Research Article Development of an Optical Fiber Sensor Interrogation System for Vibration Analysis

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1 Sesors Volume 216, Article ID , 8 pages Research Article Developmet of a Optical Fiber Sesor Iterrogatio System for Vibratio Aalysis Alfredo Lamberti, 1 Be De Pauw, 1,2 ad Steve Valaduit 1,3 1 Departmet of Mechaical Egieerig, Vrije Uiversiteit Brussel, Pleilaa 2, 15 Brussels, Belgium 2 DepartmetofAppliedPhysicsadPhotoics,VrijeUiversiteitBrussel,Pleilaa2,15Brussels,Belgium 3 Op3Mech Research Group, Faculty of Applied Egieerig, Uiversity of Atwerp, Salesiaelaa 9, 266 Atwerp, Belgium Correspodece should be addressed to Steve Valaduit; steve.valaduit@uatwerpe.be Received 21 November 215; Accepted 7 March 216 Academic Editor: Lu-Kai Cheg Copyright 216 Alfredo Lamberti et al. This is a ope access article distributed uder the Creative Commos Attributio Licese, which permits urestricted use, distributio, ad reproductio i ay medium, provided the origial work is properly cited. Sice the itroductio of dyamic optical fiber sesor iterrogatio systems o the market it has become possible to perform vibratio measuremets at frequecies up to a few khz. Nevertheless, the use of these sesors i vibratio aalysis has ot become a stadard practice yet. This is maily caused by the fact that iterrogators are stad-aloe systems which focus o strai measuremets while other types of sigals are also required for vibratio aalysis (e.g., force sigals). I this paper, we preset a fiber Bragg gratig (FBG) iterrogatio system that eables accurate strai measuremet simultaeously with other sigals (e.g., excitatio forces). The system is based o a Vertical Cavity Surface Emittig Laser () ad ca easily be assembled with relatively low-cost off-the-shelf compoets. Dyamic measuremets up to a few tes of khz with a dyamic precisio of aroud 3 aostrai per square-root Hz ca be performed. We evaluate the proposed system o two measuremet examples: a steel beam with FBG sesors glued o top ad a composite test specime with a fiber sesor itegrated withi the material. We show that i the latter case the results of the iterrogatio system are superior i quality compared to a state-of-the-art commercially available iterrogatio system. 1. Itroductio A fiber Bragg gratig (FBG) cosists of a periodic refractive idex chage over a certai legth of a optical fiber. Whe a broadbad light source is coupled ito the fiber, light at a arrow wavelegth bad is reflected by the gratig. This wavelegth is depedig, amogst others, o the pitch of the gratig. Whe a dyamic strai is applied to the gratig a shift i the reflected wavelegth ca be observed (the strai sesitivity of typical FBG sesors is 1.2 pm/με). Several iterrogatio mechaisms exist to read out the reflected so-called Braggwavelegthpeak[1 3].Mostcommerciallyavailable fiber Bragg gratig iterrogatio systems use a broadbad light source i combiatio with a full-spectrum measuremet of the reflected ad/or trasmitted light spectrum (this full-spectrum measuremet is i particular ecessary i the case of multiplexed sesors). The rate of the readout is limited by the sca speed of the spectral measuremet techique. Recetly, MEMS based tuable filter techologies have bee proposed to measure the reflected spectrum with a sample rate up to 1 khz [4]. While this method has a large potetial i the framework of vibratio aalysis, the used compoets are ot yet commercially available. A secod class of techiques uses a tuable laser istead of a tuable detector. Exteral cavity semicoductor tuable lasersthatcabeusedforthispurposearehoweverofvery high cost. Vertical Cavity Surface Emittig Lasers (s) areaattractivealterativethatcabeusedtorealizealow costtuablelaser.theworkigpricipleoftheses is simple: they produce a arrowbad laser of which the wavelegth ca be tued by chagig the drivig curret [5]. Recet work has show that these s ca be used to successfully realize a accurate FBG iterrogator system [6]. Because of the low power requiremet ad the compact size of a, miiature based iterrogators ca eve be maufactured [7]. I [8, 9] the authors showed that by usig s dyamic measuremets with a dyamic rage of 3 dbcabeperformed.

