=(1 minus 119901

119890)

119864sdot 12058230sdot 1198961198903sdot 1198813(119905) or

[[

[

Δ1205821119881

Δ1205822119881

Δ1205823119881

]]

]

= V sdot[[

[

1198811(119905)

1198812(119905)

1198813(119905)

]]

]

(4)

where1198811(119905)1198812(119905) and119881




Δ1205821119879

= 12058210sdot (120572 + 120585) sdot 119879

1(119905)

Δ1205822119879

= 12058220sdot (120572 + 120585) sdot 119879

2(119905)

Δ1205823119879

= 12058230sdot (120572 + 120585) sdot 119879

3(119905) or

[[

[

Δ1205821119879

Δ1205822119879

Δ1205823119879

]]

]

= T sdot[[

[

1198791(119905)

1198792(119905)

1198793(119905)

]]

]

(5)


1(119905) 1198792(119905) and 119879






are expressed as

Δ1198711= 119903 (1 + cos 120579) sdot sin120572

Δ1198712= 119903 [1 minus cos(120587

3+ 120579)] sdot sin120572

Δ1198713= 119903 [1 minus cos(120587


(6)



Δ1205821V = 120582


119890) sdot 119903 (1 + cos 120579) sdot sin120572

ℎ

Δ1205822V = 120582


119890) sdot 119903 [1 minus cos(120587

3+ 120579)] sdot

sin120572ℎ

Δ1205823V = 120582


119890) sdot 119903 [1 minus cos(120587


sin120572ℎ

or

[[

[

Δ1205821V

Δ1205822V

Δ1205823V

]]

]

= V sdot[[

[

1198751(119905)

1198752(119905)

1198753(119905)

]]

]

(7)


x

Y

FBG1

FBG3FBG2

120579

1

120∘ 120

∘

120∘


X

Y

Z

r

h

1

120572

120572







(119894 = 1 2 3)


3(119905) are



3(119905) are



119894119875(119894 = 1 2 3) to (7)


[[

[

Δ120582FBG1

Δ120582FBG2

Δ120582FBG3

]]

]

HHT997888rarr

[[[[[[[[[[[[[[[[[[[

[

Δ1205821119881

Δ1205822119881

Δ1205823119881

Δ1205821119879

Δ1205822119879

Δ1205823119879

Δ1205821119875

Δ1205822119875

Δ1205823119875

]]]]]]]]]]]]]]]]]]]

]

=[[

[

VT

P

]]

]

[[[[[[[[[[[[[[[[[[

[

1198811(119905)

1198812(119905)

1198813(119905)

1198791(119905)

1198792(119905)

1198793(119905)

1198751(119905)

1198752(119905)

1198753(119905)

]]]]]]]]]]]]]]]]]]

]

(8)





LightCirculator

Sense 2020


Vibrationplatform


JZ-1

YJ9A














Portablecomputer

Gauze wire


Transmission fiber


CouplerCL







120575119865=(119865FBG119894 minus 119865119881119878)

119865119881119878

sdot 100 (9)



200

minus200

Am

plitu

de

50 60 70 80 90 100 110 120 130 140 150

Frequency (Hz)

(a) 100Hz


Am

plitu

de

Frequency (Hz)455 465 475 485 495 505 515 525 535 545

(b) 500Hz

Frequency (Hz) 1004028312000110001000090008000700060005000400020001000

0minus1000

960 970 980 990 1000 1010 1020 1030 1040 1050


Am

plitu

de

Frequency (Hz)

(c) 1000Hz





100 1004028 1004028 1004028200 2008057 2008057 2008057300 3012085 3012085 3012085400 4013062 4016113 4013062500 5020142 5020142 5020142600 602417 602417 602417700 7028198 7028198 7028198800 8032227 8032227 8032227900 9036255 9036255 90362551000 10040283 10040283 10040283

where 119865FBG119894 (119894 = 1 2 3) and 119865119881119878






15405

15406

15407

15408

15409

1541

20 25 30 35 40 45 50 55 60

Cen

ter w

avele

ngth

(nm

)FBG1



Temperature (∘C)

(a)

15343

15344

15345

15346

15347

15348

15349

20 25 30 35 40 45 50 55 60

FBG2

Cen

ter w

avele

ngth

(nm

)



Temperature (∘C)

(b)

15307

15308

15309

1531

15311

15312

20 25 30 35 40 45 50 55 60

Cen

ter w

avele

ngth

(nm

)



Temperature (

FBG3

∘C)

(c)




20 1540400517 1534314647 153070388125 1540553308 153440965 153074972430 1540609982 1534470089 153080400235 1540666616 1534529987 153086077640 1540724015 1534593595 153091899245 1540780719 1534657476 153097915250 1540838631 153472566 153103974255 1540897591 1534797819 153110008660 1540952174 1534864976 1531129372






0 15400843 15352864 153047221 15400578 1535336 153043562 15400352 15353691 153039943 15400033 15354215 153036584 15399825 15354581 153032235 15399491 15354874 15302847

120582FBG2 = 00407120572 + 15353 (1198772 = 09935) and 120582FBG3 =





404550

Orig

inal

signa

l (m

V)

0 01 02 03 04 05 06 07 08 09 1

Time (s)

(a)

05

0 01 02 03 04 05 06 07 08 09 1

Time (s)

minus5

IMF1

(mV

)

(b)

05

0 01 02 03 04 05 06 07 08 09 1

Time (s)

minus5

IMF2

(mV

)

(c)

01

0 01 02 03 04 05 06 07 08 09 1

Time (s)

minus1

IMF3

(mV

)

(d)

01

minus1IMF1

1(m

V)

0 01 02 03 04 05 06 07 08 09 1

Time (s)

(e)

404550

0 01 02 03 04 05 06 07 08 09 1

Time (s)

Tren

dsig

nal (

mV

)

(f)







7 Conclusion





minus10 154031 1534899 1530858

minus5 15402125 15350854 15306487

0 15400843 15352864 15304722

5 15399491 15354874 15302847

10 15398126 1535653 1530082




Acknowledgments



References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)




119865 = 119864120576 = 119896119890sdot 119881 (119905) (3)




Δ1205821119881

=(1 minus 119901

119890)

119864sdot 12058210sdot 1198961198901sdot 1198811(119905)

Δ1205822119881

=(1 minus 119901

119890)

119864sdot 12058220sdot 1198961198902sdot 1198812(119905)

Δ1205823119881

=(1 minus 119901

119890)

119864sdot 12058230sdot 1198961198903sdot 1198813(119905) or

[[

[

Δ1205821119881

Δ1205822119881

Δ1205823119881

]]

]

= V sdot[[

[

1198811(119905)

1198812(119905)

1198813(119905)

]]

]

(4)

where1198811(119905)1198812(119905) and119881




Δ1205821119879

= 12058210sdot (120572 + 120585) sdot 119879

1(119905)

Δ1205822119879

= 12058220sdot (120572 + 120585) sdot 119879

2(119905)

Δ1205823119879

= 12058230sdot (120572 + 120585) sdot 119879

3(119905) or

[[

[

Δ1205821119879

Δ1205822119879

Δ1205823119879

]]

]

= T sdot[[

[

1198791(119905)

1198792(119905)

1198793(119905)

]]

]

(5)


1(119905) 1198792(119905) and 119879






are expressed as

Δ1198711= 119903 (1 + cos 120579) sdot sin120572

Δ1198712= 119903 [1 minus cos(120587

3+ 120579)] sdot sin120572

Δ1198713= 119903 [1 minus cos(120587


(6)



Δ1205821V = 120582


119890) sdot 119903 (1 + cos 120579) sdot sin120572

ℎ

Δ1205822V = 120582


119890) sdot 119903 [1 minus cos(120587

3+ 120579)] sdot

sin120572ℎ

Δ1205823V = 120582


119890) sdot 119903 [1 minus cos(120587


sin120572ℎ

or

[[

[

Δ1205821V

Δ1205822V

Δ1205823V

]]

]

= V sdot[[

[

1198751(119905)

1198752(119905)

1198753(119905)

]]

]

(7)


x

Y

FBG1

FBG3FBG2

120579

1

120∘ 120

∘

120∘


X

Y

Z

r

h

1

120572

120572







(119894 = 1 2 3)


3(119905) are



3(119905) are



119894119875(119894 = 1 2 3) to (7)


[[

[

Δ120582FBG1

Δ120582FBG2

Δ120582FBG3

]]

]

HHT997888rarr

[[[[[[[[[[[[[[[[[[[

[

Δ1205821119881

Δ1205822119881

Δ1205823119881

Δ1205821119879

Δ1205822119879

Δ1205823119879

Δ1205821119875

Δ1205822119875

Δ1205823119875

]]]]]]]]]]]]]]]]]]]