2 2 Sesors Computer Data acquisitio system Diode driver Photodiode FBG sesor Excitatio device Structure (device uder test) Force sesor Accelerometer Figure 1: Layout of the proposed based FBG iterrogatio system. The experimet is fully cotrolled by the multipurpose data acquisitio system. I this paper we propose a based measuremet system that ca be used for vibratio aalysis. More specifically, it will be show that the proposed system has the followig specificatios: (i) The system allows the user to perform optical fiber based strai measuremets simultaeously with other measuremet quatities (accelerometers, forces, etc.). Thisisessetialwheperformigvibratioaalysis, as, for istace, a experimetal modal aalysis [1]. (ii) All compoets i the system ca be purchased offthe-shelve ad the costructio of the setup does ot require advaced expertise i electroics or optics. (iii) The system results i fairly high resolutio full-spectrum measuremets at sample rates of a few tes of khz. (iv) The dyamic precisio is aroud 3 ε per square root Hz, which is comparable with other commercial iterrogators. (v) The iterrogator is robust with respect to distortios i the optical spectrum (which are typically caused whe itegratig a FBG sesor i a composite material). I Sectio 2 the system is described i detail. I Sectio 3 we illustrate the performace of the system o two test cases: (i) A vibratio measuremet of a steel beam with a optical fiber glued o top. (ii) A vibratio measuremet of a composite T-joit specime with a itegrated optical fiber. Curretly, there are may FBG peak wavelegth iterrogators o the market which operate o a differet measuremet strategy or peak detectio scheme. I this paper we will compare the measuremet results of the proposed tests system to the results of a commercially available iterrogator: the FBG-sca 7 iterrogator from the compay FBGS. We will illustrate that the developed based iterrogator gives equal measuremet results compared to the FBG-sca 7 for the first test case. For the secod test case, i which peak distortios occur because of the itegratio, we will show that the performace of our based iterrogator is superior tha the used commercial iterrogator. This ca be explaied by the fact that a higher wavelegth resolutio is obtaied i our iterrogator ad that a more robust peak detectio method is used [11]. 2. Materials ad Methods 2.1. The Proposed Measuremet System. Our proposed FBG iterrogatio system is built aroud a (commercially available) multifuctio data acquisitio (DAQ) board which is cotrolled by a persoal computer. The setup is show i Figure 1. The aalog outputs chaels of the DAQ board are used to geerate two sigals (see gree blocks i Figure 1): (i) A sawtooth sigal that is used to geerate a liear shift ithewavelegththatisproducedbythes. (ii) A (periodic) excitatio sigal which is used to drive the excitatio device to geerate cotrolled vibratios i the structure. Two aalog iput chaels are used to measure two sigals: (a)theopticalpowerofthesigalthatisreflectedby the FBG sesor ad (b) force trasducer ad accelerometer sesor sigals. Because these sigals are measured by the same DAQ device the measuremets ca be obtaied simultaeously. Ithispaperwehaveusedthefollowigsystemcompoets: (i) Computer: a Dell Latitude E544 laptop (the measuremets are performed, processed, ad visualized i Matlab). (ii) Data acquisitio system: a Natioal Istrumets NI- USB-6363 DAQ device (the device has a maximum sample rate of 1 MHz (whe two aalog iputs are measured). This sample rate determies the sca rate of the iterrogator system: whe usig, for example,

3 Sesors Curret (ma) curret Photodiode curret Curret (ma) Figure 2: Ceter wavelegth of the sigal i fuctio of drivig curret. a iterrogatio of 1 wavelegths, full-spectrum measuremets ca be performed at a rate of 1 khz. This priciple will be explaied i more detail i Sectio 2.2). (iii) Diode driver: Thorlabs type LDC 2C Diode driver. (iv) s: VTEC 155 m pigtailed sigle mode with a output power of.5 mw. (v) Photodiode: Hamamatsu IGaAs Photodiode (A Thorlabs type PDA2C amplifier is used to measure the curret sigals. The amplifier has six gai factors. I the paper the.1 mv/v rage was used (with this rage the measuremet badwidth is 25 khz)). (vi) FBG sesors: FBGS draw tower gratigs. (vii) Excitatio device: Bruel & Kjaer Type 481 electrodyamic shaker. (viii) Force sesor ad accelerometer: PCB piezoelectric trasducers. (ix) Device uder test: (1) steel beam ad (2) carbo fiber composite T-joit specime. The diode driver geerates a curret of 2 ma through the for each volt that is applied to the driver (the iput voltage is geerated by the DAQ board sigal geerator). By applyig a liear voltage sigal betwee.75 V ad 8.25 V oe ca thus sweep the curret betwee 1.5 ma ad 16.5 ma. This results i a sweep of the wavelegth of the betwee1538mad1548mascabeseeifigure2.the wavelegth sweep is ot perfectly liear over the complete rage, but i the cotext of vibratio measuremets this does ot pose ay problem because the wavelegth shift due to vibratios will be limited to a few picometers oly. I order to perform a measuremet i a certai wavelegth rage [λ mi,λ max ], the is drive usig a sawtooth sigal which liearly varies betwee two currets that correspod to the lower wavelegth λ mi ad upper wavelegth λ max (usig the curret coversio factors show Time (secods) 1 3 Figure 3: Illustratio of the measuremet priciple. The blue lie represets the curret ad the gree curve correspods to the photodiode curret of the sigal reflected from the FBG sesor. For each sawtooth period two Bragg peaks are visible. i Figure 2). The photodiode measures the spectrum of the reflected sigal power i the wavelegth bad [λ mi,λ max ]. This Bragg peak measuremet priciple is illustrated i Figure 3. From Figure 3 it ca be see that a Bragg peak i the photodiode curret (see gree lie) is observed twice for each period of the sawtooth shaped curret sigal (blue lie i Figure 3): both at the risig edge of the sawtooth ad at the fallig edge of the sawtooth a peak occurs i the sigal. I the remaider of the paper we will use oly the Bragg peak of the risig edge. The vector cotaiig the measured photodiode currets (see gree curve i Figure 3) ca be coverted to wavelegths by usig the coversio curve give i Figure 2. The resultig vector ca be trasformed ito a matrix by puttig every record correspodig to oe rise ad fall of the sawtooth i oe colum. I this matrix the evolutio of the Bragg peak i fuctio of time is visible as ca be see i Figure 4. I the ext paragraph we will describe how we obtai the quatitative wavelegth shift values i fuctio of time Data Processig. The objective of the proposed data processig techique is to obtai the peak locatio i fuctio of time i the matrix give i Figure 4. Classical iterrogatio methods use quadratic or cubic iterpolatio of the peak to detect the maximum with subwavelegth resolutio. It is kow that this method ca result i iaccurate results if the Bragg peak is distorted [11]. I this paper we will use the phase correlatio method that was proposed recetly i [12]. The method cosists of the followig steps: (1) Calculate the FFT of the differet colums of the data matrix A represeted i Figure 4 to obtai the complex matrix B. (2) Calculate the phase value of each elemet of the complex valued FFT matrix B (usig the Matlab commad agle(b)). Deote the resultig matrix θ B.