]

=[[

[

VT

P

]]

]

[[[[[[[[[[[[[[[[[[

[

1198811(119905)

1198812(119905)

1198813(119905)

1198791(119905)

1198792(119905)

1198793(119905)

1198751(119905)

1198752(119905)

1198753(119905)

]]]]]]]]]]]]]]]]]]

]

(8)





LightCirculator

Sense 2020


Vibrationplatform


JZ-1

YJ9A














Portablecomputer

Gauze wire


Transmission fiber


CouplerCL







120575119865=(119865FBG119894 minus 119865119881119878)

119865119881119878

sdot 100 (9)



200

minus200

Am

plitu

de

50 60 70 80 90 100 110 120 130 140 150

Frequency (Hz)

(a) 100Hz


Am

plitu

de

Frequency (Hz)455 465 475 485 495 505 515 525 535 545

(b) 500Hz

Frequency (Hz) 1004028312000110001000090008000700060005000400020001000

0minus1000

960 970 980 990 1000 1010 1020 1030 1040 1050


Am

plitu

de

Frequency (Hz)

(c) 1000Hz





100 1004028 1004028 1004028200 2008057 2008057 2008057300 3012085 3012085 3012085400 4013062 4016113 4013062500 5020142 5020142 5020142600 602417 602417 602417700 7028198 7028198 7028198800 8032227 8032227 8032227900 9036255 9036255 90362551000 10040283 10040283 10040283

where 119865FBG119894 (119894 = 1 2 3) and 119865119881119878






15405

15406

15407

15408

15409

1541

20 25 30 35 40 45 50 55 60

Cen

ter w

avele

ngth

(nm

)FBG1



Temperature (∘C)

(a)

15343

15344

15345

15346

15347

15348

15349

20 25 30 35 40 45 50 55 60

FBG2

Cen

ter w

avele

ngth

(nm

)



Temperature (∘C)

(b)

15307

15308

15309

1531

15311

15312

20 25 30 35 40 45 50 55 60

Cen

ter w

avele

ngth

(nm

)



Temperature (

FBG3

∘C)

(c)




20 1540400517 1534314647 153070388125 1540553308 153440965 153074972430 1540609982 1534470089 153080400235 1540666616 1534529987 153086077640 1540724015 1534593595 153091899245 1540780719 1534657476 153097915250 1540838631 153472566 153103974255 1540897591 1534797819 153110008660 1540952174 1534864976 1531129372






0 15400843 15352864 153047221 15400578 1535336 153043562 15400352 15353691 153039943 15400033 15354215 153036584 15399825 15354581 153032235 15399491 15354874 15302847

120582FBG2 = 00407120572 + 15353 (1198772 = 09935) and 120582FBG3 =





404550

Orig

inal

signa

l (m

V)

0 01 02 03 04 05 06 07 08 09 1

Time (s)

(a)

05

0 01 02 03 04 05 06 07 08 09 1

Time (s)

minus5

IMF1

(mV

)

(b)

05

0 01 02 03 04 05 06 07 08 09 1

Time (s)

minus5

IMF2

(mV

)

(c)

01

0 01 02 03 04 05 06 07 08 09 1

Time (s)

minus1

IMF3

(mV

)

(d)

01

minus1IMF1

1(m

V)

0 01 02 03 04 05 06 07 08 09 1

Time (s)

(e)

404550

0 01 02 03 04 05 06 07 08 09 1

Time (s)

Tren

dsig

nal (

mV

)

(f)







7 Conclusion





minus10 154031 1534899 1530858

minus5 15402125 15350854 15306487

0 15400843 15352864 15304722

5 15399491 15354874 15302847

10 15398126 1535653 1530082




Acknowledgments



References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










x

Y

FBG1

FBG3FBG2

120579

1

120∘ 120

∘

120∘


X

Y

Z

r

h

1

120572

120572







(119894 = 1 2 3)


3(119905) are



3(119905) are



119894119875(119894 = 1 2 3) to (7)


[[

[

Δ120582FBG1

Δ120582FBG2

Δ120582FBG3

]]

]

HHT997888rarr

[[[[[[[[[[[[[[[[[[[

[

Δ1205821119881

Δ1205822119881

Δ1205823119881

Δ1205821119879

Δ1205822119879

Δ1205823119879

Δ1205821119875

Δ1205822119875

Δ1205823119875

]]]]]]]]]]]]]]]]]]]

]

=[[

[

VT

P

]]