4 4 Sesors Time (secods) Figure 4: Measuremet data matrix (deoted by A) resultig by stackig the wavelegth spectrum measured at time t i (i = 1,...,) i colum i. A zoom of 2 μsec was made i order to be able to illustrate the oscillatios of the Bragg peaks (the complete measuremet period that was measured has a duratio of 4 secods). Support Optical fiber Steel beam Force sesor Shaker Figure 5: Setup of the steel beam experimet. (3) Scale the matrix θ B by multiplyig each elemet i row k of the matrix by Nλ /2πk to obtai the matrix Δ λ (where λ is the wavelegth resolutio of the measuremet). (4) Calculate the media value of the matrix Δ λ alog the colums to arrive at the vector cotaiig wavelegth shift i fuctio of time: δλ(t 1,...,t ) (with the umber of colums of A). I this paper we have applied the above-metioed phase correlatio method to obtai strai values from all based iterrogator measuremets. The subwavelegth shifts (ad hece strais) from the FBG-sca spectra show i the remaider of the paper were obtaied from the maximum of a quadratic peak fit (this is the peak detectio method that is used i the software provided by the maufacturer FBGS). I the ext sectio we will illustrate the measuremet system o two vibratio aalysis test cases: a catilevered steel beam ad a catilevered carbo fiber composite test sample. 3. Results ad Discussio 3.1. Steel Beam Test Case. I the first example, a catilever steel beam was tested. The steel beam was clamped o a steel I-profile. A electrodyamic shaker was fixed below the beam at a positio of 1 cm from the clampig (see Figure 5). A force trasducer was used to measure the excitatio force geerated by the shaker. The beam was istrumeted with a sigle mode optical fiber i which 22 FBG sesors were placed (distributed equally alog the legth of the beam). The FBG sesors were read out sequetially with the FBG-sca 7 iterrogator (from compay FBGS) ad with the proposed based iterrogator. The optical spectra of both iterrogators ad their stadard deviatio (obtaied from 1 idepedet measuremets) are show i Figure 6. FromthefigureitcabeobservedthattheSNRoftheFBGsca is aroud 5 db compared to about 35 db for the based system. This ca be explaied by the fact that the optical powerofthelightsourceofthefbg-scaiterrogatoris cosiderably higher tha that of the (the maximum power of the is oly.5 mw). Also, the badwidth of the FBG-sca iterrogator is sigificatly larger: 4 m compared to 3 m for the based iterrogator (it ca be oted from Figure 2 that the wavelegth badwidth of the ca go up to 9m, but we have limited ourselves to a smaller badwidth i i which the depedecy betwee curret ad wavelegth is liear). This meas that i the based iterrogator oly four out of twety-two gratigs ca be measured (remark that this could be exteded by usig multiple s i the measuremet system). It should be oted the badwidth ad power of the used are somewhat limited compared to the used commercial FBG iterrogator. However, both the power ad badwidth of commercially available s are cotiuously icreasig (the tests performed i the paper were performed i May 215 with a.5 mw ad six moths later 2 mw s are available o the market). I the curret experimet we aim at readig out the FBG sesors with the based system at a rate of 5 khz (compared to the 2 khz maximum readout of the FBG-sca system).becausewehaveusedasamplerateofthedaq systemof5khz(thisisthemaximumsampleratefor four iput chaels for our device) this meas that we have 1 wavelegths i each measuremet, givig a wavelegth resolutio of 3 pm (compared to 8 pm for the FBG-sca system). We could reduce this resolutio by icreasig the samplerate(upto1mhzispossiblewiththecurretdevicei case two iputs are acquired) or by decreasig the rate of the readout. I priciple it is possible to read out FBG sesors at higher rates tha the 5 khz rate used i the paper. Oe should becarefulwheusighighfrequecysawtoothsigalsto drivethebecauseofthefollowigtworeasos: (i) The laser diode driver has a limited low-pass frequecy (i our case the Thorlabs type LDC 2C hasamaximumlow-passfrequecyof25khz).this measthatathighfrequeciesthesawtoothwillbe low-pass filtered. (ii) The itroduces hysteresis at high frequecies. I order to test ad compare the dyamic respose of both iterrogatorsystemswehaveusedtwotypesofexcitatio sigals: (i) Siusoidal excitatio at 182 Hz (ear the third resoace frequecy of the beam).

5 Sesors 5 2 Optical power (db) 2 4 Optical power (db) Reflected light Stadard deviatio (a) Reflected light Stadard deviatio (b) Figure 6: Optical spectrum ad stadard deviatio. (a) FBG-sca 7 iterrogator, (b) based iterrogator. It ca be observed that the SNR of the FBG-sca system is about 15 db larger, but o the other had the wavelegth resolutio of the based iterrogator is 2.7 times higher. Note that the FBG spectra cotai a sharp power drop-off at three of the twety-two peaks. This is caused by the saturatio due to a itegratio time which was set too high. These three peaks were ot used i the aalysis preseted i the paper. 2 Strai amplitude (db) Strai amplitude (db) Frequecy (Hz) Frequecy (Hz) FBG-sca FBG-sca (a) (b) Figure 7: Measured vibratio spectra: (a) whe usig siusoidal excitatio, (b) whe usig swept sie excitatio. (ii) Periodic chirp excitatio betwee.25 Hz ad 5 Hz. The results of these measuremets usig both iterrogatio systems are show i Figure 7. From Figure 7(a) it ca be cocluded that the SNR of the vibratio measuremets is the same for both measuremet systems: about 6 db. The oise floor of the measuremets is at 5 db which gives us a strai level precisio of 3 ε (the db referece i the plot is chose equal to 1 με). The measured amplitude of the siusoid obtaied usig both systems is equal (the differece is about 1 db), but it ca be observed that the frequecy of the FBG-sca iterrogator does ot perfectly correspod with the excitatio frequecy. This is caused by the fact that the sample times of the FBGsca system are ot sychroized with the excitatio. It should be oted that several commercial iterrogators allow sychroizatio with exteral sigals but this optio was ot used i the paper. Because of this lack of sychroizatio it is ot straightforward to calculate the Frequecy Respose Fuctios (FRFs) usig the FBG-sca system (the FRF is defied by the Fourier spectrum of the strai divided by

6 6 Sesors Optical fiber 1 Support Optical fiber 2 Force sesor Composite beam Shaker Figure 8: Setup of the composite beam experimet. the Fourier spectrum of the excitatio force applied to the structure with the shaker). Sice the based iterrogator ad the shaker are cotrolled by the same DAQ board,themeasuremetsofthefbgsesorsadtheforceare obtaied simultaeously (ad hece they are automatically sychroized). From the respose of the periodic chirp (see Figure 7(b)) the first four resoace frequecies of the beam ca be idetified. The vibratio spectra correspodig to both measuremet systems match very well (ote that the strai levels are very low, below.1 με). From the experimet we ca coclude that the based iterrogator eables us to obtai measuremets with a precisio that is close to the oe of the commercially available iterrogator (FBG-sca 7). With our based system we ca simultaeously measure strai (usig the FBG sesor) ad force sigals. This allows us to more easily calculate Frequecy Respose Fuctios (FRFs). I the ext paragraph we will show that the proposed iterrogator system is much more robust for distortios of the optical FBG spectra Composite Beam Test. Ithissectiowegivetheresultsof vibratio measuremets o a carbo fiber T-joit specime (see setup i Figure 8). The structure was istrumeted with a fiber sesor (with oe FBG gratig) that was iserted i the middle of the specime durig the maufacturig process (remark that there is a secod fiber sesor attached o the specime but this oe was ot used i the test because the wavelegth is outside the rage of the iterrogator). As was thecaseithesteelbeamexample,weusedashakerto excite the beam ad a force sesor to measure the excitatio force. Agai, the FBG sesor was read out with the FBG-sca 7 iterrogator ad the proposed based system. The optical spectra (without ay mechaical excitatio applied) are show i Figure 9. The SNR values are similar to the oes measured i the steel beam case: 6 db for the FBG-sca ad 4 db for the based system. I this measuremet case there are two importat differeces compared to the steel beam case which