]

[[[[[[[[[[[[[[[[[[

[

1198811(119905)

1198812(119905)

1198813(119905)

1198791(119905)

1198792(119905)

1198793(119905)

1198751(119905)

1198752(119905)

1198753(119905)

]]]]]]]]]]]]]]]]]]

]

(8)





LightCirculator

Sense 2020


Vibrationplatform


JZ-1

YJ9A














Portablecomputer

Gauze wire


Transmission fiber


CouplerCL







120575119865=(119865FBG119894 minus 119865119881119878)

119865119881119878

sdot 100 (9)



200

minus200

Am

plitu

de

50 60 70 80 90 100 110 120 130 140 150

Frequency (Hz)

(a) 100Hz


Am

plitu

de

Frequency (Hz)455 465 475 485 495 505 515 525 535 545

(b) 500Hz

Frequency (Hz) 1004028312000110001000090008000700060005000400020001000

0minus1000

960 970 980 990 1000 1010 1020 1030 1040 1050


Am

plitu

de

Frequency (Hz)

(c) 1000Hz





100 1004028 1004028 1004028200 2008057 2008057 2008057300 3012085 3012085 3012085400 4013062 4016113 4013062500 5020142 5020142 5020142600 602417 602417 602417700 7028198 7028198 7028198800 8032227 8032227 8032227900 9036255 9036255 90362551000 10040283 10040283 10040283

where 119865FBG119894 (119894 = 1 2 3) and 119865119881119878






15405

15406

15407

15408

15409

1541

20 25 30 35 40 45 50 55 60

Cen

ter w

avele

ngth

(nm

)FBG1



Temperature (∘C)

(a)

15343

15344

15345

15346

15347

15348

15349

20 25 30 35 40 45 50 55 60

FBG2

Cen

ter w

avele

ngth

(nm

)



Temperature (∘C)

(b)

15307

15308

15309

1531

15311

15312

20 25 30 35 40 45 50 55 60

Cen

ter w

avele

ngth

(nm

)



Temperature (

FBG3

∘C)

(c)




20 1540400517 1534314647 153070388125 1540553308 153440965 153074972430 1540609982 1534470089 153080400235 1540666616 1534529987 153086077640 1540724015 1534593595 153091899245 1540780719 1534657476 153097915250 1540838631 153472566 153103974255 1540897591 1534797819 153110008660 1540952174 1534864976 1531129372






0 15400843 15352864 153047221 15400578 1535336 153043562 15400352 15353691 153039943 15400033 15354215 153036584 15399825 15354581 153032235 15399491 15354874 15302847

120582FBG2 = 00407120572 + 15353 (1198772 = 09935) and 120582FBG3 =





404550

Orig

inal

signa

l (m

V)

0 01 02 03 04 05 06 07 08 09 1

Time (s)

(a)

05

0 01 02 03 04 05 06 07 08 09 1

Time (s)

minus5

IMF1

(mV

)

(b)

05

0 01 02 03 04 05 06 07 08 09 1

Time (s)

minus5

IMF2

(mV

)

(c)

01

0 01 02 03 04 05 06 07 08 09 1

Time (s)

minus1

IMF3

(mV

)

(d)

01

minus1IMF1

1(m

V)

0 01 02 03 04 05 06 07 08 09 1

Time (s)

(e)

404550

0 01 02 03 04 05 06 07 08 09 1

Time (s)

Tren

dsig

nal (

mV

)

(f)







7 Conclusion





minus10 154031 1534899 1530858

minus5 15402125 15350854 15306487

0 15400843 15352864 15304722

5 15399491 15354874 15302847

10 15398126 1535653 1530082




Acknowledgments



References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










LightCirculator

Sense 2020


Vibrationplatform


JZ-1

YJ9A














Portablecomputer

Gauze wire


Transmission fiber


CouplerCL







120575119865=(119865FBG119894 minus 119865119881119878)

119865119881119878

sdot 100 (9)



200

minus200

Am

plitu

de

50 60 70 80 90 100 110 120 130 140 150

Frequency (Hz)

(a) 100Hz


Am

plitu

de

Frequency (Hz)455 465 475 485 495 505 515 525 535 545

(b) 500Hz

Frequency (Hz) 1004028312000110001000090008000700060005000400020001000

0minus1000

960 970 980 990 1000 1010 1020 1030 1040 1050


Am

plitu

de

Frequency (Hz)