cabeobservedifigure9(b): (i) The spectral width of the Bragg peak is almost 5 pm (comparedtoabout1pmithecaseofthesteel beam experimet). (ii) The spectrum is heavily distorted: the top is ot flat ad side lobes appear. Thispeakdistortio,admoreiparticularpeakbroadeig, is typical for sesors that are itegrated i composite materials [13]. Note that because of the limited wavelegth resolutio i the FBG-sca aalyzer these effects caot be observed i Figure 9(a). I what follows we will show, however, that these effects ca have a large ifluece o the vibratio measuremets. We ote that i our peak detectio algorithm we have assumed that the distortios are ot chagig durig the loadig of the specime. Because i vibratio egieerig the strai variatios are usually small this assumptio is realistic (we have checked that there are ideed o sigificat chages of the peak distortios betwee the sigals measured at differet strai levels durig the loadig). Ideally, oe should compare the measured strais with a referece strai gauge. However, it is ot possible to apply such a strai gauge iterally i the composite material. Therefore,wehaveusedtwomethodstovalidateourresults: firstly, we evaluate the SNR of the two ivestigated iterrogators whe a pure siusoidal excitatio is applied. Secodly, we compare the resoace frequecies obtaied from the FBG sesors with those obtaied from a accelerometer (whe applyig a periodic chirp excitatio). I the composite beam experimet the vibratio spectra obtaied usig the FBGsca iterrogator ad the based iterrogator deviate sigificatly. Because of the distortios i the spectra, the sigal-to-oise ratio (that ca be observed whe usig the siusoidal excitatio) is about 12 db lower whe usig the FBG-sca iterrogator. Also, the broadbad vibratio spectrum of the FBG-sca system show i gree i Figure 1(b) is distorted (the resoace peak at 26 Hz caot be idetified aymore, while it is clearly preset i the acceleratio spectra). The proposed techique, o the other had, is ot sesitive to these distortios because of the followig two reasos: (i) The wavelegth resolutio is high eough to capture the distortio (16 pm compared to 8 pm for the FBGsca). (ii) The peak detectio algorithm that was used (see Sectio 2.2) is robust for distortios i the spectra (as was show i [11]). Because we simultaeously measure force ad acceleratio sigals with the based iterrogator we ca also calculate Frequecy Respose Fuctios ad compare the resultig FRFs for acceleratio (from accelerometer) ad strai (from FBG). The FRFs are displayed i Figure 11 ad they were used as a iput for a modal parameter estimatio algorithm [14]. I Table 1 the results of the first four estimated modes from accelerometer ad FBG sesor data are give. It ca be see that the errors o the idetified resoace frequecies are very small (average relative error less tha

7 Sesors Optical power (db) 2 4 Optical power (db) Reflected light Stadard deviatio Reflected light Stadard deviatio (a) (b) Figure 9: Optical spectrum ad stadard deviatio. (a) FBG-sca 7 iterrogator, (b) based iterrogator. Strai amplitude (db) Strai amplitude (db) Frequecy (Hz) Frequecy (Hz) FBG-sca FBG-sca (a) (b) Figure 1: Measured vibratio spectra: (a) whe usig siusoidal excitatio, (b) whe usig swept sie excitatio..2%). The dampig value estimates show a average relative deviatio of 3% but i vibratio aalysis this is cosidered small as it is kow that dampig estimates usually have a sigificatly larger ucertaity. From the results of the composite beam experimet we ca coclude that the proposed system allows us to perform reliable vibratio measuremets eve if the optical spectra are heavily distorted. 4. Coclusios We have proposed a FBG sesor measuremet system that is dedicated for vibratio aalysis. Because the system is completely cotrolled by a multifuctio DAQ board it is possible to simultaeously acquire force ad accelerometer measuremets, ad hece it is easy to calculate Frequecy Respose Fuctios. The hardware used i the proposed setup ca be purchased off-the-shelf ad it is fairly of low cost (the total cost of the system icludig the DAQ board is 4k). Usig a vibratio measuremet of a steel beam we have show that the proposed system results i measured vibratio spectra that are comparable to the oes determied with a commercial iterrogator. I case sigificat distortios are preset i the optical spectra, the proposed system eve outperforms traditioal measuremet systems. Curretly, the system has two limitatios: (1) with curret the optical power is limited to less tha oe mw; (2) the badwidth is limited to about 9 m. Ogoig techological

8 8 Sesors Table 1: Estimated resoace frequecies ad dampig values. Mode Accelerometer FBG sesor Differece, i % f acc,ihz ξ acc,i% f FBG,iHz ξ FBG,i% (f acc f FBG )/f acc (ξ acc ξ FBG )/ξ acc First bedig 22,7 1,9 22,7 1,8 5,3 Secod bedig 145,2 2,1 144,4 2,1,6 First torsio 26,5 1,5 26,6 1,4 6,7 Third bedig 323,4,6 323,6,6,1 Amplitude (db) Strai Acceleratio Frequecy (Hz) Figure 11: Measured Frequecy Respose Fuctios (FRFs) from acceleratio (gree dots) ad FBG sesor (blue dots). advaces i techologies, however, cotiuously exted the rage of the available power ad wavelegth rage. Competig Iterests The authors declare that they have o competig iterests. Ackowledgmets This research has bee sposored by the Flemish Istitute for the Improvemet of the Scietific ad Techological Research i Idustry (IWT) i the framework of the SBO Project Self Sesig Composites. The authors also ackowledge the Fud for Scietific Research-Fladers (FWO) Belgium, the Research Coucil of the Vrije Uiversiteit Brussel (OZR), ad the Uiversity of Atwerp (BOF) for their fudig. Refereces [1]M.Majumder,T.K.Gagopadhyay,A.K.Chakraborty,K. Dasgupta, ad D. K. Bhattacharya, Fibre Bragg gratigs i structural health moitorig-preset status ad applicatios, Sesors ad Actuators, A: Physical, vol.147,o.1,pp , [2] A. Othoos, Fiber Bragg gratigs, Review of Scietific Istrumets,vol.68,o.12,pp ,1997. [3]A.D.Kersey,M.A.Davis,H.J.Patricketal., Fibergratig sesors, Lightwave Techology, vol.15,o.8,pp , [4] T. Vella, S. Chadderdo, R. Selfridge et al., Full-spectrum iterrogatio of fiber bragg gratigs at 1 khz for detectio of impact loadig, Measuremet Sciece ad Techology, vol.21, o.9,articleid949,21. [5] W. Nakwaski ad M. Osiski, Thermal properties of verticalcavity surface-emittig semicoductor lasers, i Progress i Optics,vol.38,pp ,1998. [6] T. Mizuami, S. Hirose, T. Yoshiaga, ad K.-I. Yamamoto, Power-stabilized tuable arrow-bad source usig a ad a EDFA for FBG sesor iterrogatio, Measuremet Sciece ad Techology,vol.24,o.9,ArticleID9417,213. [7] B. Va Hoe, G. Lee, E. Bosma et al., Ultra small itegrated optical fiber sesig system, Sesors, vol. 12, o. 9, pp , 212. [8]Y.H.Huag,C.Lu,P.K.A.Wai,adH.Y.Tam, FastFBG sesor iterrogatio system usig vertical cavity surface emittig laser source, i Proceedigs of the 14th OptoElectroics ad Commuicatios Coferece (OECC 9), Hog Kog, July 29. [9] Y.H.Huag,T.A.Guo,C.O.Lu,adH.-Y.Tam, -based tilted fiber gratig vibratio sesig system, IEEE Photoics Techology Letters,vol.22,o.16,pp ,21. [1] N. M. M. Maia ad J. M. M. e Silva, Theoretical ad Experimetal Modal Aalysis, Research Studies Press, Tauto, UK, [11] A. Lamberti, S. Valaduit, B. De Pauw, ad F. Berghmas, Ifluece of fiber bragg gratig spectrum degradatio o the performace of sesor iterrogatio algorithms, Sesors, vol. 14, o. 12, pp , 214. [12] A. Lamberti, S. Valaduit, B. De Pauw, ad F. Berghmas, A ovel fast phase correlatio algorithm for peak wavelegth detectio of fiber Bragg gratig sesors, Optics Express,vol.22, o. 6, pp , 214. [13] K.S.C.Kuag,R.Key,M.P.Whela,W.J.Catwell,adP. R. Chalker, Embedded fibre Bragg gratig sesors i advaced composite materials, Composites Sciece ad Techology, vol. 61, o. 1, pp , 21. [14] H. Va Der Auweraer, P. Guillaume, P. Verbove, ad S. Valaduit, Applicatio of a fast-stabilizig frequecy domai parameter estimatio method, Dyamic Systems, Measuremet ad Cotrol, Trasactios of the ASME, vol.123, o. 4, pp , 21.

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