(c) 1000Hz





100 1004028 1004028 1004028200 2008057 2008057 2008057300 3012085 3012085 3012085400 4013062 4016113 4013062500 5020142 5020142 5020142600 602417 602417 602417700 7028198 7028198 7028198800 8032227 8032227 8032227900 9036255 9036255 90362551000 10040283 10040283 10040283

where 119865FBG119894 (119894 = 1 2 3) and 119865119881119878






15405

15406

15407

15408

15409

1541

20 25 30 35 40 45 50 55 60

Cen

ter w

avele

ngth

(nm

)FBG1



Temperature (∘C)

(a)

15343

15344

15345

15346

15347

15348

15349

20 25 30 35 40 45 50 55 60

FBG2

Cen

ter w

avele

ngth

(nm

)



Temperature (∘C)

(b)

15307

15308

15309

1531

15311

15312

20 25 30 35 40 45 50 55 60

Cen

ter w

avele

ngth

(nm

)



Temperature (

FBG3

∘C)

(c)




20 1540400517 1534314647 153070388125 1540553308 153440965 153074972430 1540609982 1534470089 153080400235 1540666616 1534529987 153086077640 1540724015 1534593595 153091899245 1540780719 1534657476 153097915250 1540838631 153472566 153103974255 1540897591 1534797819 153110008660 1540952174 1534864976 1531129372






0 15400843 15352864 153047221 15400578 1535336 153043562 15400352 15353691 153039943 15400033 15354215 153036584 15399825 15354581 153032235 15399491 15354874 15302847

120582FBG2 = 00407120572 + 15353 (1198772 = 09935) and 120582FBG3 =





404550

Orig

inal

signa

l (m

V)

0 01 02 03 04 05 06 07 08 09 1

Time (s)

(a)

05

0 01 02 03 04 05 06 07 08 09 1

Time (s)

minus5

IMF1

(mV

)

(b)

05

0 01 02 03 04 05 06 07 08 09 1

Time (s)

minus5

IMF2

(mV

)

(c)

01

0 01 02 03 04 05 06 07 08 09 1

Time (s)

minus1

IMF3

(mV

)

(d)

01

minus1IMF1

1(m

V)

0 01 02 03 04 05 06 07 08 09 1

Time (s)

(e)

404550

0 01 02 03 04 05 06 07 08 09 1

Time (s)

Tren

dsig

nal (

mV

)

(f)







7 Conclusion





minus10 154031 1534899 1530858

minus5 15402125 15350854 15306487

0 15400843 15352864 15304722

5 15399491 15354874 15302847

10 15398126 1535653 1530082




Acknowledgments



References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











200

minus200

Am

plitu

de

50 60 70 80 90 100 110 120 130 140 150

Frequency (Hz)

(a) 100Hz


Am

plitu

de

Frequency (Hz)455 465 475 485 495 505 515 525 535 545

(b) 500Hz

Frequency (Hz) 1004028312000110001000090008000700060005000400020001000

0minus1000

960 970 980 990 1000 1010 1020 1030 1040 1050


Am

plitu

de

Frequency (Hz)

(c) 1000Hz





100 1004028 1004028 1004028200 2008057 2008057 2008057300 3012085 3012085 3012085400 4013062 4016113 4013062500 5020142 5020142 5020142600 602417 602417 602417700 7028198 7028198 7028198800 8032227 8032227 8032227900 9036255 9036255 90362551000 10040283 10040283 10040283

where 119865FBG119894 (119894 = 1 2 3) and 119865119881119878






15405

15406

15407

15408

15409

1541

20 25 30 35 40 45 50 55 60

Cen

ter w

avele

ngth

(nm

)FBG1



Temperature (∘C)

(a)

15343

15344

15345

15346

15347

15348

15349

20 25 30 35 40 45 50 55 60

FBG2

Cen

ter w

avele

ngth

(nm

)



Temperature (∘C)

(b)

15307

15308

15309

1531

15311

15312

20 25 30 35 40 45 50 55 60

Cen

ter w

avele

ngth

(nm

)



Temperature (

FBG3

∘C)

(c)




20 1540400517 1534314647 153070388125 1540553308 153440965 153074972430 1540609982 1534470089 153080400235 1540666616 1534529987 153086077640 1540724015 1534593595 153091899245 1540780719 1534657476 153097915250 1540838631 153472566 153103974255 1540897591 1534797819 153110008660 1540952174 1534864976 1531129372






0 15400843 15352864 153047221 15400578 1535336 153043562 15400352 15353691 153039943 15400033 15354215 153036584 15399825 15354581 153032235 15399491 15354874 15302847

120582FBG2 = 00407120572 + 15353 (1198772 = 09935) and 120582FBG3 =





404550

Orig

inal

signa

l (m

V)

0 01 02 03 04 05 06 07 08 09 1

Time (s)

(a)

05

0 01 02 03 04 05 06 07 08 09 1

Time (s)

minus5

IMF1

(mV

)

(b)

05

0 01 02 03 04 05 06 07 08 09 1

Time (s)

minus5

IMF2

(mV

)

(c)

01

0 01 02 03 04 05 06 07 08 09 1

Time (s)

minus1

IMF3

(mV

)

(d)

01

minus1IMF1

1(m

V)

0 01 02 03 04 05 06 07 08 09 1

Time (s)

(e)

404550

0 01 02 03 04 05 06 07 08 09 1

Time (s)

Tren

dsig

nal (

mV

)

(f)







7 Conclusion





minus10 154031 1534899 1530858

minus5 15402125 15350854 15306487

0 15400843 15352864 15304722

5 15399491 15354874 15302847

10 15398126 1535653 1530082




Acknowledgments



References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










15405

15406

15407

15408

15409

1541

20 25 30 35 40 45 50 55 60

Cen

ter w

avele

ngth

(nm

)FBG1



Temperature (∘C)

(a)

15343

15344

15345

15346

15347

15348

15349

20 25 30 35 40 45 50 55 60

FBG2

Cen

ter w

avele

ngth

(nm

)



Temperature (∘C)

(b)

15307

15308

15309

1531

15311

15312

20 25 30 35 40 45 50 55 60

Cen

ter w

avele

ngth

(nm

)



Temperature (

FBG3

∘C)

(c)




20 1540400517 1534314647 153070388125 1540553308 153440965 153074972430 1540609982 1534470089 153080400235 1540666616 1534529987 153086077640 1540724015 1534593595 153091899245 1540780719 1534657476 153097915250 1540838631 153472566 153103974255 1540897591 1534797819 153110008660 1540952174 1534864976 1531129372






0 15400843 15352864 153047221 15400578 1535336 153043562 15400352 15353691 153039943 15400033 15354215 153036584 15399825 15354581 153032235 15399491 15354874 15302847

120582FBG2 = 00407120572 + 15353 (1198772 = 09935) and 120582FBG3 =





404550

Orig

inal

signa

l (m

V)

0 01 02 03 04 05 06 07 08 09 1

Time (s)

(a)

05

0 01 02 03 04 05 06 07 08 09 1

Time (s)

minus5

IMF1

(mV

)

(b)

05

0 01 02 03 04 05 06 07 08 09 1

Time (s)

minus5

IMF2

(mV

)

(c)

01

0 01 02 03 04 05 06 07 08 09 1

Time (s)

minus1

IMF3

(mV

)

(d)

01

minus1IMF1

1(m

V)

0 01 02 03 04 05 06 07 08 09 1

Time (s)

(e)

404550

0 01 02 03 04 05 06 07 08 09 1

Time (s)

Tren

dsig

nal (

mV

)

(f)







7 Conclusion





minus10 154031 1534899 1530858

minus5 15402125 15350854 15306487

0 15400843 15352864 15304722

5 15399491 15354874 15302847

10 15398126 1535653 1530082




Acknowledgments



References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










404550

Orig

inal

signa

l (m

V)

0 01 02 03 04 05 06 07 08 09 1

Time (s)

(a)

05

0 01 02 03 04 05 06 07 08 09 1

Time (s)

minus5

IMF1

(mV

)

(b)

05

0 01 02 03 04 05 06 07 08 09 1

Time (s)

minus5

IMF2

(mV

)

(c)

01

0 01 02 03 04 05 06 07 08 09 1

Time (s)

minus1

IMF3

(mV

)

(d)

01

minus1IMF1

1(m

V)

0 01 02 03 04 05 06 07 08 09 1

Time (s)

(e)

404550

0 01 02 03 04 05 06 07 08 09 1

Time (s)

Tren

dsig

nal (

mV

)

(f)







7 Conclusion





minus10 154031 1534899 1530858

minus5 15402125 15350854 15306487

0 15400843 15352864 15304722

5 15399491 15354874 15302847

10 15398126 1535653 1530082




Acknowledgments



References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










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









research article study of three-component fbg vibration sensor...

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